A MULTI-SCALE INVESTIGATION OF SPECIES RICHNESS, PRODUCTIVITY
AND NUTRIENT RELATIONSHIPS IN HERBACEOUS PLANT COMMUNITIES OF
THE GRASSLANDS OF SOUTHERN INTERIOR BRITISH COLUMBIA
by
AMANDA CHRISTA SCHMIDT
B.Sc., Thompson Rivers University, 2010

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN ENVIRONMENTAL SCIENCE
in the Faculty of Science

Thesis examining committee:
Lauchlan Fraser (PhD), Professor and Thesis Supervisor,
Department of Natural Resource Sciences, Thompson Rivers University.
Wendy Gardner (PhD), Associate Professor and Committee Member,
Department of Natural Resource Sciences, Thompson Rivers University.
Jonathan Van Hamme (PhD), Associate Professor and Committee Member,
Department of Biological Sciences, Thompson Rivers University.
John Klironomos (PhD), Professor and Committee Member,
Department of Biology, The University of British Columbia - Okanagan Campus.
Jason Pither (PhD), Assistant Professor and External Examiner,
Department of Biology and Physical Geography, The University of British Columbia
- Okanagan Campus.
April 2014
Thompson Rivers University
© Amanda Christa Schmidt 2014

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Thesis Supervisor: Professor Lauchlan H. Fraser (PhD)

ABSTRACT
Philip Grime's humped-back model predicts that species richness reaches a maximum at
intermediate productivity and drops off at low and high productivities. Soil nutrient
availability is known to influence primary productivity and plant species richness. In
general, productivity increases with increasing soil nutrient availability, and experiments that
increase soil nutrients often show increases in biomass with corresponding decreases in
species richness; as such, certain patterns in soil nutrients are expected to coincide with the
humped-back model. Scale is also an important factor, as the relationship between species
richness and productivity may vary with scale. Objectives of this work were (1) to test the
explicit humped-back model prediction that the relationship between species richness and
productivity is unimodal; (2) to test implicit humped-back model predictions that species
richness is related to nutrients that are tightly associated with productivity, such as carbon
and nitrogen, by a unimodal relationship and identify patterns between soil nutrients, leaf
nutrients, productivity and species richness; and (3) to evaluate the influence of increasing
scales from 1 m2 to 64 m2 on relationships found between species richness, productivity and
nutrients. This was done using biomass and litter collections and species richness counts
from 14 multi-scale grids (8 m × 8 m grids containing 64, 1 m2 plots), soil samples from a
subset of four of the 14 multi-scale grids, and leaf samples from a subset of nine adjacent
plots in each of the four multi-scale grids that were sampled for soil nutrients. Total carbon
and nitrogen contents in soil and leaf samples were analyzed with a CE-440 Elemental
Analyzer. Total aluminum, boron, calcium, copper, iron, magnesium, manganese, sodium,
phosphorus, potassium, sulphur, and zinc were quantified in soil samples prepared by very
high-pressure closed vessel microwave acid digestion in a Milestone “Ultrawave” single
reaction chamber followed by analysis with a Teledyne/Leeman Labs “Prodigy” dual view
inductively coupled plasma-optical emission spectrometer. In principal component analyses
of soil nutrient data, the first and second principal components appeared to represent
productivity and species richness, respectively; and carbon, nitrogen, phosphorus, potassium,
boron, iron, magnesium and manganese were identified as important soil nutrients. Bivariate

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regressions of the first principal component with total biomass (R = 0.76) and the second
principal component with species richness (R2 = 0.35) returned strong R2 values. Species
richness was related to total biomass (R2 = 0.11), soil carbon (R2 = 0.15), soil nitrogen (R2 =
0.14) and iron (R2 = 0.29) by concave down relationships, to boron (R2 = 0.17) and
magnesium (R2 = 0.49) by concave up relationships, to phosphorus (R2 = 0.27) and
manganese (R2 = 0.25) by positive linear relationships and to potassium (R2 = 0.14) by a
negative linear relationship. Scaling results were inconclusive but suggested that patterns in
the literature may be partly due to sample size. Results generally support the humped-back
model and that nutrient availability is an important factor correlated with herbaceous plant
productivity and species richness. Nutrient availability is likely an important driver of plant
productivity and herbaceous plant diversity.

Keywords: carbon, humped-back model, nitrogen, phosphorus, potassium, productivitydiversity relationship, soil nutrients

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TABLE OF CONTENTS
ABSTRACT ............................................................................................................................... ii
TABLE OF CONTENTS ...........................................................................................................iv
ACKNOWLEDGEMENTS .......................................................................................................vi
LIST OF FIGURES ................................................................................................................ viii
LIST OF TABLES .................................................................................................................xxvi
LIST OF ABBREVIATIONS .............................................................................................. xxxii
NOMENCLATURE ............................................................................................................xxxiv
CHAPTER 1: INTRODUCTION ............................................................................................... 1
The unimodal curve ........................................................................................................ 1
The humped-back model................................................................................................. 2
Nutrients .......................................................................................................................... 5
Scale .............................................................................................................................. 17
Thesis overview ............................................................................................................ 18
CHAPTER 2: A MULTI-SCALE INVESTIGATION OF SPECIES RICHNESS,
PRODUCTIVITY AND NUTRIENT RELATIONSHIPS IN HERBACEOUS PLANT
COMMUNITIES OF THE GRASSLANDS OF SOUTHERN INTERIOR BRITISH
COLUMBIA ............................................................................................................................. 20
Introduction ........................................................................................................................... 20
Methods................................................................................................................................. 25
Site description.............................................................................................................. 25
Study design .................................................................................................................. 29
Marking grids ................................................................................................................ 31
Plant sampling protocol ................................................................................................ 33
Soil sampling protocol .................................................................................................. 33
Data analysis ................................................................................................................. 34
Results ................................................................................................................................... 37
Species richness and biomass regressions .................................................................... 38

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Soil nutrient PCA and PCA regressions ....................................................................... 41
Soil nutrient regressions ................................................................................................ 47
Soil and leaf nutrient PCA and PCA regressions.......................................................... 68
Soil and leaf carbon, nitrogen and carbon to nitrogen ratios PCA and regressions...... 74
Discussion ............................................................................................................................. 81
Study limitations ........................................................................................................... 81
Species richness and biomass relationships .................................................................. 82
Soil nutrients ................................................................................................................. 84
Leaf nutrients ................................................................................................................ 92
Scale .............................................................................................................................. 94
Summary ....................................................................................................................... 95
CHAPTER 3: CONCLUSION ................................................................................................. 96
Context and general findings ........................................................................................ 96
Management implications ............................................................................................. 97
Future directions ........................................................................................................... 97
LITERATURE CITED ......................................................................................................... 99
APPENDIX A: Moran's I correlograms ............................................................................. 112
APPENDIX B: Semi-variograms ....................................................................................... 118
APPENDIX C: Poisson regressions.................................................................................... 142
APPENDIX D: Species richness and biomass - scaled regressions ................................... 154
APPENDIX E: Kaiser-Guttman and PC3 biplots ............................................................... 156
APPENDIX F: PCA regressions ......................................................................................... 163
APPENDIX G: Soil nutrients - scaled regressions ............................................................. 166
APPENDIX H: Species identified ...................................................................................... 175

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ACKNOWLEDGEMENTS
I would like to express my sincerest appreciation to the many people who have given their
help, encouragement, and support during the writing of this thesis and the entire process that
comes before. I am grateful to my supervisor Lauch Fraser for welcoming me into his lab as
a research assistant, for all of his guidance, support and encouragement over the years since
then, and for offering the opportunity to work on this delightfully challenging project in
connection with the global HerbDivNet. I appreciate my committee members, Wendy
Gardner, Jonathan Van Hamme and John Klironomos, for their enthusiasm and for their
assistance with project direction and thesis editing. I am thankful to Jason Pither, my
external examiner, for his time, revisions, and feedback; and to Dr. David Hill for providing
indispensable help with interpretation of semi-variograms, and general discussion and
guidance with regards to R and GIS.
Continuing interest, positivity, and support from my parents, Patricia and Dan Schmidt, and
siblings, Mark and Valerie, has been invaluable throughout my education. I am thankful to
my mother who always had time for a phone call, and appreciate all the extra hours of
listening and cheerleading my sister put in as my roommate during my masters degree.
Thanks to Bryon Jourdain for all his support, for helping me keep things in perspective, and
for adding a much needed and appreciated sense of humour at every opportunity. Thank you
to my family, Bryon and my friends, especially Lucy Pratt-Johnson, Sally Moore and
Charlotte Bird, for sharing me with my greedy thesis, with much encouragement and
patience.
Everyone at the Fraser lab has contributed to a warm, learning atmosphere that will
characterize the memory of this experience for years to come. Special thanks, in particular,
to Cameron Carlyle and Bill Harrower for all their mentorship and encouragement, to Kathy
Baethke, Sabina Donnelly, and Justine McCulloch for being wonderful, supportive company,
to Bill and Ashleigh Gilbert for getting me addicted to field work during my first summer,
and to everyone who took me along for their field adventures!

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Many volunteers and field assistants have been instrumental in completing this project; a
huge thank you to Mandy Ross, Tessa Jongbloets, Sabina Donnelly, Kathy Baethke, Danielle
Sparks, Justine McCulloch, Tiffany Weatherston, Valerie Schmidt, Tyne Roberts, Brad
White, Kate Strangway, Taran Main, and Brian Lambert for all their hard work in the field
and lab.
Many thanks to Tod Haughton and Mike Burwash at the BC Ministry of Environment for
allowing access and research in field sites in Lac du Bois Provincial Park under permit
# 104784; and to Bruce Fraser for providing access to the Lac la Hache field site and
accommodation while we were working there. This research was supported with an NSERC
discovery grant to Lauch Fraser.

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LIST OF FIGURES
Figure 2.1. Map of the Lac du Bois Grasslands Provincial park study site (Google Earth
2014). L1-5, U1-5, and P1-2 are codes to identify each grid and indicate grid locations on
the map. ................................................................................................................................... 27
Figure 2.2. Map of the Lac la Hache study site (Google Earth 2014). P3 and P4 are codes to
identify grids and indicate grid locations on the map. ............................................................ 28
Figure 2.3. Diagram of grid layout showing smaller nested plots in the H1 corner. .............. 30
Figure 2.4. Grid P2, post-sampling. Holes are visible where soil samples were taken. ........ 32
Figure 2.5. Grid U5, post-sampling. The pin-flags used for frame placement and hummocks
left over from sampling large bunchgrasses are visible. ......................................................... 32
Figure 2.6. Square root transformed species richness with fitted curves from linear regression
models at 1 m2 having log transformed total biomass, log transformed live biomass and log
transformed litter as the explanatory variables; this is shown for the 14-grid dataset (top
panels) and the 4-grid dataset including only those grids involved in soil sampling (bottom
panels). The dotted line is the fitted linear model and the dashed line is the fitted quadratic
model. The significant model in each plot is shown in bold. ................................................ 38
Figure 2.7. Distance biplot of the first two principal component axes of the PCA on the soil
nutrient data. The red circle is the circle of equilibrium contribution. Each grid is indicated
by points of a certain colour. The L4 (red points) and L5 (green points) grids were lower
biomass grids while the P1 (blue points) and P2 (black points) grids were higher biomass
grids......................................................................................................................................... 42
Figure 2.8. Correlation biplot of the first two principal component axes of the PCA on the
soil nutrient data. Each grid is indicated by points of a certain colour. The L4 (red points)
and L5 (green points) grids were lower biomass grids while the P1 (blue points) and P2
(black points) grids were higher biomass grids. ..................................................................... 43

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Figure 2.9. Log transformed litter, log transformed live biomass, and log transformed total
biomass with fitted curves from linear regression models at 1 m2 having PC1 as the
explanatory variable (top panels); square root transformed species richness with fitted curves
from linear regression models having PC1 (bottom left panel) and PC2 (bottom center panel)
as the explanatory variables; and log transformed total biomass with fitted curves from linear
regression models having PC2 as the explanatory variable (bottom right panel). The dotted
line is the fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold. ..................................................................... 45
Figure 2.10. Fitted curves from linear regressions with soil carbon as the explanatory variable
and log transformed total biomass (top left panel), log transformed live biomass (top center
panel) and square root transformed species richness (top right panel) as response variables at
the 1 m2 scale. Fitted curves from linear regression models having soil carbon as the
explanatory variable and log transformed litter as response variables at 1 m2 (bottom left
panel), 2 m2 (bottom center panel), and 4 m2 (bottom right panel). The dotted line is the
fitted linear model and the dashed line is the fitted quadratic model. The significant model in
each plot is shown in bold. ...................................................................................................... 48
Figure 2.11. Fitted curves from linear regressions with soil nitrogen as the explanatory
variable and log transformed total biomass (top left panel), log transformed live biomass (top
center panel) and square root transformed species richness (top right panel) as response
variables at the 1 m2 scale. Fitted curves from linear regression models having soil nitrogen
as the explanatory variable and log transformed litter as response variables at 1 m2 (bottom
left panel), 2 m2 (bottom center panel), and 4 m2 (bottom right panel). The dotted line is the
fitted linear model and the dashed line is the fitted quadratic model. The significant model in
each plot is shown in bold. ...................................................................................................... 51
Figure 2.12. Fitted curves from linear regressions at the 2 m2 scale (top panels) and 4 m2
scale (bottom row) with soil carbon to nitrogen ratio as the explanatory variable, and log
transformed litter (left panels), log transformed total biomass (center panels) and square root
transformed species richness (right panels) as response variables. The dotted line is the fitted

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linear model and the dashed line is the fitted quadratic model. The significant model in each
plot is shown in bold. .............................................................................................................. 53
Figure 2.13. Fitted curves from linear regressions with soil phosphorus as the explanatory
variable at 1 m2 and 2 m2 with log transformed total biomass (left panels), at 2 m2 and 4 m2
with log transformed litter (center panels) and with square root transformed species richness
and log transformed live biomass at 1 m2 (right panels). The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ......................................................................................................................... 55
Figure 2.14. Fitted curves from linear regressions with soil potassium as the explanatory
variable at 1 m2 with square root transformed species richness and log transformed litter (left
panels), at 1 m2 and 2 m2 with log transformed live biomass (center panels) and with log
transformed total biomass at 2 m2 and 4 m2 (right panels). The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ......................................................................................................................... 58
Figure 2.15. Fitted curves from linear regressions with soil boron as the explanatory variable
at 1 m2 with log transformed litter, log transformed live biomass, and log transformed total
biomass as response variables (top panels), and with square root transformed species richness
at 1 m2, 2 m2 and 4 m2 (bottom panels). The dotted line is the fitted linear model and the
dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.
................................................................................................................................................. 60
Figure 2.16. Fitted curves from linear regressions with soil iron as the explanatory variable at
1 m2 with square root transformed species richness, log transformed live biomass, and log
transformed total biomass as response variables (top panels), and at 1 m2, 4 m2 and 16 m2
with log transformed litter (bottom panels). The dotted line is the fitted linear model and the
dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.
................................................................................................................................................. 62
Figure 2.17. Fitted curves from linear regressions with soil magnesium as the explanatory
variable at 1 m2 and 16 m2 with square root transformed species richness (left panels), at 1m2

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2

and 2 m with log transformed live biomass (center panels), and log transformed litter and
log transformed total biomass (right panels). The dotted line is the fitted linear model and the
dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.
................................................................................................................................................. 64
Figure 2.18. Fitted curves from linear regressions with soil manganese as the explanatory
variable at 1 m2 and 16 m2 with square root transformed species richness (left panels), at 1m2
and 2 m2 with log transformed litter (center panels), and log transformed live biomass and
log transformed total biomass (right panels). The dotted line is the fitted linear model and the
dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.
................................................................................................................................................. 66
Figure 2.19. Distance biplot of the first two principal component axes from the PCA on the
soil and leaf nutrient data. The red circle is the circle of equilibrium contribution. Each grid
is indicated by points of a certain colour. The L4 (red points) and L5 (green points) grids
were lower biomass grids while the P1 (blue points) and P2 (black points) grids were higher
biomass grids. ......................................................................................................................... 69
Figure 2.20. Correlation biplot of the first two principal component axes of the soil and leaf
nutrient data. Each grid is indicated by points of a certain colour. The L4 (red points) and
L5 (green) grids were lower biomass grids while the P1 (blue points) and P2 (black points)
grids were higher biomass grids. ............................................................................................ 70
Figure 2.21. Log transformed live biomass, log transformed litter and log transformed total
biomass with fitted curves from linear regression models at 1 m2 having PC1 as the
explanatory variable (top panels); and, log transformed live biomass, log transformed litter
and square root transformed species richness with fitted curves from linear regression models
having PC2 as the explanatory variable (bottom panels). The principal components are from
the PCA on the soil and leaf nutrient data. The dotted line is the fitted linear model and the
dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.
................................................................................................................................................. 72

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Figure 2.22. Distance biplot of the first two principal component axes from the PCA of the
soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient data. The red circle is the
circle of equilibrium contribution. Each grid is indicated by points of a certain colour. The
L4 (red points) and L5 (green points) grids were lower biomass grids while the P1 (blue
points) and P2 (black points) grids were higher biomass grids. ............................................. 75
Figure 2.23. Correlation biplot of the first two principal component axes from the PCA of the
soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient data. Each grid is
indicated by points of a certain colour. The L4 (red points) and L5 (green points) grids were
lower biomass grids while the P1 (blue points) and P2 (black points) grids were higher
biomass grids. ......................................................................................................................... 76
Figure 2.24. Fitted curves from linear regression models at 1 m2 having log transformed live
biomass, log transformed litter and log transformed total biomass as response variables and
PC1 (top panels); and PC2 (bottom panels) as the explanatory variables. The principal
components are from the PCA on only the soil and leaf carbon, nitrogen, and carbon to
nitrogen ratios. The dotted line is the fitted linear model and the dashed line is the fitted
quadratic model. The significant model in each plot is shown in bold.................................. 77
Figure 2.25. Fitted curves from linear regression models at 1 m2 having leaf carbon as the
response variable and soil carbon as the explanatory variable (left panel); leaf nitrogen as the
response variable and soil nitrogen as the explanatory variable (center panel), and leaf carbon
to nitrogen ratio as the response variable and soil carbon to nitrogen ratio as the explanatory
variable (bottom panel). The dotted line is the fitted linear model and the dashed line is the
fitted quadratic model. The significant model in each plot is shown in bold. ....................... 79
Figure A.1. Correlograms of Moran's I Statistic plotted against distance classes for species
richness in each grid. Red filled points indicate significant correlation, hollow points indicate
non-significant values. .......................................................................................................... 112
Figure A.2. Correlograms of Moran's I Statistic plotted against distance classes for total
biomass in each grid. Red filled points indicate significant correlation, hollow points indicate
non-significant values. .......................................................................................................... 113

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Figure A.3. Correlograms of Moran's I Statistic plotted against distance classes for live
biomass in each grid. Red filled points indicate significant correlation, hollow points indicate
non-significant values. .......................................................................................................... 114
Figure A.4. Correlograms of Moran's I Statistic plotted against distance classes for litter in
each grid. Red filled points indicate significant correlation, hollow points indicate nonsignificant values. ................................................................................................................. 115
Figure A.5. Correlograms of Moran's I Statistic plotted against distance classes for soil
nutrients for each grid that had soil samples taken. Carbon (row 1), nitrogen (row 2), carbon
to nitrogen ratio (row 3), phosphorus (row 4), potassium (row 5), boron (row 6), iron (row 7),
magnesium (row 8) and manganese (row 9). Red filled points indicate significant
correlation, hollow points indicate non-significant values. .................................................. 117
Figure B.1. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and log
transformed total biomass as the explanatory variable, for each grid (L1-5, U1-5, P1-4). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 119
Figure B.2. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and log
transformed live biomass as the explanatory variable, for each grid (L1-5, U1-5, P1-4). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 121
Figure B.3. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and log
transformed litter as the explanatory variable, for each grid (L1-5, U1-5, P1-4). The second
and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. .................... 123
Figure B.4. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
carbon as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and

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P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 124
Figure B.5. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
nitrogen as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 124
Figure B.6. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
carbon to nitrogen ratio as the explanatory variable, for each grid that involved soil sampling
(L4, L5, P1 and P2). The second and fourth columns show directional semi-variograms at 0,
45, 90, and 135º..................................................................................................................... 125
Figure B.7. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
phosphorus as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 125
Figure B.8. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
potassium as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 126
Figure B.9. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
boron as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 126

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Figure B.10. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
iron as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 127
Figure B.11. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
magnesium as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 127
Figure B.12. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
manganese as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 128
Figure B.13. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil carbon as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 128
Figure B.14. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil nitrogen as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 129
Figure B.15. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil carbon to
nitrogen ratio as the explanatory variable, for each grid that involved soil sampling (L4, L5,
P1 and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90,
and 135º................................................................................................................................. 129

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Figure B.16. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil phosphorus
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. . 130
Figure B.17. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil potassium as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 130
Figure B.18. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil boron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 131
Figure B.19. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil iron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 131
Figure B.20. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil magnesium
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. . 132
Figure B.21. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed total biomass as the response variable and soil manganese
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. . 132
Figure B.22. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil carbon as the

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explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 133
Figure B.23. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil nitrogen as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 133
Figure B.24. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil carbon to
nitrogen ratio as the explanatory variable, for each grid that involved soil sampling (L4, L5,
P1 and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90,
and 135º................................................................................................................................. 134
Figure B.25. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil phosphorus
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. . 134
Figure B.26. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil potassium as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 135
Figure B.27. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil boron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 135
Figure B.28. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil iron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 136

xviii
Figure B.29. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil magnesium
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. . 136
Figure B.30. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed live biomass as the response variable and soil manganese
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. . 137
Figure B.31. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil carbon as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 137
Figure B.32. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil nitrogen as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 138
Figure B.33. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil carbon to nitrogen
ratio as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º. ...................................................................................................................................... 138
Figure B.34. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil phosphorus as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 139
Figure B.35. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil potassium as the

xix
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 139
Figure B.36. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil boron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 140
Figure B.37. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil iron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 140
Figure B.38. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil magnesium as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 141
Figure B.39. Normalized semi-variograms of the standardize residuals computed for linear
regressions with, log transformed litter as the response variable and soil manganese as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º. ........ 141
Figure C.1. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and log transformed total biomass (top row), live biomass (center
row), and litter (bottom row) as the explanatory variables using the 14-grid dataset across
scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic
model. The significant model in each plot is shown in bold. .............................................. 143
Figure C.2. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and log transformed total biomass (top row), live biomass (center
row), and litter (bottom row) as the explanatory variables using the four soil grids dataset

xx
across scales. The dotted line is the fitted linear model and the dashed line is the fitted
quadratic model. The significant model in each plot is shown in bold................................ 145
Figure C.3. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and PC1, PC2, and PC3 from the soil nutrient PCA. The dotted line
is the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold...................................................................................... 146
Figure C.4. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and soil carbon (top row), soil nitrogen (center row), and soil carbon
to nitrogen ratio (bottom row) as the explanatory variables using the four soil grids dataset
across scales. The dotted line is the fitted linear model and the dashed line is the fitted
quadratic model. The significant model in each plot is shown in bold................................ 149
Figure C.5. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and soil phosphorus (top row), soil potassium (center row), and soil
boron (bottom row) as the explanatory variables using the four soil grids dataset across
scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic
model. The significant model in each plot is shown in bold. .............................................. 150
Figure C.6. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and soil iron (top row), soil magnesium (center row), and soil
manganese (bottom row) as the explanatory variables using the four soil grids dataset across
scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic
model. The significant model in each plot is shown in bold. .............................................. 151
Figure C.7. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and PC1, PC2, and PC3 from the soil and leaf nutrient PCA. The
dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold. ................................................................... 152
Figure C.8. Linear and quadratic fitted curves from Poisson regressions with species richness
as the response variable and PC1, PC2, and PC3 from the PCA of only soil carbon, nitrogen

xxi
and carbon to nitrogen ratio and leaf carbon, nitrogen and carbon to nitrogen ratio. The
dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold. ................................................................... 153
Figure D.1. Square root transformed species richness with fitted curves from linear
regression models with log transformed total biomass (top row) and log transformed live
biomass (center panels) and log transformed litter (bottom panels) as the explanatory
variables, across scales, using the 14-grid dataset. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold. .................................................................................................................................. 154
Figure D.2. Square root transformed species richness with fitted curves from linear
regression models with log transformed total biomass (top row) and log transformed live
biomass (center panels) and log transformed litter (bottom panels) as the explanatory
variables, across scales, using the 4-grid dataset. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold. .................................................................................................................................. 155
Figure E.1. Kaiser-Guttman criterion (upper panel) and broken stick model (lower panel)
evaluation of the PCA axes on the soil nutrient data. ........................................................... 156
Figure E.2. Distance biplot of PC1 and PC3 from the PCA of the soil nutrient data. Each
grid is indicated by points of a certain colour. The L4 (red points) and L5 (green points)
grids were lower biomass grids while the P1 (blue points) and P2 (black points) grids were
higher biomass grids. ............................................................................................................ 157
Figure E.3. Correlation biplot of PC1 and PC3 from the PCA on the soil nutrient data. Each
grid is indicated by points of a certain colour. The L4 (red points) and L5 (green points)
grids were lower biomass grids while the P1 (blue points) and P2 (black points) grids were
higher biomass grids. ............................................................................................................ 158
Figure E.4. Plots of the Kaiser-Guttman criterion and broken stick models of the PCA on the
soil and leaf nutrient data. The Kaiser-Guttman plot shows the first four principal component

xxii
axes contain relevant information while the more conservative broken stick model indicates
only two axes need be considered. ........................................................................................ 159
Figure E.5. Distance biplot of PC1 and PC3 from the PCA on the soil and leaf nutrient data.
Each grid is indicated by points of a certain colour. The L4 (red points) and L5 (green
points) grids were lower biomass grids while the P1 (blue points) and P2 (black points) grids
were higher biomass grids. ................................................................................................... 160
Figure E.6. Correlation biplot of PC1 and PC3 from the PCA on the soil and leaf nutrient
data. Each grid is indicated by points of a certain colour. The L4 (red points) and L5 (green)
grids were lower biomass grids while the P1 (blue points) and P2 (black points) grids were
higher biomass grids. ............................................................................................................ 161
Figure E.7. Plots of the Kaiser-Guttman criterion and broken stick models of the PCA on the
soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient data. The Kaiser-Guttman
plot suggests the first two PCA axes contain relevant information while the more
conservative broken stick model indicates only PC1 need be considered. ........................... 162
Figure F.1. Square root transformed species richness, log transformed total biomass, log
transformed live biomass, and log transformed litter with the soil nutrient PCA axes. Fitted
curves from linear regression models at 1 m2 having PC1 (left panels) PC2 (center panels)
and PC3 (right panels) as the explanatory variables are shown. The dotted line is the fitted
linear model and the dashed line is the fitted quadratic model. The significant model in each
plot is shown in bold. ............................................................................................................ 163
Figure F.2. Square root transformed species richness, log transformed total biomass, log
transformed live biomass, and log transformed litter with the soil and leaf nutrient PCA axes.
Fitted curves from linear regression models at 1 m2 having PC1 (left panels) PC2 (center
panels) and PC3 (right panels) as the explanatory variables are shown. The dotted line is the
fitted linear model and the dashed line is the fitted quadratic model. The significant model in
each plot is shown in bold. .................................................................................................... 164

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Figure F.3. Square root transformed species richness, log transformed total biomass, log
transformed live biomass, and log transformed litter with the soil and leaf carbon, nitrogen
and carbon to nitrogen ratio PCA axes. Fitted curves from linear regression models at 1 m2
having PC1 (left panels) PC2 (center panels) and PC3 (right panels) as the explanatory
variables are shown. The dotted line is the fitted linear model and the dashed line is the fitted
quadratic model. The significant model in each plot is shown in bold................................ 165
Figure G.1. Fitted curves from linear regressions with soil carbon as the explanatory variable
and square root transformed species richness (first column), log transformed total biomass
(second column), log transformed live biomass (third column) and log transformed litter
(fourth column) as response variables across scales. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold. .................................................................................................................................. 166
Figure G.2. Fitted curves from linear regressions with soil nitrogen as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ....................................................................................................................... 167
Figure G.3. Fitted curves from linear regressions with soil carbon to nitrogen ratio as the
explanatory variable and square root transformed species richness (first column), log
transformed total biomass (second column), log transformed live biomass (third column) and
log transformed litter (fourth column) as response variables across scales. The dotted line is
the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold...................................................................................... 168
Figure G.4. Fitted curves from linear regressions with soil phosphorus as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear

xxiv
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ....................................................................................................................... 169
Figure G.5. Fitted curves from linear regressions with soil potassium as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ....................................................................................................................... 170
Figure G.6. Fitted curves from linear regressions with soil boron as the explanatory variable
and square root transformed species richness (first column), log transformed total biomass
(second column), log transformed live biomass (third column) and log transformed litter
(fourth column) as response variables across scales. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold. .................................................................................................................................. 171
Figure G.7. Fitted curves from linear regressions with soil iron as the explanatory variable
and square root transformed species richness (first column), log transformed total biomass
(second column), log transformed live biomass (third column) and log transformed litter
(fourth column) as response variables across scales. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold. .................................................................................................................................. 172
Figure G.8. Fitted curves from linear regressions with soil magnesium as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ....................................................................................................................... 173
Figure G.9. Fitted curves from linear regressions with soil manganese as the explanatory
variable and square root transformed species richness (first column), log transformed total

xxv
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold. ....................................................................................................................... 174

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LIST OF TABLES
Table 2.1. Identification, elevation and GPS location (datum: NAD83) of the fourteen study
grids. Soil sampling was done in grids marked "*". .............................................................. 29
Table 2.2. Regressions using data from all 14 grids with square root transformed species
richness as the response variable. Form codes are as follows: CD = concave down quadratic
model, CU = concave up quadratic model, POS = positive linear model, and NEG = negative
linear model. For quadratic models degrees of freedom are 2 on: 893 at 1 m2, 445 at 2 m2,
221 at 4 m2, 53 at 16 m2, 11 at 64 m2; and for linear models are 1 on: 894 at 1 m2, 446 at
2 m2, 222 at 4 m2, 54 at 16 m2, and 12 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 39
Table 2.3. Regressions using data from only the four grids involved in soil sampling with
square root transformed species richness as the response variable. Form codes are as follows:
CD = concave down quadratic model, CU = concave up quadratic model, POS = positive
linear model, and NEG = negative linear model. For quadratic models degrees of freedom
are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models
are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights
show regressions at the 1 m2 scale. Non-significant results are left blank............................. 40
Table 2.4. Results for the first four axes from a PCA of the soil nutrient data collected from
four 8 m × 8 m grids (L4, L5, P1 and P2). .............................................................................. 41
Table 2.5. Bivariate regressions for PC1, PC2 and PC3 (from the soil nutrient PCA) as
explanatory variables and species richness, total biomass, live biomass and litter as the
response variables at the 1 m2 scale. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on 253 and for
linear models are 1 on 254. Non-significant results are left blank. ....................................... 46
Table 2.6. Bivariate regressions of soil carbon with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down

xxvii
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 49
Table 2.7. Bivariate regressions of soil nitrogen with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 52
Table 2.8. Bivariate regressions of soil carbon to nitrogen ratio with species richness, total
biomass, live biomass and litter as the response variables. Form codes are as follows: CD =
concave down quadratic model, CU = concave up quadratic model, POS = positive linear
model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on:
253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on:
254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show
regressions at the 1 m2 scale. Non-significant results are left blank. ..................................... 54
Table 2.9. Bivariate regressions of soil phosphorus with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 56
Table 2.10. Bivariate regressions of soil potassium with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down

xxviii
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 59
Table 2.11. Bivariate regressions of soil boron with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 61
Table 2.12. Bivariate regressions of soil iron with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 63
Table 2.13. Bivariate regressions of soil magnesium with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 65
Table 2.14. Bivariate regressions of soil manganese with species richness, total biomass, live
biomass and litter as the response variables. Form codes are as follows: CD = concave down

xxix
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125
at 2 m2, 61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126
at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show regressions at the 1 m2
scale. Non-significant results are left blank. .......................................................................... 67
Table 2.15. Results for the first four axes from a PCA of the soil and leaf nutrient data
collected from four 3 m × 3 m subsamples within the four 8 m × 8 m grids (L4, L5, P1 and
P2). .......................................................................................................................................... 68
Table 2.16. Bivariate regressions with PC1, PC2 and PC3 (from the soil and leaf nutrient
PCA) as explanatory variables and species richness, total biomass, live biomass and litter as
the response variables at the 1 m2 scale. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on 33 and for linear
models are 1 on 34. Non-significant results are left blank. ................................................... 73
Table 2.17. Results for the first four axes from a PCA on soil and leaf carbon, nitrogen, and
carbon to nitrogen ratio data collected from four 3 m × 3 m subsamples within the four 8 m ×
8 m soil grids (L4, L5, P1 and P2). ......................................................................................... 74
Table 2.18. Bivariate regressions for PC1, PC2 and PC3 (from the soil and leaf carbon,
nitrogen and carbon to nitrogen ratio nutrient PCA) as explanatory variables and species
richness, total biomass, live biomass and litter as the response variables at the 1 m2 scale.
Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic
model, POS = positive linear model, and NEG = negative linear model. For quadratic
models degrees of freedom are 2 on 33 and for linear models are 1 on 34. Non-significant
results are left blank. ............................................................................................................... 78
Table 2.19. Bivariate regressions for soil carbon, nitrogen and carbon to nitrogen ratio as
explanatory variables and leaf carbon, nitrogen, and carbon to nitrogen ratio as response
variables at the 1 m2 scale. Form codes are as follows: CD = concave down quadratic model,
CU = concave up quadratic model, POS = positive linear model, and NEG = negative linear

xxx
model. For quadratic models degrees of freedom are 2 on 33 and for linear models are 1 on
34. Non-significant results are left blank. ............................................................................... 80
Table C.1. Poisson regressions using data from all 14 grids with species richness as the
response variable. Form codes are as follows: CD = concave down quadratic model, CU =
concave up quadratic model, POS = positive linear model, and NEG = negative linear model.
For quadratic models degrees of freedom for the null and residual deviance respectively are
895 and 893 at 1 m2, 447 and 445 at 2 m2, 223 and 221 at 4 m2, 55 and 53 at 16 m2, 13 and
11 at 64 m2; and for linear models are 895 and 894 at 1 m2, 447 and 446 at 2 m2, 223 and 222
at 4 m2, 55 and 54 at 16 m2, and 13 and 12 at 64 m2. Grey highlights show regressions at the
1 m2 scale. Non-significant results are left blank. ............................................................... 142
Table C.2. Poisson regressions using data from the four soil grids with species richness as the
response variable. Form codes are as follows: CD = concave down quadratic model, CU =
concave up quadratic model, POS = positive linear model, and NEG = negative linear model.
For quadratic models degrees of freedom for the null and residual deviance respectively are
255 and 253 at 1 m2, 127 and 125 at 2 m2, 63 and 61 at 4 m2, 15 and 13 at 16 m2, 3 and 1 at
64 m2; and for linear models are 255 and 254 at 1 m2, 127 and 126 at 2 m2, 63 and 62 at 4 m2,
15 and 16 at 16 m2, and 3 and 2 at 64 m2. Grey highlights show regressions at the 1 m2 scale.
Non-significant results are left blank. ................................................................................... 144
Table C.3. Poisson regressions with soil nutrient PCA axes using data from the four soil grids
with species richness as the response variable. Form codes are as follows: CD = concave
down quadratic model, CU = concave up quadratic model, POS = positive linear model, and
NEG = negative linear model. For quadratic models degrees of freedom for the null and
residual deviance respectively are 255 and 253; and for linear models are 255 and 254. Nonsignificant results are left blank. ........................................................................................... 146
Table C.4. Poisson regressions of soil nutrients as the explanatory variable with species
richness as the response variable. Form codes are as follows: CD = concave down quadratic
model, CU = concave up quadratic model, POS = positive linear model, and NEG = negative
linear model. For quadratic models degrees of freedom for the null and residual deviance

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2

2

2

respectively are 255 and 253 at 1 m , 127 and 125 at 2 m , 63 and 61 at 4 m , 15 and 13 at 16
m2, 3 and 1 at 64 m2; and for linear models are 255 and 254 at 1 m2, 127 and 126 at 2 m2, 63
and 62 at 4 m2, 15 and 16 at 16 m2, and 3 and 2 at 64 m2. Grey highlights show regressions
at the 1 m2 scale. Non-significant results are left blank. ...................................................... 147
Table C.5. Poisson regressions with axes from the PCA of all soil and leaf nutrients as the
explanatory variables and species richness as the response variable. Form codes are as
follows: CD = concave down quadratic model, CU = concave up quadratic model, POS =
positive linear model, and NEG = negative linear model. For quadratic models degrees of
freedom for the null and residual deviance respectively are 35 and 33; and for linear models
are 35 and 34. Non-significant results are left blank. .......................................................... 152
Table H.1. Plant species occurring in the study plots. Species presence in a grid (L1-5, U1-5,
P1-4) is indicated by and "X". There were 41 species that could not be identified, not shown
here. ....................................................................................................................................... 175

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LIST OF ABBREVIATIONS
Al = aluminum
ADP = adenosine diphosphate
AMP = adenosine monophosphate
a.s.l = above sea level
ATP = adenosine triphosphate
B = boron
BC = British Columbia
B(OH)3 = boric acid
Ca = calcium
CAR = conditional autoregressive model
Cu = copper
DNA = deoxyribonucleic acid
Fe = iron
GLM = generalized linear model
GLMM = generalized linear mixed model
GLS = generalized least squares
H2PO4- = dihydrogen phosphate
HPO42- = hydrogen phosphate

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HBM = humped-back model
ICP-OES = inductively coupled plasma-optical emission spectrometer
i.i.d = independently and identically distributed errors
K = potassium
LRMP = land and resource management plan
Mg = magnesium
Mn = manganese
Na = sodium
NH4+ = ammonium
NO3- = nitrate
P = phosphorus
PCA = principal component analysis
RNA = ribonucleic acid
S = sulphur
SAR = simultaneous autoregressive model
VHP = very high pressure
Zn = zinc

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NOMENCLATURE
Plant species were identified according to the Illustrated Flora of British Columbia, all eight
volumes of which are currently available at URL
http://www.for.gov.bc.ca/hfd/pubs/docs/Mr/MR_IllustratedFlora.htm.

1
CHAPTER 1: INTRODUCTION

Recent trends of declining biodiversity have emphasized the relevance of the factors that
control species richness. Consider planet-wide losses of diversity that have led to major
species conservation initiatives in natural communities (Pimm et al. 1995); or eutrophication
caused by centuries of fertilizer use to increase soil nutrient availability and boost the
productivity of a given area of land while driving species numbers down (Vitousek 1994).
The notion of a causal relationship between productivity and species richness has endured
since at least Darwin's days (Darwin 1859). Fertilization is known to increase yield and
reduce species richness; these responses are well documented in terrestrial and hydrological
systems and highlight the important role that nutrients play as drivers of the productivity and
diversity of ecosystems (Huston 1979, DiTommaso and Aarssen 1989, Goldberg and Miller
1990, Correll 1998). Dependence on scale has also emerged as an important consideration in
understanding patterns of biodiversity, productivity and nutrients (Gross et al. 2000). It is
important to strive for a more complete understanding of productivity, species richness and
soil nutrient relationships not only because of their implications for the field of ecology but
also in order to better direct management, conservation and restoration efforts towards
sustainable use of the lands and waters.
The unimodal curve
There is general consensus that productivity can influence species richness, but despite
extensive research, there is controversy on the form of the relationship, and on the underlying
mechanisms that drive it. One recent review notes six common processes responsible for
unimodal species richness curves including disturbance, predation and herbivory,
productivity, environmental gradients, time, and latitude (Graham and Duda 2011). Of these,
perhaps the most well-known pattern relates to productivity; in this case species richness is
low at low productivity, rises to a maximum at intermediate productivity, and drops off again
as productivity increases to high levels (Currie 1991, Rosenzweig and Abramsky 1993,
Tilman and Pacala 1993, Grace 1999). This unimodal relationship was observed by Grime
and termed the ‘humped-back model’ (HBM) (Grime 1973a, 1973b, 1979, Al-Mufti et al.
1977). Although originally developed to describe the species richness-productivity

2
relationship in herbaceous plant communities, the HBM has since been generalized to many
other types of plant (Al-Mufti et al. 1977, Wheeler and Giller 1982, Walker and Peet 1983,
Day et al. 1988, Moore and Keddy 1989, Puerto et al. 1990) and animal (Leibold 1999,
Dodson et al. 2000, Reed et al. 2006) communities. While there is a range of empirical
evidence that supports the HBM there are also studies that do not (see following section for
references); after nearly four decades of investigation the debate has not been resolved.
Questions that remain are as basic as whether the HBM can be applied to all herbaceous plant
communities, to how the scale of measurement influences the relationship between species
richness and plant productivity.
The humped-back model
Theory
Grime’s humped-back model states that maximum species richness occurs at intermediate
standing crop (Al-Mufti et al. 1977, Grime 1979). The unimodal curve of the model
delineates the upper boundary of possible species richness-productivity values that may be
found in nature (Safford et al. 2001). In other words, productivity is thought to set a limit for
species richness, rather than control it strictly (Cornwell and Grubb 2003); so, values should
not occur above the line of the curve but may occur below it, in which case the full potential
productivity has not been realized. It is thought that at low levels of biomass (proxy for
productivity) species richness is limited by high levels of stress or disturbance allowing only
species with specific adaptations for those conditions to survive. These plant species tend to
be small in stature, slow growing and long lived (Grime 1979). Even if limiting nutrients
become abundant, these types of species continue to absorb nutrients slowly and maintain
slow growth rates (Chapin 1980, Chapin and Shaver 1985). In high biomass environments,
diversity is thought to be restricted by competitively dominant plant species which reduce
community richness through interspecific competition; only a few competitively superior
species will persist. These species of plants are usually large in stature, grow quickly and can
rapidly acquire nutrients if they suddenly become more available. At intermediate levels of
biomass there is some release from the constraints of stress, disturbance and competition
allowing for the highest levels of species richness (Al-Mufti et al. 1977, Grime 1979). Grime
described this medium level of productivity as a "corridor of species richness" which in

3
2

English herbs occurred between 350 - 750 g/m of live biomass + standing crop (Grime
1979).
Debate
The HBM has been widely debated ever since its proposal four decades ago (Guo and Berry
1998, Waide et al. 1999, Safford et al. 2001). Although there is a large body of empirical
evidence that supports the model (e.g. Al-Mufti et al. 1977, Wheeler and Giller 1982, Walker
and Peet 1983, Tilman 1986, Austin 1987, Day et al. 1988, Wilson and Shay 1990, Shipley et
al. 1991, Wheeler and Shaw 1991), including a study with belowground root biomass
included in productivity estimates (Liira and Zobel 2000), there are also studies that do not
(e.g. Moore and Keddy 1989, Gough et al. 1994, Adler et al. 2011).
Three meta-analyses have also been published looking at the comparative frequency of
different species richness-productivity patterns in the literature (Mittelbach et al. 2001,
Gillman and Wright 2006, Pärtel et al. 2007) but there is uncertainty in the utility of such
studies due to complications involved in classifying datasets into categories and inconsistent
scales of analysis (Whittaker and Heegaard 2003, Whittaker 2010). In a recent study by
Adler et al. (2011) featuring sites in 48 herbaceous plant communities on five continents, it
was concluded that there was no clear relationship between productivity and species richness
as predicted by the HBM; however, their study has been criticized because litter was not
collected for inclusion in estimates of productivity, high productivity sites were
underrepresented, and anthropogenically influenced sites were excluded from the analysis
(Fridley et al. 2012). In another recent study, Isbell et al. (2013) conclude that the
relationship between species richness and productivity seems to "flatten" out over time and
may eventually result in no relationship (as found in the Adler et al. 2011 study). They
suggest that where there is a relationship it is simply a system in flux, and that it will flatten
out with time (Isbell et al. 2013). Cornwell and Grubb (2003) also suggest that it is possible
that positive correlations are simply a feature of "transient dynamics". As such, the debate
concerning the validity of the HBM is ongoing.

4
The variety of methods available to estimate productivity (Sala and Austin 2000) has led to
further ambiguity in what relationship emerges between productivity and species richness
(Cardinale et al. 2009b). The original study leading to the proposal of the HBM measured
standing biomass plus litter (Al-Mufti et al. 1977) hence researchers assessing the model
since then typically follow suit (Fridley et al. 2012). The leading determinants of biomass,
and therefore of litter, are disturbance and productivity (Cornwell and Grubb 2003). In areas
of high productivity, litter accumulation may reduce species richness through inhibition of
species establishment by shading and physical obstruction of seedlings (Foster and Gross
1998); this in turn reduces competition and plant density resulting in better growing
conditions for the plants that are able to establish (Fowler 1986, Carson and Peterson 1990).
Litter can also be important in low productivity areas because it can help negate stressful
conditions such as low soil moisture or high variability of soil temperature (Fowler 1986,
Willms et al. 1986, Facelli and Pickett 1991). Similarly, litter removal has been shown to
decrease productivity by reducing soil moisture (Heady 1956). Litter is imperative to
estimates of productivity for testing the HBM because it has significant effects on the plant
community, it provides an indicator of site history, and because including litter allows a more
accurate comparison of the results with those of previous studies, including the original.
The opposite relationship
Lately, the reverse relationship, where species richness is treated as the explanatory variable
and productivity is appointed as the response variable, has been receiving considerable
attention (Chapin et al. 2000, Cardinale et al. 2009a, Isbell et al. 2013). There are over 150
studies indicating that species richness exerts some control over productivity (Cardinale et al.
2006, 2009a). One version of the theory suggests that fewer species leads to reduced
efficiency in the use of soil nutrients and results in reduced plant biomass compared with
more diverse communities (Tilman et al. 1996). Other authors insist that research focussed
on the dependence of species richness on productivity has actually been investigating the
limitation of productivity and species richness by resources, and the limitation of standing
biomass by species richness (Cardinale et al. 2009a). In this view resource supply rate has a
direct effect on standing biomass, as well as an indirect influence through its control of

5
species richness (Cardinale et al. 2009a). A study by Isbell et al. (2013) also discusses direct
and indirect effects. These ideas are discussed further in reference to nitrogen later on.
Nutrients
Soil nutrient availability is known to influence primary productivity and plant species
richness. At the very least, the presence and availability of nutrients may, or may not, meet
the nutrient requirements of different species and therefore defines a species' potential to
survive in a given area. Productivity generally increases with increasing nutrient availability
and, as such, nutrients and rate of nutrient supply are commonly used as proxies for
estimating productivity (Waide et al. 1999, Cardinale et al. 2009a). The availability of
limiting resources determines the potential productivity of a site; this may differ from the
realized productivity based on how efficiently occupant species convert available resources
into biomass (Loreau et al. 2001, Schmid 2002, Cardinale et al. 2009b).
Nutrients can be used as proxies of productivity (Waide et al. 1999, Cardinale et al. 2009a); it
follows that certain patterns of soil nutrient availability can be expected to coincide with the
HBM. The increasing phase of the humped-back curve that occurs from low to intermediate
productivity is thought to be caused by decreasing levels of stress and disturbance (Al-Mufti
et al. 1977, Grime 1979). One type of stress is limited resource availability such as limited
nutrient, water, or light availability. Species richness is low when nutrients are less available
because few species are able to tolerate the resource poor conditions, but as nutrient
availability increases the minimum nutrient requirements of more species will be satisfied
resulting in increasing species richness. Eventually, at high productivity, high availability of
nutrients allows competitively superior species to dominate, thus reducing species richness
through competitive exclusion. High biomass tends to lead to intense competition for light
(Grime 1979, Grace 1999, Aerts et al. 2003, Cornwell and Grubb 2003). Nutrient limitation
and availability are partly responsible for driving the relationship observed between species
richness and productivity.
Experiments that increase soil nutrients often show increases in biomass with corresponding
decreases in species richness (Kirchner 1977, Goldberg and Miller 1990, Bobbink 1991,
Wilson and Tilman 1993, Chapin et al. 1995, Wedin and Tilman 1996, Gough et al. 2000,

6
Baer et al. 2003, Cornwell and Grubb 2003, Crawley et al. 2005). This pattern is observed in
the Park Grass experiment at Rothemsted in England, the longest running plant ecology
experiment in the world (1856 to present), where enrichment of soils with nitrogen,
phosphorus, potassium and organic manures, separately and in various combinations,
resulted in increased productivity and reduced species richness (Crawley et al. 2005).
Shifts in diversity likely occur because of differences in the traits of individual species that
cause the outcome of competition to change under nutrient enrichment. However, with
controlled fertilizer additions the productivity of naturally low productivity sites has been
noted to respond less than that of high productivity sites (DiTommaso and Aarssen 1989),
and the magnitude of species diversity response has been found to be independent of initial
community productivity (Gough et al. 2000). The immobilization of added nutrients to low
productivity soils may contribute to this trend (Chapin et al. 1986). It is also possible that the
disappearance of species as a result of fertilization of moderate to high productivity plots
happens faster than the addition of species caused by fertilization of low to moderate
productivity plots. Loss and gain of species are caused through different mechanisms. While
the loss of species may result from increased competition resulting in competitive exclusion,
the gain of species would depend on dispersal and colonization capacity and other traits of
individual species in the regional species pool (Zobel 1997, Gough et al. 2000, Safford et al.
2001).
Gough et al. (2000) and Suding et al. (2005) suggest that species richness-productivity
relationships on natural gradients behave differently than those in experimental
manipulations; however, humped-shape relationships have been identified in one
observational study between species richness and extractable phosphorus, extractable
potassium and total nitrogen (Janssens et al. 1998). Cornwell and Grubb (2003) point out
that there is a scarcity of information in the literature on species richness patterns and their
relation to the resources that control productivity. This knowledge gap motivates further
study of soil nutrient patterns to see if they align with what the HBM predicts should
coincide at different levels of productivity and richness in nature.

7
Relationships between soil nutrients and plant health can be complex and have extensive
effects on productivity and species richness (Chapin 1980, DiTommaso and Aarssen 1989,
Brady and Weil 1996). The concentration of nutrients required for optimal growth of
individual plant species is often different, consequently nutrient additions are likely to have
varying effects between species. The level of one nutrient that results in toxicity or
deficiency is often influenced by the availability in the soil, plant uptake, and plant tissue
content of one or more other nutrients (Chapin 1980, DiTommaso and Aarssen 1989, Brady
and Weil 1996). Along the same lines, symptoms of toxicity or deficiency of one nutrient
can sometimes be treated by increasing or decreasing concentrations of others (Ward et al.
2008). The identity of the limiting resource may change over time, for example over a
season (Farrior et al. 2013). In addition, the pH of soils is important to nutrient availability
and can also be a good predictor of species diversity (Roem and Berendse 2000). In some
cases, an adequate supply of a nutrient can result in luxury consumption and storage of the
nutrient. The range of supply in which sufficient nutrients are available but are not at high
enough levels to cause negative effects on growth is usually wide for macronutrients, but
often much narrower for micronutrients (Brady and Weil 1996). Too little or too much will
be detrimental to plant health; this results in a spectrum ranging from deficiency to toxicity
and the location of an environment on this spectrum has consequences for both its
productivity and species richness (Brady and Weil 1996). Richness tends to be greatest when
nutrients are somewhat limiting but conditions are not extremely stressful (Grime 1979,
Moore and Keddy 1989). In systems with significant remineralization and decomposition
rates productivity can also feed back to influence the rate at which limiting nutrient resources
become available (Cardinale et al. 2009a). What follows is a brief overview of key mineral
nutrients for plant growth.
Carbon
As the most basic component of all organic matter, carbon plays a fundamental role for living
organisms. Plants fix carbon from atmospheric carbon dioxide through the process of
photosynthesis and some of this carbon eventually reaches the soil as litter or dead root
material. In this way plants remove carbon dioxide from the atmosphere, and through
humification it is stored in the soil. Alternatively, some carbon is re-released into the

8
atmosphere as carbon dioxide during decomposition by microorganisms and animals that
consume the plant matter (Brady and Weil 1996). The sequestration of carbon in the soil by
plants is of interest in recent years because carbon dioxide is a greenhouse gas implicated in
climate change (Brady and Weil 1996) and soil is the largest terrestrial pool of organic
carbon (Batjes 1996). The total carbon content of soils also includes inorganic carbon stored
as carbonate and bicarbonates (Brady and Weil 1996).
Levels of soil organic matter are regulated by productivity. Soils with higher plant
productivity tend to have higher organic matter content because more litter is generated
(Batjes 1996). Soil organic matter content lends soil many properties that influence plant
growth, for example the organic content of soil confers much of its water holding and ion
exchange capacity (Brady and Weil 1996). Organic material also contains nitrogen and other
mineral nutrients necessary for plant health which are released slowly over time (Brady and
Weil 1996). Soils with higher soil organic carbon content are thus able to support higher
levels of productivity (Brady and Weil 1996).
Nitrogen
Nitrogen is the most commonly lacking nutrient in soils and as such the productivity of most
ecosystems is nitrogen limited (Salisbury and Ross 1978, White 1993, Brady and Weil 1996).
The majority of nitrogen in the soil is held in organic matter which releases about 2-3% per
year in plant available forms. Some plants are able to fix their own nitrogen with the help of
symbiotic bacteria in the genera Rhizobium or Bradyrhizobiam (Brady and Weil 1996).
Plants absorb nitrogen mainly as ammonium (NH4+) and nitrate (NO3-), but these forms of
nitrogen are mobile and readily lost from the soil by leaching (Brady and Weil 1996).
Attraction to negatively charged clay particles prevents leaching of ammonium to some
extent but over time this affinity may cause it to become trapped in the crystal structure of
the clay particles rendering it unavailable to plants (this also occurs with potassium ions)
(Brady and Weil 1996). Biological nitrogen fixation by free-living soil micro-organisms is
another source of plant available forms of nitrogen (Brady and Weil 1996).

9
Nitrogen is a central component of many essential compounds including amino acids, nucleic
acids and chlorophyll (Brady and Weil 1996, Smith and Smith 2001). A good supply of
nitrogen stimulates plant growth below and, especially, above ground; it also promotes
absorption of other nutrients and gives leaves their deep green colour (Brady and Weil 1996).
Symptoms of nitrogen deficiency include pale yellow leaves (chlorosis) affecting older
leaves first, and slowed or arrested growth possibly resulting in early leaf senescence (Brady
and Weil 1996). Some species may exhibit purplish coloration of the stems, petioles and
undersides of the leaves when nitrogen is deficient (Salisbury and Ross 1978). Plants not
acquiring enough nitrogen tend to mature more quickly and have lower shoot to root ratios
than those that do (Brady and Weil 1996). With excess nitrogen, vegetation has been shown
to develop a higher shoot to root ratio and very dark green foliage (Salisbury and Ross 1978,
Brady and Weil 1996). Plants may become top heavy because of extreme but structurally
weak above ground growth which may result in lodging (falling over) (Brady and Weil
1996); delayed maturity and increased susceptibility to disease are other common side effects
(Brady and Weil 1996). Productivity is affected in cases of nitrogen toxicity as nitrogen
assimilation, photosynthesis, biomass production (root and shoot), and starch accumulation
in plants is hindered (Andreeva et al. 1998).
Experimental nutrient additions strongly influence both productivity and diversity. The
majority of controlled fertilization studies manipulate nitrogen because it is such a common
limitation to vegetative growth. A study by Cornwell and Grubb (2003) at regional scales, in
biomes of central Europe, reported a humped-shape curve between nitrogen and species
richness. Collins et al. (1998) showed that the dominance of grasses shifts with varying
nitrogen availability and further that the productivity of the dominant grasses is inversely
related to community diversity. More recently, a study by Isbell et al. (2013) reported that
nitrogen additions had direct positive effects on productivity and direct negative effects on
species richness; however, decreases in species richness were also noted to have indirect
negative effects on productivity. In other words, although increased nitrogen availability
initially boosted production, enrichment also had the effect of decreasing species richness
which fed back to reduce the magnitude of productivity benefits over time. Interestingly,
enrichment of atmospheric carbon dioxide gave different results in the same study. There

10
were similar direct effects on productivity but there was no drop in species richness and the
magnitude of fertilization benefits to production did not diminish over time.
Carbon to nitrogen ratio
Climate and vegetation are major determinants of soil organic carbon and nitrogen content.
The ratio of organic carbon to nitrogen in soils is important because it determines the
decomposition rate of dead material, the total amount of organic matter present in the soil,
and the amount of nitrogen available, all of which have bearing on productivity and species
richness. Nitrogen availability depends highly on the rate of nitrogen mineralization by
microbes which, in turn, depends on the supply rates of above and below ground litter, and
soil moisture, aeration status, temperature, and texture (Brady and Weil 1996). The ratio of
organic carbon to nitrogen in soils is fairly stable because of the rate-limiting effects of
nitrogen availability on the activity of microorganisms (Brady and Weil 1996). Additionally,
the rate of increase in soil carbon with increasing productivity is generally greater than that
of soil nitrogen so that soil carbon to nitrogen ratio generally increases with increasing
productivity. This occurs because in productive areas there is high nutrient turnover;
proportionally more of the total nitrogen in soil is available to plants and is taken up and held
in the vegetation because plants from high resource environments tend to have high nitrogen
uptake potential, and corresponding high levels of tissue nitrogen (Chapin et al. 1993). The
activity of soil microorganisms is limited by the relative availability of nitrogen; generally
about 24 parts carbon are required for every part nitrogen used. If plant residues entering the
soil have carbon to nitrogen ratios higher than ~25:1 then there will be very little nitrogen
available to plants due to competition for nitrogen by microorganisms. This, in turn, reduces
the rate of decomposition, makes the availability of nitrogen for plant uptake extremely low,
and ultimately results in lower plant productivity. The addition of organic material with a
carbon to nitrogen ratio lower than ~20:1 to the soil will typically supply enough nitrogen to
soil microbes with excess available for plant use. Under these circumstances higher levels of
plant productivity could be maintained (Brady and Weil 1996).
The concentration of nutrients in plant tissues does not necessarily reflect the total quantities
of nutrients present in soil because plants regulate the uptake of different nutrients to varying

11
extents and because much of the nutrients present in soil may be in insoluble forms which are
unavailable for plant absorption (Brady and Weil 1996). Plant species that typically grow in
nutrient poor soils tend to have lower nutrient concentrations in their tissues than those that
typically grow in more fertile areas (Chapin 1980, Poorter et al. 1990). The percentage dry
weight of plants can range in carbon content from 45-58% and in nitrogen from less than 1%
to over 6% (Brady and Weil 1996); however, changes in the carbon to nitrogen ratio of
biomass (and therefore litter) of an area are usually brought about by species replacement
rather than by shifts in nutrient contents within a species. Changes of carbon to nitrogen
ratio within species are relatively small compared to differences brought about by species
turnover (Wedin and Tilman 1990, 1996). Plant species from nutrient poor environments
tend to have slow leaf turnover and invest more to maintain antiherbivore defences, usually
carbon-based, while plants from fertile environments usually have more rapid leaf turnover
and lower levels of defences, usually nitrogen-based compounds (Bryant et al. 1983, Coley et
al. 1985). Coincident with shifts in species composition, biomass carbon to nitrogen ratios
have been shown to decrease with increasing productivity (Wedin and Tilman 1996).
Phosphorus
Phosphorus is second to nitrogen as the most limiting soil nutrient and plays many important
roles in plants. Phosphorus is absorbed mainly in the form of dihydrogen phosphate
(H2PO4-) and hydrogen phosphate (HPO42-), the first being more readily available in acidic
soils and the second being more available under alkaline conditions (Salisbury and Ross
1978). Phosphate tends to react with soil components making it unavailable for plant uptake;
for example, insoluble precipitates form when iron and phosphate interact with each other
thereby limiting the availability of both nutrients (Dalton et al. 1983). Generally, there is
only about 0.001 mg of phosphorus per litre of soil in infertile soils, and up to about 1 mg
phosphorus per litre of soil in heavily fertilized soils. Approximately 0.01% of the total
phosphorus present in soils is actually available for plant absorption (Brady and Weil 1996)
but root hairs and symbioses with root colonizing (mycorrhizal) fungi aide in its acquisition
(Bolan 1991, Brady and Weil 1996). In fact, these associations offer the greatest benefit to
plants in acquiring nutrients that diffuse slowly in soil such as phosphorus, ammonium,
potassium, and nitrate (Chapin 1980).

12
In plants, phosphorus is used in phospholipids as part of cell membranes and in sugar
phosphates which are fundamental components of deoxyribonucleic acids (DNA) and
ribonucleic acids (RNA). It is also involved in energy metabolism as part of adenosine
triphosphate (ATP), adenosine diphosphate (ADP), and adenosine monophosphate (AMP)
and plays important roles in photosynthesis, respiration and many other metabolic processes
(Salisbury and Ross 1978, Brady and Weil 1996). When phosphorus supplies are adequate
plants tend to have higher root to shoot ratios; this is opposite to when nitrogen is abundant
and plants tend to have lower root to shoot ratios (Salisbury and Ross 1978). Nitrogen and
phosphorus balance also affects timing of plant maturity with abundant phosphorus bringing
on earlier maturity and abundant nitrogen causing delays (Salisbury and Ross 1978).
Deficiency of the macronutrient phosphorus also causes slowed or arrested growth, stunted
roots and dark green foliage. Yellowing of leaves or purple or red coloration also occurs in
some plants (Salisbury and Ross 1978, Brady and Weil 1996). For nitrogen fixing plants,
low phosphorus levels can result in poor nodulation and inhibition of the biological nitrogenfixation process (Brady and Weil 1996). High levels of phosphorus may lead to zinc and
iron deficiencies (Parks et al. 2000) and toxicity results in decreased photosynthetic rates
(Shane et al. 2004), inhibition of growth, development of chlorotic leaves, and early leaf
senescence (Parks et al. 2000).
Higher levels of species richness are usually associated with lower levels of available
phosphorus (Janssens et al. 1998, Venterink et al. 2001, 2003) and a negative relationship
between phosphorus and species richness has been reported in several studies (Janssens et al.
1998, Venterink et al. 2001, Lambers et al. 2010). Janssens et al. (1998) reported a humpedback curve with soil extractable phosphorus. They found that the highest species richness
always occurred at low phosphorus concentrations that were suboptimal for most plants. In
their study there were never more than 20 species per 100 m2 if there was greater than 5 mg
of phosphorus per 100 g of soil. From the functions of phosphorus in plants, the effects of
deficiency and toxicity, and studies investigating its role in directing species richness and
productivity, it is clear that phosphorus availability plays an important role in community
dynamics.

13
Other ratios
Plant productivity and species richness respond to the identity of the most limiting nutrient
and ratio of available nutrients. The number of different forms of available nutrients may
contribute to the species richness of systems, while the most limiting nutrient and nitrogen to
phosphorus ratio correlate directly with the productivity of vegetation (Venterink 2011).
Additionally, the species composition of communities can be very different depending on
whether nitrogen or phosphorus is limiting (Honsova et al. 2007, Chytrý et al. 2009,
Venterink 2011) and species richness may be higher under phosphorus limitation than under
nitrogen limitation (Venterink 2011). Braakhekke and Hooftman (1999) proposed the
'resource balance hypothesis of plant species diversity', a hypothesis which predicts a
humped curve between species richness and nitrogen to phosphorus, phosphorus to
potassium, and potassium to nitrogen ratios such that the highest diversity is expected to
occur at ratios that are balanced to best meet the requirements of the community on average.
Several studies have found empirical evidence to support this theory (Braakhekke and
Hooftman 1999, Roem and Berendse 2000, Daufresne et al. 2005, Güsewell et al. 2005,
Wassen and Venterink 2005, Cardinale et al. 2009b). However, Aerts et al. (2003) tested this
idea with experimentally manipulated nutrient levels and found that nitrogen addition in
nitrogen poor grasslands (low nitrogen to phosphorus ratio) decreased richness and increased
biomass. Phosphorus addition decreased species richness without evoking any change in
productivity. Their work also indicated that a nitrogen to phosphorus ratio of ~6 is a strong
indicator of nitrogen limited growth and ~16 indicates phosphorus limitation.
Potassium
Potassium is another macronutrient that can affect plant productivity and is the third most
commonly limiting nutrient in soils next to nitrogen and phosphorus (Brady and Weil 1996).
Although most soils contain an abundance of potassium the majority of it is insoluble and
therefore unavailable to plants. In fact, only about 1-2% of total soil potassium is actually
available for absorption (Brady and Weil 1996). Accessible potassium is even more easily
leached than phosphorus, especially from acidic soils, but liming and the affinity of
potassium to clay particles helps to reduce losses (Brady and Weil 1996, Janssens et al.

14
1998). Plants need almost as much potassium as they do nitrogen and can absorb and store
excess when it is available (Brady and Weil 1996). Potassium activates many enzymes
including those that form sugars, starches and proteins, and is essential for photosynthesis,
respiration, osmotic balance, and (in legumes) nitrogen fixation (Brady and Weil 1996,
Mäser et al. 2002). Potassium is also important in stress adaptations such as drought and
salinity tolerance, winter hardiness, and resistance to fungal and insect pests (reviewed in
Wang et al. 2013). High calcium and magnesium levels may reduce potassium uptake from
the soil (Brady and Weil 1996) and low potassium availability has been linked to iron
toxicity (Li et al. 2001). Potassium deficiency results in yellowing and necrosis of older
leaves starting at the outer edges and in some species white necrotic spots form (Brady and
Weil 1996). Plants without enough potassium are also more vulnerable to pathogens and
pests. With excess potassium, reduced growth rate and chlorosis of leaves may result
(Ingestad 1973) and Nam et al. (2006) reported increased risk of infection by pathogenic
anthracnose in strawberries. The highest species richness was found to occur around 20 mg
exchangeable potassium per 100 g of soil which is a level optimal for the majority of plants
(Janssens et al. 1998). Although potassium typically has less control of diversity than
phosphorus (because it is usually less limiting), the roles of potassium and the results of its
deficiency or excess in plants make it an important potential contributor to the determination
of productivity and species richness.
Boron
The essential micronutrient boron is involved in at least 15 functions in plants including roles
in cell division, pollen germination, carbohydrate metabolism, and water metabolism (Smith
and Smith 2001); it is also responsible for helping stabilize cell walls and regulating
membrane pore size (Brown et al. 2002). Boron is one of the most commonly deficient
micronutrients (Brady and Weil 1996) and deficient soils can be found worldwide (Shorrocks
1997). Soils are considered to be low in boron when they contain less than 10 ppm of soil
and high in boron at levels greater than 10 ppm of soil (Power and Woods 1997). Plant
available boron (mostly boric acid B(OH)3) is released into soil through microbial
mineralization and weathering of rocks (Brady and Weil 1996) and makes up about 10% of
the total boron in soils (Woods 1994, Power and Woods 1997). Soil pH affects boron

15
availability such that in neutral to marginally acidic soils it is available for absorption but is
also easily leached; as a result, boron deficiencies actually occur more often in acidic soils
(Brady and Weil 1996, Goldberg 1997). Boron availability can have direct effects on
productivity because plants without adequate boron supply show reduced leaf and root
growth, yellowing of leaves (Smith and Smith 2001) and inhibited development of
reproductive structures (Brown et al. 2002). For years, levels of soluble boron greater than 5
ppm of soil were thought to be detrimental to agronomics, but many species native to arid
and semi-arid environments can handle higher levels (Nable et al. 1997). Boron toxicity may
result in chlorosis or necrosis of the outer margins of older leaves, deformed fruits or stem
die back and reductions in overall productivity (Brown and Hu 1996, Nable et al. 1997).
Iron
Of all the essential micronutrients, plants require iron in the greatest quantities (Kobayashi
and Nishizawa 2012). It is involved in production of chlorophyll, helps activate and carry
oxygen in mitochondria and chloroplasts and is involved in respiration and photosynthesis
(Smith and Smith 2001, Kobayashi and Nishizawa 2012). To meet iron requirements but
prevent toxicity, plants strictly regulate iron uptake, storage and use (Puig et al. 2007,
Kobayashi and Nishizawa 2012). Plants that are deficient in iron exhibit extreme chlorosis
and reduced growth (Märschner 2012). Although total iron content in soils is generally high,
at neutral or higher pH levels iron and some other minerals precipitate as hydroxides and
become unavailable to roots (Puig et al. 2007, Jeong and Guerinot 2009). To some extent
iron and copper can be used in the same reactions in plants and therefore iron may be a
suitable replacement for copper in copper deficient plants and vice versa (Puig et al. 2007).
The relative levels of phosphorus and iron are also important to plant health and symptoms of
phosphate deficiency may be improved by reducing the amount of iron available in soil
(Ward et al. 2008). Iron and phosphate interact to form insoluble precipitates which can limit
the availability of both nutrients (Dalton et al. 1983). Iron toxicity has been implicated in
phosphorus deficiency and in reduced root growth in Arabidopsis thaliana (Ward et al.
2008), and iron toxicity in rice plants can be aided by increasing potassium levels (Li et al.
2001). Generally, excess iron (and copper) causes damage to cell membranes, proteins and
nucleic acids (Halliwell and Gutteridge 1984).

16
Magnesium
Magnesium is an essential macronutrient that is almost never limiting to plant growth in
natural soils but is sometimes added with calcium during liming to increase soil pH in
agriculture (Brady and Weil 1996). It is taken up by plants as Mg2+ (Smith and Smith 2001)
and is critical for the activation of enzymes involved in protein synthesis, synthesis of RNA
and DNA, photosynthesis and respiration; it also allows many other reactions to take place
by the transfer of phosphates converting ATP to ADP (Smith and Smith 2001). Magnesium
is the central atom of the chlorophyll molecule (Shaul 2002) and is also an integral part of the
middle lamella of plants (Smith and Smith 2001). Magnesium deficiency leads to chlorosis
of older leaves and limited chlorophyll production; when magnesium is completely absent
chlorophyll does not form at all (Salisbury and Ross 1978). Excess soil magnesium (or
calcium) can lead to phosphorus and boron deficiencies due to high associated pH values. In
this case, phosphorus may become bound in insoluble calcium and magnesium phosphates
rendering it unavailable to plants (Brady and Weil 1996).
Manganese
Plants take up the essential micronutrient manganese primarily in its Mn2+ form which
becomes most available in acidic conditions (Mukhopadhyay and Sharma 1991, Brady and
Weil 1996). One of the primary reasons to limit soil acidity is to prevent manganese and
aluminum toxicity; however, care must be taken as manganese deficiencies may result if soils
are over-limed (Brady and Weil 1996). Absorption of manganese is affected by magnesium
and calcium such that calcium stimulates uptake while magnesium hinders it. Present
together, calcium and magnesium produce an even greater inhibitory effect on absorption
(Maas et al. 1969). In plants, manganese is important for nitrogen metabolism and
assimilation, photosynthesis, and activation of numerous enzymes; particularly for fatty acid
synthesis (Salisbury and Ross 1978, Smith and Smith 2001). Manganese is thought to play a
structural role in the chloroplast and, during photosynthesis, is involved in the transfer of
electrons from water molecules to chlorophyll, splitting the water molecule and releasing
oxygen (Livorness and Smith 1982). Deficiencies of manganese are uncommon but may
result in necrotic lesions, interveinal chlorosis of leaves (Salisbury and Ross 1978), hindrance

17
of cell elongation, and reduced uptake of many other essential nutrients such as aluminum,
calcium, copper, iron, potassium, magnesium, nitrogen, phosphorus, and silicon
(Mukhopadhyay and Sharma 1991). Productivity, chlorophyll content and photosynthesis
also suffer dramatically (Mukhopadhyay and Sharma 1991). How much manganese is
required to cause toxicity depends on how much magnesium is co-occurring in the soil (Goss
and Carvalho 1992) but generally plant homeostatic mechanisms are able to maintain optimal
manganese concentrations (Clemens 2001). Similar to deficiency symptoms, the toxic
effects of manganese include compromised photosynthesis, respiration, nitrogen and protein
metabolism and reduced levels of chlorophyll (Foy et al. 1978, Mukhopadhyay and Sharma
1991, El-Jaoual and Cox 1998).
Scale
An important consideration in understanding patterns of biodiversity is recognizing their
dependence on scale. It is suggested that much of the variation in the productivity-diversity
patterns that are reported in the literature is due, at least in part, to investigations being done
at different spatial scales (Waide et al. 1999, Mittelbach et al. 2001, Chase and Leibold 2002,
Cardinale et al. 2009b). Specifically, there seems to be no relationship between species
richness and plant biomass at local scales within a community type (Moore and Keddy 1989,
Guo and Berry 1998, Adler et al. 2011), a unimodal relationship is often reported across
community boundaries or if plots are done in multiple community types (Waide et al. 1999),
and at regional or geographic scales the relationship is most often reported as a
monotonically increasing relationship (Pianka 1966, Currie 1991). Chase and Leibold (2002)
suggest that the relationship shifts from being unimodal at local scales, to monotonically
increasing at regional scales and that a positive correlation between productivity and
β-diversity explains this shift with increasing scale of investigation.
The majority of studies investigating the HBM have typically been done using small plot
sizes – usually close to 1 m2. Oksanen (1996) asserted that the unimodal curve could be an
artefact arising from small plot size because fewer large individuals (and therefore fewer
species) than small individuals can fit inside a small plot frame. This ‘no-interaction model’
overlooks many known biological processes and interactions between plants (Grime 1997).

18
Additionally, different mechanisms govern species diversity at different scales (Moore and
Keddy 1989, Grime 1997) and the relationship between species richness and productivity has
been shown to have varying forms of scale dependence (Waide et al. 1999, Scheiner and
Jones 2002, Chase and Leibold 2002, Fridley et al. 2006). At geographical scales, species
richness is probably determined by broadly operating factors, such as climate, whereas at
regional and local scales interactions between individual plants or species are likely to play a
much greater role in determining diversity (Currie 1991). Richness at varying scales is
clearly connected because large-scale species pools are ultimately a summation of species
richness at local scales (Taylor et al. 1990, Currie 1991, Zobel 1997); however, species pool
size also directs richness at local scales (Pärtel et al. 1996, Huston 1999). It is important to
determine how broadly the HBM can be applied because some models are useful over many
levels of organization while others apply only at specific scales (Moore and Keddy 1989,
Waide et al. 1999, Chase and Leibold 2002, Cardinale et al. 2009b). In moving forward it
will be important for researchers to clarify the ecological context and scale they are working
at so that the conditions that produce one pattern or another and the responsible mechanisms
can be elucidated (Waide et al. 1999).
Thesis overview
Several areas requiring further research have been identified. After nearly 40 years of
investigation the nature of the relationship between species richness and productivity remains
uncertain. The influence of scale on the forms of relationship between productivity and
species richness needs to be clarified to assess the generalization of the HBM or other
patterns found. There is also the call for further study of soil nutrient patterns and their
control of productivity and species richness using an observational approach in natural
systems in addition to the manipulative experiments that have been done.
In Chapter 2, live-biomass and litter weights, species counts, and data from soil and leaf
nutrient analysis are analyzed to determine patterns between productivity, species richness
and soil nutrients. The influence of scale on these patterns and (in a subsample of plots)
relationships between soil carbon and nitrogen content, and leaf carbon and nitrogen content
are also assessed. The data to evaluate species richness and productivity was collected from

19
896 one square meter plots in fourteen grids, and nutrient data was collected in 256 one
square meter plots in four of the fourteen grids. The grid design, where each grid contains
side by side plots, facilitates the process of analyzing species richness, productivity and
nutrient relationships at various scales increasing from 1 m2 up to 64 m2. In Chapter 3 of my
thesis I put the results of Chapter 2 in a broader ecological context, discuss implications for
management and suggest directions for future research.

20
CHAPTER 2: A MULTI-SCALE INVESTIGATION OF SPECIES RICHNESS,
PRODUCTIVITY AND NUTRIENT RELATIONSHIPS IN HERBACEOUS PLANT
COMMUNITIES OF THE GRASSLANDS OF SOUTHERN INTERIOR BRITISH
COLUMBIA

INTRODUCTION
The relationship between species richness and productivity has spurred a great deal of
investigative effort over the years (see Tilman and Pacala 1993 and Waide et al. 1999 for
overview), and out of this research ‘the humped-back model’ (HBM) (Grime 1979) has
gained support. Grime's HBM predicts that the greatest species richness occurs at
intermediate productivity because of constraint by high stress and disturbance at low
productivity and by intense competition and competitive exclusion at high productivity
(Grime 1973a, 1973b, 1979, Al-Mufti et al. 1977). While there is considerable empirical
evidence to support the HBM (e.g. Al-Mufti et al. 1977, Wheeler and Giller 1982, Walker
and Peet 1983, Tilman 1986, Austin 1987, Day et al. 1988, Wilson and Shay 1990, Shipley et
al. 1991, Wheeler and Shaw 1991), there are also studies that do not (e.g. Moore and Keddy
1989, Gough et al. 1994, Adler et al. 2011). In a recent study by Adler et al. (2011) that
featured sites in 48 herbaceous plant communities on five continents, it was concluded that
productivity is not related to species richness as predicted by the HBM. This study has been
criticized because litter was not collected for inclusion in estimates of productivity, high
productivity sites were underrepresented, and anthropogenically influenced sites were
excluded (Fridley et al. 2012). After close to four decades of research, the debate concerning
the validity of the HBM has not been resolved. Characterizing the nature of the relationship
between species richness and productivity remains a critical gap in our understanding of
plant communities.
One source of confusion may be variation in the spatial scale of investigation between
studies. The mechanisms that govern species diversity are different at different scales
(Moore and Keddy 1989, Grime 1997) and some studies show that the relationship between
species richness and productivity changes at different scales (Waide et al. 1999, Scheiner and
Jones 2002, Chase and Leibold 2002, Fridley et al. 2006). The spatial scale of investigation
is therefore likely an important determinant of the form of relationship between species

21
richness and productivity. A unimodal relationship is often reported when samples are taken
across community boundaries or when plots are from different community types (Waide et
al. 1999). Oksanen (1996) asserted that the unimodal curve could be an artefact caused by
the small plot sizes that are typical to vegetation sampling because fewer large individuals
(and therefore fewer species) than small individuals can fit inside a small plot frame. Grime
(1997) points out that this ‘no-interaction model’ overlooks many known biological
processes and interactions between plants. Determining how scale influences relationships
between productivity and species richness will be an important step to clarify what form or
forms of relationship can be expected at specific scales and to identify scales of application
for the HBM.
Decreases from high levels of stress and disturbance are thought to drive the increasing phase
of the HBM. Limited resource availability, such as limited nutrient, water or light
availability, is a form of stress and soil nutrient availability is known to influence both
primary productivity and plant species richness. Because the nutrient requirements of a
species determine what environments are suitable for it to live in, a gradient of nutrient
availability ranges from being able to support zero species, when nutrients are absent, to
being able to meet the minimum nutrient requirements of many species as well support
greater biomass production when nutrients are abundant. However, as nutrients become less
limiting to growth, the increased biomass typically leads to intense competition for light
(Grime 1979, Grace 1999, Aerts et al. 2003, Cornwell and Grubb 2003).
Systems may be limited by different soil nutrients, but are most often limited by nitrogen
(Salisbury and Ross 1978, White 1993, Brady and Weil 1996). The importance of a nutrient
in determining species richness and productivity in the increasing phase of the curve depends
on how limiting it is to growth compared to other nutrients (Braakhekke and Hooftman
1999); the more limiting a nutrient, the greater its potential role in structuring communities.
In the decreasing phase of the curve nutrients are available in adequate supply and support
high biomass, and intense competition becomes the mechanism by which species richness is
determined. Because different species have varying nutrient requirements it is also possible
that more than one, rather than just the most limiting, influence production, species richness
and species composition in communities (Braakhekke and Hooftman 1999).

22
Many studies have investigated the effect of nutrient additions on species richness and
productivity and seem to support Grime's HBM (Al-Mufti et al. 1977, Grime 1979).
Productivity generally increases with increasing soil nutrient availability and experiments
that add soil nutrients often show increases in biomass at the expense of species richness
(Kirchner 1977, Goldberg and Miller 1990, Bobbink 1991, Wilson and Tilman 1993, Chapin
et al. 1995, Wedin and Tilman 1996, Gough et al. 2000, Baer et al. 2003, Cornwell and
Grubb 2003, Crawley et al. 2005). These findings and the HBM theory suggest that certain
patterns of nutrients should coincide with the HBM in nature.
However, in nutrient addition experiments, productivity has been reported to respond less in
sites that were initially unproductive compared to sites that started out at high productivity
(DiTommaso and Aarssen 1989). Additionally the magnitude and sometimes the direction of
species diversity response has been found to be independent of initial community
productivity, contrary to the predictions of the HBM (Gough et al. 2000). These findings
have been attributed to the immobilization of added nutrients in low productivity sites
(Chapin et al. 1986), the easier loss than gain of species, and species pool effects (Zobel
1997, Gough et al. 2000, Safford et al. 2001). Additionally, Gough et al. (2000) and Suding
et al. (2005) indicate that relationships between species richness and productivity in
experimental manipulations respond differently than species richness-productivity
relationships in natural systems. Gough et al. (2000) also state that even long term studies
are poor predictors of the relationship between species richness and productivity because
"they are relatively small-scale perturbations whereas the pattern of species richness over
natural productivity gradients is influenced by long-term ecological and evolutionary
processes".
There are relatively few publications on non-manipulative observational studies between
species richness, productivity and soil nutrients. Janssens et al. (1998) evaluated
relationships between species richness and extractable phosphorus, extractable potassium and
total nitrogen and reported a unimodal relationship. Cornewll and Grubb (2003) also found a
unimodal relationship between soil nutrient supply and species richness within biomes at the
regional scale. García et al. (1993) reported a peak in species richness at intermediate
productivity and a negative relationship between salinity and species richness in a salt marsh

23
of the Guadalquivir delta (SW Spain). Cornwell and Grubb point out that there is a paucity
of work on species richness patterns and their relation to the resources that control
productivity. This motivates further observational study of soil nutrient patterns to determine
if they align with those patterns that would be expected to coincide with the HBM in nature.
The knowledge-gaps outlined above include the need to characterize the nature of the
relationship between species richness and productivity, the need to determine how scale
influences relationships between productivity and species richness to assess the
generalization of the HBM, and the need for further study of soil nutrient patterns and their
control of productivity and species richness. The objectives that follow are intended to
contribute towards addressing these knowledge-gaps.
Objectives
1) Determine the form of the relationship between species richness and productivity in
the study area.
2) Identify patterns, in relation to those expected to coincide with the HBM, between
total soil aluminum, boron, carbon, calcium, copper, iron, magnesium, manganese,
nitrogen, sodium, phosphorus, potassium, sulphur, zinc (Al, B, C, Ca, Cu, Fe, Mg,
Mn, N, Na, P, K, S, and Zn, respectively), leaf nitrogen and carbon content, biomass
weight (as a proxy for productivity) and species richness in unmanipulated natural
plots. For some nutrients, prediction of expected patterns is not straightforward
because of lack of previous research; in these cases the nature of my work will be
exploratory rather than hypothesis driven.
3) Evaluate the influence of increasing scale from 1 m2 to 64 m2 on relationships found
in the species richness, productivity and nutrient investigations stated in objectives 1
and 2.
Predictions
I expected that the relationship between species richness and total biomass would be
unimodal as predicted by the HBM. Soil nutrients that commonly limit growth such as

24
nitrogen, phosphorus and potassium were expected to be positively correlated with
productivity; and species richness was expected to increase to a maximum and then decrease
with increasing soil concentrations of the most limiting nutrients in accordance with the
HBM. Because carbon is the most basic constituent of all organic matter I predicted that it
would also be positively correlated with productivity and that species richness would
increase to a maximum and then decrease with increasing soil carbon concentrations in
accordance with the HBM. Soil carbon and nitrogen were expected to be positively
correlated with each other because they are known to be tightly connected in systems, a
positive correlation between soil carbon to nitrogen ratio and productivity was expected
because of higher turnover of nutrients combined with the plant-uptake of a greater
proportion of total nitrogen in the form of available nitrogen in productive systems, and a
unimodal relationship was expected between soil carbon to nitrogen ratio and species
richness in accordance with the HBM. Relationships between species richness, productivity
and other soil nutrients are not readily predictable.
Leaf carbon and nitrogen are expected to be highly positively correlated with each other, to
be higher in plants living in high productivity areas on fertile soils and to vary positively with
soil carbon and nitrogen content. Leaf carbon to nitrogen ratio is predicted to decrease with
increasing productivity because of, increased soil nutrient availability, and species turnover.
Based on this last prediction, it is expected that there will be a negative correlation between
soil carbon to nitrogen ratio and leaf carbon to nitrogen ratio.
Increasing scale is expected to weaken, and may completely break, the unimodal relationship
between species richness and biomass. It is thought that this will occur because the
mechanisms (especially competition) operating between plants in close contact within a 1 m2
plot may not be able to operate at larger scales where plants within a plot are not all in close
range of each other. Because productivity is expected to increase with higher concentrations
of limiting soil nutrients the same hypothesis, wherein increasing scale is predicted to result
in a weakening or complete breakdown of the relationship, applies to the expected unimodal
relationship between species richness and limiting soil nutrients (likely nitrogen, phosphorus
and potassium) when plot size is scaled up. The study objectives will be carried out by
sampling low and high productivity sites for species richness, live biomass, litter, total

25
biomass, leaf nutrients, and soil nutrients; and aggregating data from plots within grids to
investigate scales from 1 m2 - 64 m2.

METHODS
Site description
This study took place in the semi-arid, bunchgrass, grasslands of Lac du Bois Provincial Park
(Figure 2.1) and at a field site in Lac La Hache (Figure 2.2). Lac du Bois Provincial Park is
located immediately northwest of Kamloops, British Columbia, Canada and the site at Lac la
Hache is located at the southeast end of the lake approximately 25 km northwest of 100 Mile
House, British Columbia, Canada.
In the park the elevation of the grasslands increases from ~350 m a.s.l. to ~1100 m a.s.l. over
a distance of about 10 km. The elevation gradient is linked to changes in precipitation and
temperature (van Ryswyk et al. 1966). The Kamloops region has an average annual
precipitation of 279.0 mm and an annual average daily temperature of 8.9 °C with the
warmest month being July, 21.0 °C, and the coldest being January, -4.2 °C (Environment
Canada 2012). The differences in precipitation and temperature maintain a productivity
gradient across the park such that productivity increases with altitude. The grasslands in the
park have been classified into three vegetation types that relate to elevation:
Pseudoroegneria – Artemesia, Pseudoroegneria – Poa, and Pseudoroegneria – Festuca,
which dominate the lower, middle and upper grasslands, respectively (van Ryswyk et al.
1966). Work by van Ryswyk et al. (1966) in Lac du Bois documents that soils were brown
chernozemic at low elevation (~520 m.a.s.l), dark brown chernozemic at medium elevation
(~695 m.a.s.l) and black chernozemic at high elevation (~950 m.a.s.l) and that corresponding
pH values were 7.3, 7.5, and 7.2, respectively. The grasslands are used for recreation and
grazed by wildlife and cattle. In the 1930s the park area was severely overgrazed (van
Ryswyk et al. 1966). Now, cattle-grazing occurs from April to November following a restrotation schedule as outlined by the Kamloops LRMP Policy for Domestic Livestock Grazing
in Protected Areas (Ministry of Environment 2000).

26
The elevation of the Lac la Hache site is ~810 m a.s.l. (Erskine 1964). The 100 Mile House
region has an average annual precipitation of 453.3 mm and an annual average daily
temperature of 4.2 °C with the warmest month being July, 15.2 °C, and the coldest being
January, -8.4 °C (Environment Canada 2012). The site is dominated by Phalaris
arundinacea, Carex utriculata, Poa pratensia and an unknown species of borage, and is a
privately owned field that is hayed once yearly in August. The field is grazed by cattle from
approximately October to April.

27

F
Figure 2.1. Map
p of the Lac du Bois
B Grasslandss Provincial park
k study site (Goo
ogle Earth 20144). L1-5, U1-5, and P1-2
aare codes to iden
ntify each grid and
a indicate grid
d locations on th
he map.

28

F
Figure 2.2. Map
p of the Lac la Hache
H
study site (Google Earth 2014). P3 and P4 are codes to identify grids annd
iindicate grid loccations on the map.
m

29
Study design
Fourteen 8 m × 8 m grids, each containing 64, 1 m2 plots, were located at a range of biomass
levels: five grids at low ( L1-5, ~50 – 300 g/m2) and intermediate (U1-5, ~300 – 750 g/m2)
biomass levels and four at high biomass levels (P1-4, ~750 – 2000 g/m2)(Table 2.1)(see
Fraser et al. 2014). Grid columns were labelled A-H and rows were labelled 1-8. For two
grids at each biomass level, four of the 1 m2 plots (G1-2, and H1-2) had smaller nested
1/4 m2 plots with columns labelled a-d and rows labelled i-iv. In four of the 1/4 m2 plots
(ci-ii, and di-ii) there were smaller nested 1/16 m2 plots with columns labelled w-z and rows
labelled 100, 200, 300 and 400 (Figure 2.3).

Table 2.1. Identification, elevation and GPS location (datum: NAD83) of the fourteen study
grids. Soil sampling was done in grids marked "*".
Grid
ID
L1
L2
L3
L4*
L5*
U1
U2
U3
U4
U5
P1*
P2*
P3
P4

Elevation at A1
(m a.s.l.)
753
715
688
522
687
914
914
855
781
894
775
833
807
806

GPS Location
at A1 (Lat/Lon)
N50 45.611 W120 26.092
N50 45.160 W120 23.933
N50 44.323 W120 26.284
N50 43.014 W120 24.800
N50 44.360 W120 26.171
N50 47.349 W120 26.844
N50 47.216 W120 27.009
N50 47.684 W120 23.561
N50 47.886 W120 24.792
N50 47.445 W120 26.264
N50 48.140 W120 24.386
N50 46.811 W120 25.942
N51 47.565 W121 27.803
N51 47.450 W121 27.472

Total Biomass Range
(g/m2)
74.13 ‒ 270.65
81.48 ‒ 334.14
54.56 ‒ 301.43
50.64 ‒ 190.70
55.62 ‒ 335.92
139.23 ‒ 782.69
133.92 ‒ 387.28
72.37 ‒ 241.58
166.39 ‒ 498.44
275.40 ‒ 1337.81
791.53 ‒ 1844.40
572.48 ‒ 1226.63
546.20 ‒ 1380.84
1022.42 ‒ 1869.17

30

Figurre 2.3. Diagrram of grid layout showiing smaller nnested plots in the H1 coorner.

Wood
dy species were
w avoided
d as much as possible whhen selectingg grid locatioons. Areas w
were
not used if they were
w grazed during the th
hree months before samppling becausse recent
disturrbance may be a confoun
nding factorr in the relatiionship betw
ween biomasss and speciees
richn
ness and it may have been
n difficult to
o identify plaants from reccently grazed areas. Griids
were placed to minimize
m
visib
bility from roads
r
in an eeffort to reduuce the potenntial for
vandaalism or distturbance to the
t grids so that
t they maay be used inn future studiies.

31
Marking grids
Once selected, grid areas were swept with a metal detector to check for background readings.
Notes about the location of extra signals from the metal detector were taken as a guide for
reference if the grids need to be located in the future. A measuring tape was used to lay out
the grid by first measuring an 8 m line and then using Pythagorean Theorem to measure a
square.
Each grid was marked using four buried 20.3 cm (8'') nails, one of which had a circular wire
antenna (~10 cm diameter). The purpose of the antenna was to make that nail easier to find
so that it can be used as a starting point when searching for the grids in the future. If there
were interfering background readings detected by the metal detector then copper wire
antennas (~5cm diameter) were used instead. Copper induces a higher pitch from the metal
detector which allows identification of the correct signals while searching for the points. The
markers were buried ~15 cm deep, and the metal detector was used to verify detection. The
locations of all four corners of the grids were recorded using GPS. The slope, aspect and
orientation of the grid were measured. For reference, photos were taken of each grid and
surrounding area before and after sampling. Notes about the site were taken such as about
recent disturbance, appearance, grazing, and background metal readings.
Sampling was scheduled for late July and early August to capture the height of the growing
season. In 2011, grids L1-3 and U1-3 were sampled; all other grids were sampled 2012.
Plant sampling was conducted in each of the 1 m2 plots in all 14 grids (Figure 2.4, Figure
2.5). In six grids (two each at low, intermediate and high productivity) plant sampling was
done in smaller nested 1/4 m2 and 1/16 m2 plots, but I restricted my analysis of plant data to a
scale no less than 1 m2. Soil sampling involved only the 1 m2 plots from four grids: two each
at low (L4 and L5) and high (P1 and P2) productivity.

32

Figurre 2.4. Grid P2,
P post-sam
mpling. Holees are visiblee where soil samples weere
taken
n.

Figurre 2.5. Grid U5,
U post-sam
mpling. The pin-flags ussed for frame placementt
and hummocks
h
leeft over from
m sampling large bunchggrasses are vvisible.

33
Plant sampling protocol
Plant sampling in each grid was done one plot at a time in two steps: species identification
and harvesting. First, all plant species present in the plot were identified and recorded. A
plant species was counted as being in a 1 m2 plot if it was rooted in, or overhanging, the plot.
Woody species in plots were noted and any plants that could not be identified in the field
were collected for later identification and their weights were added to their corresponding
biomass sample afterwards. Second, all live biomass and litter was separated in the field and
collected. Live biomass was cut to ground level and included any material produced during
the current year, but woody plants were not collected. Litter was raked up after live biomass
was cut, and dead material was collected from bunchgrasses as much as possible; however,
for large bunchgrasses hummocks were left to avoid collection of soil with the litter and for
time efficiency (Figure 2.5). Samples were stored in a greenhouse until they could be dried
in a Yamato oven (Model No. DKN812) at 80 ºC for 48 hours and weighed with an
analytical balance (Fisher Scientific accuseries 4102).
Four of the grids were sampled for soil (see below). Of those four grids, samples of ~5 mg of
mixed plant biomass from nine plots (A-C × 1-3) were analyzed separately for total carbon
and nitrogen content using a CE-440 Elemental Analyzer.
Soil sampling protocol
Each 1 m2 plot in four grids was sampled for soil, two at low (L4 and L5) and two at high (P1
and P2) productivity. After plant sampling a 10 cm × 10 cm × 10 cm soil core was taken
from the center of each plot using a knife, four putty knives and a shovel. The top layer of
organic matter (~3 cm) was removed from soil samples in the field with the knife. The soil
was stored in open plastic zip lock bags in a greenhouse to air dry. The soil was sieved to
<355 μm and total carbon and nitrogen content in subsamples of soil of ~10 mg was analyzed
with a CE-440 Elemental Analyzer. Samples were also sent to the BC Ministry of
Environment’s Analytical Chemistry Laboratory (in Victoria, British Columbia) for soil
nutrient analysis of total aluminum, boron, calcium, copper, iron, magnesium, manganese,
sodium, phosphorus, potassium, sulphur, and zinc. Samples were prepared by very highpressure (VHP) closed vessel microwave acid digestion. Sample extractions were done in

34
concentrated nitric acid (0.2 g soil per 4 ml acid) at 230 ºC and ~1500 psi in a Milestone
“Ultrawave” single reaction chamber digester, then cooled and made up to 15 ml with 10%
hydrochloric acid and analyzed using a Teledyne/Leeman Labs “Prodigy” dual view
inductively coupled plasma-optical emission spectrometer (ICP-OES). Multiple sub-samples
were oven-dried at 105 ºC to obtain the 'moisture factor' used to correct the analysis results to
an oven-dry basis.
Data analysis
Data was managed in Excel worksheets. Statistical analyses were done using R version
2.15.2 (R Development Core Team 2012).
Outliers and missing values
One extreme litter value (originally over 2000 g/m2) was corrected to 1000 g/m2 to bring it in
range with other high values from that grid. I think this value was high because it was the
first plot with a large bunchgrass and we demolished every bit of it for collection. This
methodology was not continued in other plots (Figure 2.5).
Two 1 m2 plots had missing values for live biomass and, therefore, also for total biomass
weights. One missing value was replaced with the average plot biomass for the grid it was
in; this grid was not involved in soil sampling. The other plot that was missing a value was
in one of the four grids involved in soil sampling and was a plot that was originally sampled
in 16 parts; two of these samples were missing. In this case I had biomass measurements
from 14 of the 16 subplots and simply averaged these to replace the two missing parts. These
replacement weights for the plots were added to litter weights to calculate total biomass for
the plots.
Principal component analyses
Only the soil nutrient data was included in the soil nutrient principal component analysis
(PCA) while the soil and leaf nutrient PCA included all soil nutrients as well as soil carbon to
nitrogen ratio and leaf carbon, nitrogen and carbon to nitrogen ratio. A soil and leaf carbon,
nitrogen and carbon to nitrogen PCA, including only those nutrients, was also run. There

35
were no missing values but there were several potential outliers in the data. All PCAs were
carried out on the correlation matrices (to standardize for very different ranges and
quantities) of the nutrient variables to extract the major trends from the data and evaluate the
relationship between nutrients, biomass variables, and species richness. The Kaiser–Guttman
criterion and broken stick models were calculated to identify important axes (Borcard et al.
2011). Distance and correlation biplots of the important axes from the principal component
analyses were made to visualize patterns in the data.
The circle in the distance biplots of the first two PCA axes is known as the 'circle of
equilibrium contribution'. Its radius is equal to the number of axes represented in the biplot
divided by the total number of PCA components. If the arrow of a variable extends exactly
to the circle, it contributes equally to all dimensions of the PCA space. Those variables with
arrows extending out past the circle contribute more than average and those with arrows that
do not extend to the circle are not well represented by the first two axes and cannot be
interpreted with confidence (Borcard et al. 2011). Distance and correlation biplots of the
important axes were used to select the important soil nutrients for regression analyses.
Regression analyses
All of the regression analyses that were done were linear bivariate regressions. Quadratic
models with both a linear and quadratic term were fit first; if the quadratic term was not
significant (α=0.01) it was dropped to fit a linear model. If the linear term was not
significant, a non-significant relationship was reported.
Regressions were run with species richness as the response variable and total biomass, live
biomass, and litter as explanatory variables. This was done twice, once using data from all
14 grids and again using only the four grids involved in soil sampling. Regression analyses
were used to evaluate the relationships between species richness, total biomass, live biomass,
litter and the soil and leaf nutrients that were indicated as important by the PCA ordinations.
Regressions were also done between the first, second and third axes of PCA ordinations and
species richness, total biomass, live biomass, and litter. Data from adjacent plots within grids
were summed for total biomass, live biomass and litter, aggregated for species richness and

36
averaged for soil nutrient measurements to analyze scale dependency relationships from plots
at the 1 m2, 2 m2, 4 m2, 16 m2, and 64 m2 scales.
Plots within a grid are side by side, so violation of the assumption of independently and
identically distributed errors (i.i.d) required for basic regression analysis is extremely likely.
This can elevate Type I error, the act of falsely rejecting the null hypothesis or in other words
finding significance in tests when there actually is none. Moran's I statistic was calculated
for each grid and, indeed, indicated significant spatial autocorrelation in many cases.
Residuals from each of the nutrient regressions with species richness, total biomass, live
biomass and litter were plotted in semi-variograms by grid and Dr. David Hill was consulted
for help with their interpretation. They often had large nugget effects corresponding to local
variation occurring at scales smaller than our sample plot size of 1 m2. The patterns
displayed in the rest of the semi-variograms (usually less than half of the semi-variogram if
normalized) were shallow increases or erratic patterns suggesting that either the strength of
spatial autocorrelation effects, if present, were probably weak to moderate, or that patterns
were spurious. In addition, these plots indicate severe violation of the assumptions of spatial
stationarity and isotropic spatial autocorrelation that should be met to proceed with the vast
majority of spatial analyses routinely used to account for spatial autocorrelation. Examples
of these approaches include generalized least squares (GLS), generalized linear models
(GLM), spatial generalized linear mixed models (GLMM), and simultaneous and conditional
autoregressive models (SAR and CAR). These and others are reviewed by Dormann et al.
(2007) and Beale et al. (2010). In the interest of reducing the potential for committing a
Type I error, I elected to adjust to an α of 0.01, an approach recommended as conservative by
Dale and Fortin (2002). Correlograms of Moran's I statistics and semi-variograms of
residuals from linear models are presented in APPENDIX A and APPENDIX B respectively.
Semi-variograms of residuals for quadratic models looked nearly identical to those for linear
models in the vast majority of cases, so they have not been included.
Species richness is not strictly normally distributed because it is count data, therefore
regression models including this response variable were also fit using generalized linear
modelling (non-spatial) with a Poisson distribution as it may be more suitable than standard
linear regression (which assumes a Gaussian distribution). The Poisson regressions were

37
evaluated for over and underdispersion and because all had dispersion parameters close to 1
(0.5 - 1.5) no corrections were necessary (Zuur et al. 2009). Gaussian and Poisson
regressions gave very similar results at the 1 m2 scale and almost always returned the same
form of significant model. Exceptions were regressions between species richness and PC2
from the soil nutrient PCA, species richness and phosphorus, species richness and
manganese, and species richness and PC1 from the PCA of soil and leaf nutrients. Summary
tables and plots of Poisson regressions are available in APPENDIX C. Influential points
were identified with Cook's distance and leverage for all Poisson and Gaussian regressions at
the 1 m2 scale. Only two instances of influential points occurred however these points were
not removed for the final analysis because removing them did not change the form of model
selected (quadratic or linear) and only influenced multiple R2 values by as much as 0.05; as
well, removing points would have caused problems when combining plots to evaluate larger
scales. Species richness was square root transformed and total biomass, live biomass and
litter were log10 transformed to improve normality. Improvements by transforming nutrient
variables were negligible, so they were not transformed. In nearly all cases models exhibited
heterogeneity in residuals, which could be expected considering the presumed violation of
the assumption of i.i.d, the fitting of non-optimal bivariate regression models and probable
missing covariates.

RESULTS
Plots for all regressions included in the summary tables are available in APPENDIX D,
APPENDIX F, and APPENDIX G; a small selection of these are also shown here, in Chapter
2. Biplots with PC3 axes are available in APPENDIX E. A list of the species that were
identified is provided in APPENDIX H. For all regressions, the greatest difference between
multiple R2 values and adjusted R2 values was 0.06, but most differences were less than 0.03.
Multiple R2 values were reported, rather than adjusted R2 values, so that results could be
expressed in terms of proportion of variation in the response variable explained by the
explanatory variable.

38
Species richness and biomass regressions
With all 14 grids at the 1 m2 scale, litter and total biomass explained 12% and 11% of the
variation in species richness respectively and live biomass explained 1% of the variation.
Where regressions were significant, the form of relationship between species richness with
total biomass and litter was consistently concave down while with live biomass was
consistently negative linear (Figure 2.6). For biomass and litter significant forms were
comparable at the 1 m2, 2 m2, and 4 m2 scales between the full 14-grid dataset (Table 2.2)
and the dataset including only the four grids involved in soil sampling (Table 2.3); for live
biomass significant forms occurred in both datasets only at the 1 m2 scale.

2

4

5

6

2

2

2

5.5

6.0

6.5

7.0

7.5

5

6

7

6

7

3.0

3.5

2

2.5

Species Richness

3.0
2.5

1.5

Species Richness

1.5
5.0

4

Scale  1 m

2.0

3.0
2.5
2.0

4.5

Total Biomass (g) (Log10)

3

Litter (g) (Log10)

3.5

Scale  1 m

1.5
4.0

3.5

7

Live Biomass (g) (Log10)

3.5

Scale  1 m

3.0
2.0
1.5

7

Total Biomass (g) (Log10)

2.0

6

2.5

Species Richness

3.5
3.0
2.0
1.5

5

2

4.0

Scale  1 m

2.5

Species Richness

3.5
3.0
2.5

Species Richness

2.0
1.5
4

Species Richness

2

4.0

Scale  1 m

4.0

Scale  1 m

3.5

4.0

4.5

5.0

5.5

6.0

6.5

Live Biomass (g) (Log10)

7.0

2

3

4

5

Litter (g) (Log10)

Figure 2.6. Square root transformed species richness with fitted curves from linear regression
models at 1 m2 having log transformed total biomass, log transformed live biomass and log
transformed litter as the explanatory variables; this is shown for the 14-grid dataset (top
panels) and the 4-grid dataset including only those grids involved in soil sampling (bottom
panels). The dotted line is the fitted linear model and the dashed line is the fitted quadratic
model. The significant model in each plot is shown in bold.

39
Table 2.2. Regressions using data from all 14 grids with square root transformed species richness as the response variable. Form
codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG
= negative linear model. For quadratic models degrees of freedom are 2 on: 893 at 1 m2, 445 at 2 m2, 221 at 4 m2, 53 at 16 m2, 11 at
64 m2; and for linear models are 1 on: 894 at 1 m2, 446 at 2 m2, 222 at 4 m2, 54 at 16 m2, and 12 at 64 m2. Grey highlights show
regressions at the 1 m2 scale. Non-significant results are left blank.
Explanatory Variable
Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2) Form
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CD
CD
CD
CD

8.95
7.38
5.20
3.20

1.94E-18
7.96E-13
4.63E-07
2.33E-03

-9.27
-7.57
-5.35
-3.27

1.31E-19
2.18E-13
2.18E-07
1.89E-03

53.91
34.16
19.50
7.20

7.86E-23
1.58E-14
1.59E-08
1.71E-03

0.11
0.13
0.15
0.21

NEG
NEG
NEG

-3.69
-2.81
-2.82

2.39E-04
5.18E-03
5.21E-03

13.61
7.89
7.96

2.39E-04
5.18E-03
5.21E-03

0.01
0.02
0.03

CD
CD
CD

9.14
7.96
5.23

4.20E-19
1.48E-14
3.89E-07

62.13
40.50
20.33

5.44E-26
6.91E-17
7.89E-09

0.12
0.15
0.16

-9.92
-8.35
-5.52

4.66E-22
8.92E-16
9.47E-08

40
Table 2.3. Regressions using data from only the four grids involved in soil sampling with square root transformed species richness as
the response variable. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS =
positive linear model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2,
61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2.
Grey highlights show regressions at the 1 m2 scale. Non-significant results are left blank.
Explanatory Variable
Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2) Form
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CD
CD
CD

5.11
4.05
3.45

6.28E-07
9.08E-05
1.04E-03

-5.21
-4.10
-3.47

4.00E-07
7.46E-05
9.53E-04

14.92
9.04
6.29

7.49E-07
2.15E-04
3.28E-03

0.11
0.13
0.17

NEG

-3.31

1.06E-03

10.97

1.06E-03

0.04

CD
CD
CD
CD

6.75
6.79
5.97
4.20

1.03E-10
4.01E-10
1.29E-07
1.03E-03

22.79
23.06
17.89
9.01

7.96E-10
2.98E-09
7.68E-07
3.51E-03

0.15
0.27
0.37
0.58

-6.73
-6.77
-5.94
-4.17

1.12E-10
4.58E-10
1.47E-07
1.10E-03

41
Soil nutrient PCA and PCA regressions
The PCA of the soil nutrients indicated that the cumulative percentage of variation in the data
accounted for by the first two axes is 76.5% and this rises to 84.4% if the third axis (PC3) is
included. The first axis (PC1) alone explains 43.8% of the variation while the second axis
(PC2) alone explains 32.6%. The percentage of variation in the data explained by the third
axis alone is 8.0% (Table 2.4).

Table 2.4. Results for the first four axes from a PCA of the soil nutrient data collected from
four 8 m × 8 m grids (L4, L5, P1 and P2).
Eigenvalues
Proportion Explained
Cumulative Proportion

PC1
6.1376
0.4384
0.4384

PC2
4.5651
0.3261
0.7645

PC3
1.1139
0.0796
0.8440

PC4
0.6711
0.0479
0.8920

In the Kaiser-Guttman criterion for the PCA of the soil nutrients the first three axes were
greater than the average eigenvalue. In the broken stick model only the first two axes were
greater than the corresponding pieces of broken stick (APPENDIX E).
The distance biplot showing the first two axes of the soil nutrient PCA indicates that soil
carbon, nitrogen, phosphorus, potassium, boron, magnesium, manganese and iron are
variables that have contributed more than average to the ordination space (Figure 2.7). Soil
carbon and nitrogen align in the opposite direction to soil iron and align slightly more with
PC1 than with PC2. Soil magnesium and manganese also point in opposite directions from
each other and align well with PC2.

42

3

Mg

2

K
S

Ca
Na

Cu

0

PC2

1

Fe

B

-2

-1

Al

C
N
P

-3

Zn
Mn

-4

-2

0

2

PC1

Figure 2.7. Distance biplot of the first two principal component axes of the PCA on the
soil nutrient data. The red circle is the circle of equilibrium contribution. Each grid is
indicated by points of a certain colour. The L4 (red points) and L5 (green points) grids
were lower biomass grids while the P1 (blue points) and P2 (black points) grids were
higher biomass grids.

Of the variables that contributed more than average to the ordination space in the distance
biplot (Figure 2.7), the correlation biplot of PC1 and PC2 from the PCA of the soil nutrient
data (Figure 2.8) shows that soil magnesium, potassium and boron are positively correlated,
that soil carbon and nitrogen are tightly positively correlated, and that soil iron and
manganese are not closely positively correlated with any of the other important nutrient
variables. Instead, they are strongly negatively correlated with soil nitrogen and carbon, and

43
magnesium respectively. Soil iron is most tightly associated with the L4 grid and soil
potassium and boron appear to be mostly associated with the P1 and P2 grids. Manganese is
associated primarily with the P2 grid but about equally associated with the L5 grid while the
P1 and P2 grids both seem about equally correlated to soil carbon and nitrogen. Soil
aluminum is highly contributory to PC3 (APPENDIX E).

Mg

K

1

B
S
Ca
Na

Cu

0

PC2

Fe

-1

Al

NC
P
Zn
Mn

-2

-1

0

1

2

PC1

Figure 2.8. Correlation biplot of the first two principal component axes of the PCA on
the soil nutrient data. Each grid is indicated by points of a certain colour. The L4 (red
points) and L5 (green points) grids were lower biomass grids while the P1 (blue points)
and P2 (black points) grids were higher biomass grids.

44
Regressions with species richness, total biomass, live biomass or litter as the response
variables were done with PC1, PC2, or PC3 as the explanatory variables. Variation in litter
was 82% explained by the first principal component of the soil nutrient PCA with a concave
down relationship, and live biomass variation was 67% explained by PC1 with a positive
linear relationship. The first principal component was able to explain 32% of the variation in
species richness, also in a concave down relationship. The variation in species richness was
35% explained in a regression with PC2 in a negative linear relationship (Figure 2.9).
Variation in species richness, total biomass, live biomass and litter were all less than 10%
explained in regressions with PC3 (Table 2.5).

45
2

Scale  1 m

Scale  1 m

2

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

6.5
6.0
5.5
4.0

3.5

2

4.5

5.0

Total Biomass (g) (Log10)

6.0
5.5
5.0
4.0

4.5

Live Biomass (g) (Log10)

5
4
3

Litter (g) (Log10)

6

7.0

6.5

7

7.5

7.0

Scale  1 m

2

-0.4

-0.2

0.0

0.2

PC1

0.4

0.6

0.8

-0.4

-0.2

0.0

0.2

PC1

2

0.6

0.8

2

Scale  1 m

Scale  1 m

2

-0.4

-0.2

0.0

0.2

PC1

0.4

0.6

0.8

6.5
6.0
5.5
4.0

1.5

1.5

4.5

5.0

Total Biomass (g) (Log10)

7.0

3.5
3.0
2.0

2.5

Species Richness

3.0
2.5
2.0

Species Richness

3.5

7.5

Scale  1 m

0.4

PC1

-0.6

-0.4

-0.2

0.0

PC2

0.2

0.4

0.6

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

PC2

Figure 2.9. Log transformed litter, log transformed live biomass, and log transformed
total biomass with fitted curves from linear regression models at 1 m2 having PC1 as the
explanatory variable (top panels); square root transformed species richness with fitted
curves from linear regression models having PC1 (bottom left panel) and PC2 (bottom
center panel) as the explanatory variables; and log transformed total biomass with fitted
curves from linear regression models having PC2 as the explanatory variable (bottom
right panel). The dotted line is the fitted linear model and the dashed line is the fitted
quadratic model. The significant model in each plot is shown in bold.

46
Table 2.5. Bivariate regressions for PC1, PC2 and PC3 (from the soil nutrient PCA) as explanatory variables and species richness,
total biomass, live biomass and litter as the response variables at the 1 m2 scale. Form codes are as follows: CD = concave down
quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG = negative linear model. For quadratic
models degrees of freedom are 2 on 253 and for linear models are 1 on 254. Non-significant results are left blank.
Explanatory
Variable
PC1

PC2

PC3

Response Variable
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)

Form
CD
CD
POS
CD
NEG
CU
CU
CU
NEG
POS
POS

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

3.55
27.99
22.80
33.74
-11.81
-3.32
-1.60
-5.16
-4.14
3.44
4.28

4.61E-04
1.93E-79
2.19E-63
1.26E-95
5.89E-26
1.04E-03
1.11E-01
4.90E-07
4.76E-05
6.80E-04
2.63E-05

-10.82
-5.96

1.10E-22
8.65E-09

-10.64

4.32E-22

7.11
6.99
6.62

1.21E-11
2.41E-11
2.15E-10

58.63
401.19
519.84
570.26
139.55
29.99
25.37
34.12
17.13
11.83
18.33

1.20E-21
3.42E-79
2.19E-63
1.84E-94
5.89E-26
2.05E-12
9.09E-11
7.60E-14
4.76E-05
6.80E-04
2.63E-05

0.32
0.76
0.67
0.82
0.35
0.19
0.17
0.21
0.06
0.04
0.07

47
Soil nutrient regressions
Carbon
At 1 m2, soil carbon explained the greatest amount of variation in litter, 80%, in a concave
down relationship (Figure 2.10). Soil carbon explained 72% and 61% of the variation in total
biomass and live biomass respectively in positive linear relationships. With species richness,
a concave down curve with soil carbon explained 15% of the variation. The forms of these
relationships were consistent with increasing scale up to 16 m2 for total biomass and live
biomass and up to 4 m2 for species richness. For litter the relationship switched from
concave down to positive linear between 2 m2 and 4 m2 (Table 2.6).

48
2

Scale  1 m

Scale  1 m

4.0

3.5

3.5

3.0
1.5

4.0

2.0

2.5

Species Richness

5.5
5.0
4.5

Live Biomass (g) (Log10)

6.0

6.5

7.5
7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

2

7.0

Scale  1 m

2

2e+04

4e+04

6e+04

8e+04

1e+05

2e+04

Soil Carbon (ppm)

6e+04

8e+04

2e+04

1e+05

2

Scale  2 m

4e+04

6e+04

8e+04

1e+05

Soil Carbon (ppm)

Soil Carbon (ppm)

2

Scale  4 m

2

3

4

2

4

5

6

Litter (g) (Log10)

6
5

Litter (g) (Log10)

5
4
3

Litter (g) (Log10)

7

6

7

8

7

Scale  1 m

4e+04

2e+04

4e+04

6e+04

8e+04

Soil Carbon (ppm)

1e+05

2e+04

4e+04

6e+04

Soil Carbon (ppm)

8e+04

1e+05

20000

40000

60000

80000

Soil Carbon (ppm)

Figure 2.10. Fitted curves from linear regressions with soil carbon as the explanatory
variable and log transformed total biomass (top left panel), log transformed live biomass
(top center panel) and square root transformed species richness (top right panel) as
response variables at the 1 m2 scale. Fitted curves from linear regression models having
soil carbon as the explanatory variable and log transformed litter as response variables at
1 m2 (bottom left panel), 2 m2 (bottom center panel), and 4 m2 (bottom right panel). The
dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold.

49
Table 2.6. Bivariate regressions of soil carbon with species richness, total biomass, live biomass and litter as the response variables.
Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and
NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13 at 16 m2, 1
at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show
regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2) Form
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CD
CD
CD

6.21
5.37
4.20

2.14E-09
3.70E-07
8.69E-05

-5.31
-4.68
-3.67

2.38E-07
7.49E-06
5.19E-04

22.80
16.68
10.49

7.88E-10
3.78E-07
1.22E-04

0.15
0.21
0.26

POS
POS
POS
POS

25.37
19.23
14.23
7.79

1.43E-71
2.72E-39
3.40E-21
1.87E-06

643.39
369.76
202.45
60.67

1.43E-71
2.72E-39
3.40E-21
1.87E-06

0.72
0.75
0.77
0.81

POS
POS
POS
POS

20.06
15.04
10.99
5.72

2.78E-54
6.72E-30
3.44E-16
5.29E-05

402.33
226.12
120.77
32.72

2.78E-54
6.72E-30
3.44E-16
5.29E-05

0.61
0.64
0.66
0.70

CD
CD
POS
POS

12.79
8.65
18.53
11.50

3.12E-29
2.08E-14
5.77E-27
1.61E-08

503.86
308.11
343.33
132.24

5.84E-89
4.85E-49
5.77E-27
1.61E-08

0.80
0.83
0.85
0.90

-4.81
-2.62

2.56E-06
9.89E-03

50
Nitrogen
At the 1 m2 scale soil nitrogen best explained the variation in litter accounting for 81% with a
concave down relationship. Positive linear relationships explained 73% and 63% of the
variation in total biomass and live biomass respectively. Soil nitrogen explained 14% of the
variation in species richness in a concave down curve. The forms of relationships were
consistent with increasing scale up to 16 m2 for total biomass and live biomass and up to 4 m2
for species richness; for litter the form of relationship switched from concave down to
positive linear between 2 m2 and 4 m2 (Figure 2.11). The results for soil nitrogen were very
similar to those of soil carbon at all scales (Table 2.7).

51
Scale  1 m

2

Scale  1 m

4.0

3.5

3.5

3.0
1.5

4.0

2.0

2.5

Species Richness

5.5
5.0
4.5

Live Biomass (g) (Log10)

6.0

6.5

7.5
7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

2

7.0

Scale  1 m

2

2000

4000

6000

8000

2000

Soil Nitrogen (ppm)

6000

2000

8000

4000

6000

8000

Soil Nitrogen (ppm)

2

2

Scale  2 m

Scale  4 m

3

4

2

4

5

6

Litter (g) (Log10)

6
5

Litter (g) (Log10)

5
4
3

Litter (g) (Log10)

7

6

7

8

7

Scale  1 m

4000

Soil Nitrogen (ppm)

2

2000

4000

6000

Soil Nitrogen (ppm)

8000

2000

4000

6000

Soil Nitrogen (ppm)

8000

1000

2000

3000

4000

5000

6000

7000

8000

Soil Nitrogen (ppm)

Figure 2.11. Fitted curves from linear regressions with soil nitrogen as the explanatory
variable and log transformed total biomass (top left panel), log transformed live biomass
(top center panel) and square root transformed species richness (top right panel) as
response variables at the 1 m2 scale. Fitted curves from linear regression models having
soil nitrogen as the explanatory variable and log transformed litter as response variables
at 1 m2 (bottom left panel), 2 m2 (bottom center panel), and 4 m2 (bottom right panel).
The dotted line is the fitted linear model and the dashed line is the fitted quadratic
model. The significant model in each plot is shown in bold.

52
Table 2.7. Bivariate regressions of soil nitrogen with species richness, total biomass, live biomass and litter as the response variables.
Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and
NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13 at 16 m2, 1
at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show
regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CD
CD
CD

5.87
5.06
3.90

1.37E-08
1.46E-06
2.40E-04

-5.09
-4.47
-3.45

6.91E-07
1.71E-05
1.01E-03

21.07
15.15
9.18

3.42E-09
1.28E-06
3.28E-04

0.14
0.20
0.23

POS
POS
POS
POS

26.14
19.73
14.57
7.92

5.78E-74
2.43E-40
1.09E-21
1.53E-06

683.14
389.09
212.27
62.79

5.78E-74
2.43E-40
1.09E-21
1.53E-06

0.73
0.76
0.77
0.82

POS
POS
POS
POS

20.58
15.39
11.28
5.86

4.99E-56
9.93E-31
1.18E-16
4.12E-05

423.38
236.92
127.14
34.37

4.99E-56
9.93E-31
1.18E-16
4.12E-05

0.63
0.65
0.67
0.71

CD
CD
POS
POS

12.48
8.61
18.53
11.22

3.54E-28
2.61E-14
5.69E-27
2.21E-08

532.35
324.19
343.51
125.82

2.18E-91
3.41E-50
5.69E-27
2.21E-08

0.81
0.84
0.85
0.90

-5.36
-3.25

1.87E-07
1.50E-03

53
Soil carbon to nitrogen ratio
At the 1 m2 scale soil carbon to nitrogen ratio was a concave down relationship with litter,
total biomass, species richness and live biomass as response variables and explained 42%,
29%, 24%, and 20% of the variation at this scale, respectively. With increases in scale the
form of the significant relationship switched from concave down to a positive linear
relationship. For all response variables this change occurred between 2 m2 and 4 m2 (Figure
2.12), except for live biomass for which it occurred between 1 m2 and 2 m2 (Table 2.8).

2

Scale  2 m

2

Scale  2 m

2

3.5
3.0
2.5

Species Richness

7.5
7.0
6.5
6.0

Total Biomass (g) (Log10)

3

5.0

2.0

5.5

6
5
4

Litter (g) (Log10)

7

8.0

Scale  2 m

10

11

12

8

9

2

Scale  4 m

11

12

8

9

2

Scale  4 m

11

12

4.0

2

Species Richness

8.0
7.5
7.0

2.0

4

6.0

2.5

6.5

Total Biomass (g) (Log10)

7
6

10

Soil Carbon to Nitrogen Ratio

8.5

8

Scale  4 m

5

Litter (g) (Log10)

10

Soil Carbon to Nitrogen Ratio

3.5

9

Soil Carbon to Nitrogen Ratio

3.0

8

8.5

9.0

9.5

10.0

10.5

11.0

Soil Carbon to Nitrogen Ratio

11.5

8.5

9.0

9.5

10.0

10.5

11.0

Soil Carbon to Nitrogen Ratio

11.5

8.5

9.0

9.5

10.0

10.5

11.0

11.5

Soil Carbon to Nitrogen Ratio

Figure 2.12. Fitted curves from linear regressions at the 2 m2 scale (top panels) and 4 m2
scale (bottom row) with soil carbon to nitrogen ratio as the explanatory variable, and log
transformed litter (left panels), log transformed total biomass (center panels) and square
root transformed species richness (right panels) as response variables. The dotted line is
the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

54
Table 2.8. Bivariate regressions of soil carbon to nitrogen ratio with species richness, total biomass, live biomass and litter as the
response variables. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS =
positive linear model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2,
61 at 4 m2, 13 at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2.
Grey highlights show regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CD
CD
POS
POS

4.68
3.42
5.64
3.03

4.72E-06
8.57E-04
4.52E-07
8.95E-03

-4.33
-3.14

2.18E-05
2.14E-03

39.69
28.16
31.78
9.20

1.02E-15
8.00E-11
4.52E-07
8.95E-03

0.24
0.31
0.34
0.40

CD
CD
POS

4.08
3.03
4.92

5.96E-05
2.99E-03
6.65E-06

-3.65
-2.74

3.19E-04
7.06E-03

52.54
28.24
24.23

8.26E-20
7.60E-11
6.65E-06

0.29
0.31
0.28

CD
POS
POS

3.46
5.33
3.82

6.36E-04
4.40E-07
3.12E-04

-3.12

2.00E-03

32.38
28.40
14.58

3.02E-13
4.40E-07
3.12E-04

0.20
0.18
0.19

CD
CD
POS
POS

4.75
3.61
6.65
3.46

3.35E-06
4.43E-04
8.60E-09
3.79E-03

-4.18
-3.22

4.09E-05
1.63E-03

89.91
49.68
44.24
12.00

3.17E-30
1.32E-16
8.60E-09
3.79E-03

0.42
0.44
0.42
0.46

55
Phosphorus
At the 1 m2 scale, linear regressions with litter and total biomass as response variables and
soil phosphorus as the explanatory variable resulted in concave down curves explaining 39%
and 25% of their variation respectively. These changed to positive linear relationships with
increasing scale; for total biomass this occurred between the 1 m2 and 2 m2 scales and for
litter between the 2 m2 and 4 m2 scales (Figure 2.13). The relationships for both species
richness and live biomass with soil phosphorus as the explanatory variable were consistently
positive linear and the amount of variation explained was 27% and 14% at the 1 m2 scale
respectively (Table 2.9).

2

2

2

Scale  2 m

Scale  1 m

4

2.0

2.5

Species Richness

3.0

7
6
5

Litter (g) (Log10)

6.5
6.0
5.5
5.0

1.5

3

4.0

4.5

Total Biomass (g) (Log10)

7.0

3.5

7.5

Scale  1 m

800

1000

1200

800

1400

900

1100

1200

1300

1400

800

2

1000

1200

1400

Soil Phosphorus (ppm)

2

Scale  4 m

Scale  1 m

2

5

6.0
5.5
5.0
4.0

4.5

6

Litter (g) (Log10)

7

Live Biomass (g) (Log10)

7.5
7.0
6.5
6.0
5.5
800

900

1000

1100

1200

1300

Soil Phosphorus (ppm)

1400

3.5

4

5.0

Total Biomass (g) (Log10)

6.5

8

8.0

7.0

Scale  2 m

1000

Soil Phosphorus (ppm)

Soil Phosphorus (ppm)

800

900

1000

1100

1200

1300

Soil Phosphorus (ppm)

1400

800

1000

1200

1400

Soil Phosphorus (ppm)

Figure 2.13. Fitted curves from linear regressions with soil phosphorus as the explanatory
variable at 1 m2 and 2 m2 with log transformed total biomass (left panels), at 2 m2 and
4 m2 with log transformed litter (center panels) and with square root transformed species
richness and log transformed live biomass at 1 m2 (right panels). The dotted line is the
fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

56
Table 2.9. Bivariate regressions of soil phosphorus with species richness, total biomass, live biomass and litter as the response
variables. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear
model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13
at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights
show regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1
t Statistic

p Value

POS
POS
POS
POS

9.81
8.32
6.76
4.43

1.83E-19
1.24E-13
5.63E-09
5.71E-04

CD
POS
POS

3.86
6.42
4.70

1.46E-04
2.56E-09
1.48E-05

POS
POS
POS

6.36
4.72
3.47

9.20E-10
6.16E-06
9.51E-04

CD
CD
POS
POS

5.85
4.16
6.37
3.50

1.52E-08
5.92E-05
2.59E-08
3.56E-03

Term 2
t Statistic

-3.03

-4.73
-3.39

p Value

2.71E-03

3.66E-06
9.34E-04

Model
F Statistic

p Value

Multiple R2

96.19
69.19
45.67
19.62

1.83E-19
1.24E-13
5.63E-09
5.71E-04

0.27
0.35
0.42
0.58

42.33
41.18
22.11

1.39E-16
2.56E-09
1.48E-05

0.25
0.25
0.26

40.48
22.28
12.05

9.20E-10
6.16E-06
9.51E-04

0.14
0.15
0.16

80.02
46.33
40.61
12.22

1.18E-27
8.83E-16
2.59E-08
3.56E-03

0.39
0.43
0.40
0.47

57
Potassium
In regressions with species richness as the response variable and soil potassium as the
explanatory variable 14% of the variation was explained; the form of the significant
relationship was always negative linear and this held up to the 4 m2 scale. In regressions with
soil potassium as the explanatory variable and total biomass, live biomass and litter as
response variables the relationship was concave up and explained 22%, 25% and 18% of the
variation respectively at the 1 m2 scale. This relationship switched to a positive linear form
between 2 m2 and 4 m2 for total biomass and litter and between 1 m2 and 2 m2 for live
biomass. In the case of litter, which had no significant relationship at 16 m2, the form of the
relationship switched back to concave up and was significant, at 64 m2 (Figure 2.14, Table
2.10).

58
2

Scale  1 m

2

Scale  2 m

5000

6000

7000

7.5
7.0
6.5
6.0
5.0

5.5

Total Biomass (g) (Log10)

6.5
6.0
5.5
5.0
3.5

1.5

4.0

4.5

Live Biomass (g) (Log10)

3.0
2.5
2.0

Species Richness

3.5

8.0

7.0

Scale  1 m

2

8000

5000

Soil Potassium (ppm)

6000

7000

4500

8000

5000

2

5500

2

6500

7000

7500

2

Scale  2 m

Scale  4 m

8.0
7.5
7.0

4.5

2

6.0

6.5

Total Biomass (g) (Log10)

6.5
6.0
5.5

Live Biomass (g) (Log10)

5.0

5
4
3

Litter (g) (Log10)

6

7.0

8.5

7

7.5

Scale  1 m

6000

Soil Potassium (ppm)

Soil Potassium (ppm)

5000

6000

7000

Soil Potassium (ppm)

8000

4500

5000

5500

6000

6500

7000

Soil Potassium (ppm)

7500

5000

5500

6000

6500

7000

7500

Soil Potassium (ppm)

Figure 2.14. Fitted curves from linear regressions with soil potassium as the explanatory
variable at 1 m2 with square root transformed species richness and log transformed litter
(left panels), at 1 m2 and 2 m2 with log transformed live biomass (center panels) and
with log transformed total biomass at 2 m2 and 4 m2 (right panels). The dotted line is
the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

59
Table 2.10. Bivariate regressions of soil potassium with species richness, total biomass, live biomass and litter as the response
variables. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear
model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13
at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights
show regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

t Statistic

p Value

t Statistic

NEG
NEG
NEG

-6.47
-4.91
-3.61

5.15E-10
2.75E-06
6.11E-04

CU
CU
POS

-3.02
-2.29
4.01

2.76E-03
2.36E-02
1.64E-04

3.60
2.67

CU
POS
POS

-2.99
6.12
4.50

3.10E-03
1.11E-08
3.06E-05

CU
CU
POS

-3.22
-2.53
3.43

CU

-431.58

p Value

Model
F Statistic

p Value

Multiple R2

41.80
24.12
13.04

5.15E-10
2.75E-06
6.11E-04

0.14
0.16
0.17

3.90E-04
8.53E-03

35.95
19.75
16.11

1.81E-14
3.52E-08
1.64E-04

0.22
0.24
0.21

3.61

3.64E-04

42.20
37.42
20.24

1.53E-16
1.11E-08
3.06E-05

0.25
0.23
0.25

1.46E-03
1.28E-02
1.07E-03

3.70
2.86

2.61E-04
5.01E-03

28.03
16.14
11.78

1.01E-11
5.83E-07
1.07E-03

0.18
0.21
0.16

1.48E-03

436.49

1.46E-03 123076.48 2.02E-03

1.00

60
Boron
Soil boron explained the most variation in live biomass accounting for 54% at 1 m2. The
form of the relationship with total biomass, live biomass, and litter was concave down at
1 m2, 2 m2, and 4 m2 and for total biomass and live biomass switched to positive linear at
16 m2. For litter at 16 m2 no form was significant. Soil boron explained 17% of the variation
in species richness at 1 m2 in a concave up relationship. This form of relationship also held
at 2 m2 but changed to negative linear at 4 m2 (Figure 2.15, Table 2.11)

2

2

2

Scale  1 m

Scale  1 m

10

20

30

40

6.5
6.0
5.5
4.0

3.5

2

4.5

5.0

Total Biomass (g) (Log10)

6.0
5.5
5.0
4.0

4.5

Live Biomass (g) (Log10)

5
4
3

Litter (g) (Log10)

6

7.0

6.5

7

7.5

7.0

Scale  1 m

10

Soil Boron (ppm)

30

40

10

2

20

30

40

Soil Boron (ppm)

2

2

Scale  2 m

Scale  4 m

3.5
2.0

1.5

2.0

2.5

3.0

Species Richness

3.0
2.5

Species Richness

3.0
2.5
2.0

Species Richness

3.5

4.0

3.5

Scale  1 m

20

Soil Boron (ppm)

10

20

30

Soil Boron (ppm)

40

10

20

30

Soil Boron (ppm)

40

5

10

15

20

25

30

35

40

Soil Boron (ppm)

Figure 2.15. Fitted curves from linear regressions with soil boron as the explanatory
variable at 1 m2 with log transformed litter, log transformed live biomass, and log
transformed total biomass as response variables (top panels), and with square root
transformed species richness at 1 m2, 2 m2 and 4 m2 (bottom panels). The dotted line is
the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

61
Table 2.11. Bivariate regressions of soil boron with species richness, total biomass, live biomass and litter as the response variables.
Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and
NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13 at 16 m2, 1
at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show
regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CU
CU
NEG

-5.02
-4.20
-3.32

9.78E-07
4.97E-05
1.50E-03

4.00
3.45

8.29E-05
7.63E-04

26.26
17.15
11.04

4.33E-11
2.61E-07
1.50E-03

0.17
0.22
0.15

CD
CD
CD
POS

10.25
7.56
5.47
3.43

7.89E-21
7.42E-12
8.76E-07
4.06E-03

-7.98
-5.99
-4.38

4.94E-14
2.06E-08
4.82E-05

120.72
65.78
34.42
11.77

1.54E-37
3.04E-20
9.83E-11
4.06E-03

0.49
0.51
0.53
0.46

CD
CD
CD
POS

11.34
8.63
6.28
3.91

2.30E-24
2.38E-14
3.97E-08
1.58E-03

-8.86
-6.88
-5.03

1.41E-16
2.59E-10
4.54E-06

145.94
83.28
44.57
15.26

7.13E-43
1.03E-23
1.17E-12
1.58E-03

0.54
0.57
0.59
0.52

CD
CD
CD

8.25
6.04
4.38

8.50E-15
1.65E-08
4.73E-05

-6.36
-4.71
-3.46

9.40E-10
6.41E-06
9.98E-04

82.33
44.95
23.39

2.88E-28
1.96E-15
2.88E-08

0.39
0.42
0.43

62
Iron
Soil iron explained the most variation in litter and accounted for 87% in a concave up
relationship at 1 m2. This relationship held at smaller scales but switched to negative linear
at 16 m2 (Figure 2.16). At 1 m2 soil iron accounted for 85% and 79% of total biomass and
live biomass respectively and for these response variables the relationship was consistently
concave up at scales up to 16 m2. A concave down curve was found at scales up to 16 m2 for
regressions with species richness as the response variable and soil iron as the explanatory
variable; at 1 m2 this accounted for 29% of the variation (Table 2.12).

2

Scale  1 m

2

2

Scale  1 m

25000

30000

35000

40000

45000

7.5
6.5
6.0
5.5
4.5
4.0
25000

30000

Soil Iron (ppm)

35000

40000

25000

45000

30000

2

35000

40000

45000

Soil Iron (ppm)

Soil Iron (ppm)
2

2

Scale  4 m

Scale  16 m

8
7

Litter (g) (Log10)

4

6

2

5

6

Litter (g) (Log10)

5
4
3

Litter (g) (Log10)

7

6

9

8

7

Scale  1 m

5.0

Total Biomass (g) (Log10)

7.0

6.5
6.0
5.5
5.0
3.5

1.5

4.0

4.5

Live Biomass (g) (Log10)

3.0
2.5
2.0

Species Richness

3.5

7.0

Scale  1 m

25000

30000

35000

Soil Iron (ppm)

40000

45000

30000

35000

Soil Iron (ppm)

40000

30000

35000

40000

Soil Iron (ppm)

Figure 2.16. Fitted curves from linear regressions with soil iron as the explanatory
variable at 1 m2 with square root transformed species richness, log transformed live
biomass, and log transformed total biomass as response variables (top panels), and at
1 m2, 4 m2 and 16 m2 with log transformed litter (bottom panels). The dotted line is the
fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

63
Table 2.12. Bivariate regressions of soil iron with species richness, total biomass, live biomass and litter as the response variables.
Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and
NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13 at 16 m2, 1
at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights show
regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CD
CD
CD
CD

9.45
8.78
7.44
4.46

2.31E-18
1.03E-14
4.08E-10
6.38E-04

-9.68
-8.97
-7.60
-4.57

4.56E-19
3.60E-15
2.18E-10
5.21E-04

52.67
44.57
31.96
12.12

7.54E-20
2.44E-15
3.20E-10
1.07E-03

0.29
0.42
0.51
0.65

CU
CU
CU
CU

-11.76
-9.76
-8.19
-5.14

9.18E-26
4.61E-17
2.10E-11
1.90E-04

9.49
8.03
6.83
4.34

1.84E-18
6.18E-13
4.52E-09
7.98E-04

732.47
459.73
301.01
108.40

5.84E-106
2.38E-58
2.49E-32
7.79E-09

0.85
0.88
0.91
0.94

CU
CU
CU
CU

-12.73
-10.54
-8.74
-5.30

5.02E-29
5.70E-19
2.41E-12
1.43E-04

10.95
9.19
7.68
4.70

4.12E-23
1.10E-15
1.58E-10
4.14E-04

483.19
306.15
199.86
67.89

3.96E-87
6.75E-49
1.65E-27
1.32E-07

0.79
0.83
0.87
0.91

CU
CU
CU
NEG

-6.55
-5.89
-5.15
-15.16

3.23E-10
3.39E-08
2.96E-06
4.43E-10

4.07
3.90
3.57

6.34E-05
1.59E-04
6.99E-04

818.49
570.89
378.42
229.76

3.33E-111
1.37E-63
4.13E-35
4.43E-10

0.87
0.90
0.93
0.94

64
Magnesium
At the 1 m2 scale linear regressions with soil magnesium as the explanatory variable
explained the most variation in species richness, accounting for 49%. Soil magnesium
explained 9%, 11%, and 10% of the variation in total biomass, live biomass and litter at the
same scale. The form of the curve was concave up for every regression that was significant
except in the case of live biomass where it switched to positive linear between the 1 m2 and
2 m2 scale and was not significant at larger scales (Figure 2.17, Table 2.13). The observation
with over 20,000 ppm soil magnesium was identified by Cook's distance as an influential
point; however, removing it did not change the forms of relationships that were significant.

2

2

2

Scale  1 m

Scale  1 m

5

3.5

1.5

2

4.0

3

4

Litter (g) (Log10)

6.0
5.5
5.0
4.5

Live Biomass (g) (Log10)

3.0
2.5
2.0

Species Richness

6

6.5

3.5

7

7.0

Scale  1 m

15000

20000

10000

Soil Magnesium (ppm)

15000

20000

10000

Soil Magnesium (ppm)

2

2

7.5

7.5

Scale  1 m

12000

14000

6.5
6.0
4.5
4.0

4.5
10000

Soil Magnesium (ppm)

5.5

Total Biomass (g) (Log10)

6.5
6.0
5.5
5.0

Live Biomass (g) (Log10)

7.0

7.0

4.5
4.0
3.5

Species Richness

3.0

8000

20000

2

Scale  2 m

Scale  16 m

15000

Soil Magnesium (ppm)

5.0

10000

6000

8000

10000

12000

14000

Soil Magnesium (ppm)

16000

18000

10000

15000

20000

Soil Magnesium (ppm)

Figure 2.17. Fitted curves from linear regressions with soil magnesium as the
explanatory variable at 1 m2 and 16 m2 with square root transformed species richness
(left panels), at 1m2 and 2 m2 with log transformed live biomass (center panels), and log
transformed litter and log transformed total biomass (right panels). The dotted line is
the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

65
Table 2.13. Bivariate regressions of soil magnesium with species richness, total biomass, live biomass and litter as the response
variables. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear
model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13
at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights
show regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

CU
CU
CU
CU

-9.62
-8.72
-7.94
-6.21

7.34E-19
1.44E-14
5.48E-11
3.16E-05

7.45
7.14
6.73
5.33

1.52E-12
6.73E-11
6.71E-09
1.37E-04

122.96
95.83
79.57
49.83

4.94E-38
5.89E-26
1.00E-17
8.02E-07

0.49
0.61
0.72
0.88

CU
CU
CU

-3.41
-3.10
-2.70

7.66E-04
2.42E-03
8.92E-03

3.98
3.45
2.92

8.89E-05
7.67E-04
4.95E-03

12.97
8.57
5.60

4.33E-06
3.24E-04
5.83E-03

0.09
0.12
0.16

CU
POS

-2.08
3.29

3.87E-02
1.28E-03

2.89

4.23E-03

15.09
10.85

6.46E-07
1.28E-03

0.11
0.08

CU
CU
CU

-4.99
-4.35
-3.66

1.13E-06
2.84E-05
5.31E-04

5.28
4.53
3.77

2.84E-07
1.37E-05
3.75E-04

14.77
10.73
7.33

8.55E-07
4.99E-05
1.40E-03

0.10
0.15
0.19

66
Manganese
Of the response variables, soil manganese was able to explain the greatest amount of
variation in species richness; at the 1 m2 scale it accounted for 25% and had a positive linear
relationship. Soil manganese explained 8%, 6%, and 12% of total biomass, live biomass and
litter respectively (Figure 2.18). The relationship remained positive linear between soil
manganese and species richness from 1 m2 up to 16 m2 after which it became insignificant.
For total biomass and live biomass the relationship was concave up at 1 m2 and 2 m2 and
insignificant at larger scales. For litter, the relationship was concave up at 1 m2, positive
linear at 2 m2 and was not significant at larger scales (Table 2.14).

2

2

2

Scale  1 m

Scale  1 m

3.5

1.5

2

4.0

4.5

5.0

5.5

6.0

Live Biomass (g) (Log10)

5

2.0

3

4

Litter (g) (Log10)

3.0
2.5

Species Richness

6

6.5

3.5

7

7.0

Scale  1 m

700

800

900

1000

700

800

Soil Manganese (ppm)

1000

700

2

800

900

1000

Soil Manganese (ppm)

2

2

Scale  2 m

Scale  1 m

3

6.5
6.0
5.5
4.0

3.0

4.5

5.0

Total Biomass (g) (Log10)

6
4

5

Litter (g) (Log10)

4.0
3.5

Species Richness

7

7.0

4.5

7.5

Scale  16 m

900

Soil Manganese (ppm)

800

850

900

Soil Manganese (ppm)

950

1000

700

750

800

850

900

950

Soil Manganese (ppm)

1000

700

800

900

1000

Soil Manganese (ppm)

Figure 2.18. Fitted curves from linear regressions with soil manganese as the
explanatory variable at 1 m2 and 16 m2 with square root transformed species richness
(left panels), at 1m2 and 2 m2 with log transformed litter (center panels), and log
transformed live biomass and log transformed total biomass (right panels). The dotted
line is the fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold.

67
Table 2.14. Bivariate regressions of soil manganese with species richness, total biomass, live biomass and litter as the response
variables. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear
model, and NEG = negative linear model. For quadratic models degrees of freedom are 2 on: 253 at 1 m2, 125 at 2 m2, 61 at 4 m2, 13
at 16 m2, 1 at 64 m2; and for linear models are 1 on: 254 at 1 m2, 126 at 2 m2, 62 at 4 m2, 14 at 16 m2, and 2 at 64 m2. Grey highlights
show regressions at the 1 m2 scale. Non-significant results are left blank.
Response Variable
√Species Richness

Total Biomass (g) (log10)

Live Biomass (g) (log10)

Litter (g) (log10)

Scale (m2)
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

t Statistic

p Value

t Statistic

POS
POS
POS
POS

9.20
8.43
7.61
4.72

1.36E-17
6.68E-14
1.86E-10
3.27E-04

CU
CU

-3.70
-2.64

2.67E-04
9.34E-03

3.85
2.74

CU
CU

-3.66
-2.70

3.05E-04
7.82E-03

CU
POS

-3.36
3.36

9.15E-04
1.02E-03

p Value

Model
F Statistic

p Value

Multiple R2

84.63
71.10
57.96
22.30

1.36E-17
6.68E-14
1.86E-10
3.27E-04

0.25
0.36
0.48
0.61

1.49E-04
6.97E-03

11.74
6.22

1.33E-05
2.66E-03

0.08
0.09

3.74
2.76

2.28E-04
6.71E-03

8.03
4.43

4.14E-04
1.38E-02

0.06
0.07

3.59

3.94E-04

17.04
11.31

1.14E-07
1.02E-03

0.12
0.08

68
Soil and leaf nutrient PCA and PCA regressions
The percentage of variation in the soil and leaf nutrient data accounted for by the first two
PCA axes is 70.0% and rises to 79.5% if PC3 is included. Alone, PC1 explains 42.9% of the
variation in the soil and leaf nutrient data while PC2 alone explains 27.1%. The percentage
of variation in the data explained by PC3 alone is 9.5% (Table 2.15).

Table 2.15. Results for the first four axes from a PCA of the soil and leaf nutrient data
collected from four 3 m × 3 m subsamples within the four 8 m × 8 m grids (L4, L5, P1 and
P2).
Eigenvalues
Proportion Explained
Cumulative Proportion

PC1
7.7210
0.4289
0.4289

PC2
4.8719
0.2707
0.6996

PC3
1.7125
0.0951
0.7948

PC4
1.0511
0.0584
0.8531

The Kaiser-Guttman criterion for the PCA of the soil and leaf nutrient data shows the first
four axes were greater than the average eigenvalue but in the broken stick model only the
first two axes were greater than the corresponding pieces of broken stick (APPENDIX E).
The distance biplot of the first two axes of the PCA on the soil and leaf nutrient data
indicates that soil sodium, calcium, potassium, boron, magnesium and iron are nutrients that
have contributed more than average to the ordination space (Figure 2.19). Soil carbon and
nitrogen point the opposite direction of iron and these are well aligned with PC1. None of
the leaf nutrients contribute more than average to the PCA. Soil magnesium again lines up
with PC2.

2.0

69

B

Mg

1.5

K
Ca

S

1.0

Leaf N
Leaf C

0.5

Al

0.0

PC2

Na

C:N

Fe
Cu

-0.5

NC

-1.0

P

Leaf C:N
Zn
Mn

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PC1

Figure 2.19. Distance biplot of the first two principal component axes from the PCA on
the soil and leaf nutrient data. The red circle is the circle of equilibrium contribution.
Each grid is indicated by points of a certain colour. The L4 (red points) and L5 (green
points) grids were lower biomass grids while the P1 (blue points) and P2 (black points)
grids were higher biomass grids.

The correlation biplot shows soil sodium, calcium, potassium, boron and magnesium (at a
slightly larger angle) grouped together in a similar direction indicating positive correlation
(Figure 2.20). Again, these nutrients are associated with the P2 grid. The L4 grid is again
tightly associated with soil iron which is not tightly correlated with any other nutrients but is

70
slightly positively associated with leaf carbon and nitrogen content, however these variables
contributed less than average to the PCA ordination space. Soil aluminum aligns strongly

1.0

1.5

2.0

with PC3; variation in this element dominates this axis (APPENDIX E).

BK
Ca

Mg

Na

Leaf N
Leaf C

0.5

PC2

S

0.0

Al

Fe

C:N
N
C

Cu

-0.5

P

-1.0

Leaf C:N
Zn
Mn

-2

-1

0

1

PC1

Figure 2.20. Correlation biplot of the first two principal component axes of the soil and
leaf nutrient data. Each grid is indicated by points of a certain colour. The L4 (red
points) and L5 (green) grids were lower biomass grids while the P1 (blue points) and P2
(black points) grids were higher biomass grids.

71
2

At the 1 m scale the first principal component explained the most variation in litter with a
positive linear relationship accounting for 76% of the variation in the data. Total biomass
and live biomass gave high R2 values with PC1 which accounted for 75% and 71% of the
variation respectively with concave up relationships. The second principal component
explained 37%, 35%, and 33% of the variation in live biomass, total biomass and litter
respectively with concave up relationships. Variation in species richness was 34% explained
by a negative linear relationship with PC2 as the explanatory variable (Figure 2.21, Table
2.16).

72
2

2

Scale  1 m

Scale  1 m

6.5
6.0
5.5
4.0

4.0

2

4.5

5.0

Total Biomass (g) (Log10)

5
4

Litter (g) (Log10)

3

5.5
5.0
4.5

Live Biomass (g) (Log10)

6.0

6

7.0

6.5

Scale  1 m

2

-1.0

-0.5

0.0

0.5

-1.0

-0.5

0.0

PC1

0.5

-1.0

-0.5

0.0

PC1
2

Scale  1 m

Scale  1 m

2

3.0
2.0

2.5

Species Richness

5
4

Litter (g) (Log10)

3

5.5
5.0

2

4.5

1.5

4.0

Live Biomass (g) (Log10)

6.0

6

6.5

3.5

Scale  1 m

0.5

PC1
2

-0.5

0.0

0.5

PC2

1.0

-0.5

0.0

0.5

PC2

1.0

-0.5

0.0

0.5

1.0

PC2

Figure 2.21. Log transformed live biomass, log transformed litter and log transformed
total biomass with fitted curves from linear regression models at 1 m2 having PC1 as the
explanatory variable (top panels); and, log transformed live biomass, log transformed
litter and square root transformed species richness with fitted curves from linear
regression models having PC2 as the explanatory variable (bottom panels). The
principal components are from the PCA on the soil and leaf nutrient data. The dotted
line is the fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold.

73
Table 2.16. Bivariate regressions with PC1, PC2 and PC3 (from the soil and leaf nutrient PCA) as explanatory variables and species
richness, total biomass, live biomass and litter as the response variables at the 1 m2 scale. Form codes are as follows: CD = concave
down quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG = negative linear model. For
quadratic models degrees of freedom are 2 on 33 and for linear models are 1 on 34. Non-significant results are left blank.
Explanatory
Variable
PC1

PC2

PC3

Response Variable
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)

Form

CU
CU
POS
NEG
CU
CU
CU

Term 1

Term 2

Model

t Statistic

p Value

t Statistic

p Value

F Statistic

p Value

Multiple R2

9.60
8.93
10.48
-4.16
-1.20
-0.41
-1.80

4.43E-11
2.56E-10
3.49E-12
2.05E-04
2.39E-01
6.87E-01
8.06E-02

3.37
4.05

1.95E-03
2.91E-04

3.87
3.68
3.95

4.87E-04
8.20E-04
3.82E-04

50.65
41.20
109.78
17.29
8.71
9.74
8.19

8.75E-11
1.07E-09
3.49E-12
2.05E-04
9.18E-04
4.74E-04
1.29E-03

0.75
0.71
0.76
0.34
0.35
0.37
0.33

74
Soil and leaf carbon, nitrogen and carbon to nitrogen ratios PCA and regressions
The percentage of variation in the soil and leaf carbon, nitrogen and carbon to nitrogen ratio
nutrient data accounted for by the first two PCA axes is 87.3% and rises to 94.4% if PC3 is
included. The first axis alone explains 70.2% of the variation while the second alone
explains 17.1%. The percentage of variation in the data explained by the third axis alone is
7.1% (Table 2.17).

Table 2.17. Results for the first four axes from a PCA on soil and leaf carbon, nitrogen, and
carbon to nitrogen ratio data collected from four 3 m × 3 m subsamples within the four 8 m ×
8 m soil grids (L4, L5, P1 and P2).
Eigenvalues
Proportion Explained
Cumulative Proportion

PC1
4.2127
0.7021
0.7021

PC2
1.0234
0.1706
0.8727

PC3
0.4253
0.0709
0.9436

PC4
0.2940
0.0490
0.9926

The Kaiser-Guttman criterion of the PCA of the soil and leaf carbon, nitrogen and carbon to
nitrogen ratio nutrient data suggests that the first two axes are relevant while the broken stick
model indicates only the first axis contains important information (APPENDIX E).
The distance biplot of the first two axes of the PCA of the soil and leaf carbon, nitrogen and
carbon to nitrogen ratio nutrient data indicates that soil carbon and nitrogen, as well as leaf
nitrogen, are nutrients that have contributed more than average to the ordination space
(Figure 2.22). Leaf carbon, soil carbon to nitrogen ratio and leaf carbon to nitrogen ratio
contribute less than average to the PCA ordination space.

1.5

75

0.0
-0.5

PC2

0.5

1.0

Leaf C:N

-1.5

-1.0

C:N

Leaf C
Leaf N
C
N

-2

-1

0

1

2

PC1

Figure 2.22. Distance biplot of the first two principal component axes from the PCA
of the soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient data. The
red circle is the circle of equilibrium contribution. Each grid is indicated by points of
a certain colour. The L4 (red points) and L5 (green points) grids were lower biomass
grids while the P1 (blue points) and P2 (black points) grids were higher biomass
grids.

The correlation biplot (Figure 2.23) shows that soil carbon and nitrogen are slightly
negatively correlated with leaf carbon and nitrogen. High leaf carbon and nitrogen is

76
associated with the lower biomass L4 grid while high soil carbon and nitrogen are correlated

1.0

1.5

with the higher biomass P1 and P2 grids.

0.5
0.0

PC2

Leaf C:N

-0.5

C:N
Leaf C
Leaf N

-1.0

NC

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PC1

Figure 2.23. Correlation biplot of the first two principal component axes from the
PCA of the soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient data.
Each grid is indicated by points of a certain colour. The L4 (red points) and L5
(green points) grids were lower biomass grids while the P1 (blue points) and P2
(black points) grids were higher biomass grids.

At the 1 m2 scale, regressions with PC1 as the explanatory variable explained the most
variation in litter accounting for 56% of the variation with a positive linear form (Figure

77
2.24). The relationships with total biomass and live biomass were also positive linear and
accounted for 45% and 36% of the variation respectively. Relationships between the same
response variables, in regressions with PC2, were all negative linear; there were no
significant relationships between any of the PCA axes and species richness. The variation in
total biomass and live biomass were both 27% explained by PC2; variation in litter was 23%
explained by PC2 (Table 2.18).

2

Scale  1 m

2

Scale  1 m

2

6.5
6.0
5.5
4.0

4.0

2

4.5

5.0

Total Biomass (g) (Log10)

5
4

Litter (g) (Log10)

3

5.5
5.0
4.5

Live Biomass (g) (Log10)

6.0

6

7.0

6.5

Scale  1 m

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

PC1

1.0

-1.0

-0.5

0.0

2

Scale  1 m

0.5

1.0

PC1

2

Scale  1 m

2

6.5
6.0
5.5
4.0

4.0

2

4.5

5.0

Total Biomass (g) (Log10)

5
4

Litter (g) (Log10)

3

5.5
5.0
4.5

Live Biomass (g) (Log10)

6.0

6

7.0

6.5

Scale  1 m

0.5

PC1

-0.4

-0.2

0.0

0.2

PC2

0.4

0.6

0.8

-0.4

-0.2

0.0

0.2

PC2

0.4

0.6

0.8

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

PC2

Figure 2.24. Fitted curves from linear regression models at 1 m2 having log transformed
live biomass, log transformed litter and log transformed total biomass as response
variables and PC1 (top panels); and PC2 (bottom panels) as the explanatory variables.
The principal components are from the PCA on only the soil and leaf carbon, nitrogen,
and carbon to nitrogen ratios. The dotted line is the fitted linear model and the dashed
line is the fitted quadratic model. The significant model in each plot is shown in bold.

78
Table 2.18. Bivariate regressions for PC1, PC2 and PC3 (from the soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient
PCA) as explanatory variables and species richness, total biomass, live biomass and litter as the response variables at the 1 m2 scale.
Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and
NEG = negative linear model. For quadratic models degrees of freedom are 2 on 33 and for linear models are 1 on 34. Nonsignificant results are left blank.
Explanatory
Variable
PC1

PC2

PC3

Response Variable
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)
√Species Richness
Total Biomass (g) (log10)
Live Biomass (g) (log10)
Litter (g) (log10)

Form

Term 1
t Statistic

p Value

POS
POS
POS

5.32
4.35
6.57

NEG
NEG
NEG

-3.55
-3.58
-3.17

Term 2
t Statistic

p Value

Model
F Statistic

p Value

Multiple R2

6.62E-06
1.18E-04
1.59E-07

28.29
18.90
43.13

6.62E-06
1.18E-04
1.59E-07

0.45
0.36
0.56

1.15E-03
1.07E-03
3.18E-03

12.61
12.80
10.08

1.15E-03
1.07E-03
3.18E-03

0.27
0.27
0.23

79
2

At the 1 m scale, soil carbon accounted for 23% of the variation in leaf carbon in a negative
linear relationship. Soil nitrogen explained 27% of the variation in leaf nitrogen, also, in a
negative linear relationship (Figure 2.25). The explanatory variable soil carbon to nitrogen
ratio was able to explain 34% of the variation in leaf carbon to nitrogen ratio and this
relationship was positive linear (Table 2.19).

Scale  1 m

2

2

2e+04

4e+04

6e+04

8e+04

Soil Carbon (ppm)

1e+05

40
35
30
20

25

Leaf Carbon to Nitrogen Ratio

20000
15000

Leaf Nitrogen (ppm)

25000

45

Scale  1 m

10000

Leaf Carbon (ppm)

2

360000 370000 380000 390000 400000 410000 420000 430000

Scale  1 m

2000

4000

6000

Soil Nitrogen (ppm)

8000

8

9

10

11

12

Soil Carbon to Nitrogen Ratio

Figure 2.25. Fitted curves from linear regression models at 1 m2 having leaf carbon as the
response variable and soil carbon as the explanatory variable (left panel); leaf nitrogen as the
response variable and soil nitrogen as the explanatory variable (center panel), and leaf carbon
to nitrogen ratio as the response variable and soil carbon to nitrogen ratio as the explanatory
variable (bottom panel). The dotted line is the fitted linear model and the dashed line is the
fitted quadratic model. The significant model in each plot is shown in bold.

80
Table 2.19. Bivariate regressions for soil carbon, nitrogen and carbon to nitrogen ratio as explanatory
variables and leaf carbon, nitrogen, and carbon to nitrogen ratio as response variables at the 1 m2
scale. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic
model, POS = positive linear model, and NEG = negative linear model. For quadratic models
degrees of freedom are 2 on 33 and for linear models are 1 on 34. Non-significant results are left
blank.
Variables Form
C (ppm)
N (ppm)
C:N

NEG
NEG
POS

Term 1
t Statistic

p Value

-3.22
-3.57
4.19

2.82E-03
1.09E-03
1.89E-04

Term 2
t Statistic

p Value

Model
F Statistic

p Value

Multiple R2

10.36
12.74
17.53

2.82E-03
2.85E-11
6.79E-28

0.23
0.27
0.34

81
DISCUSSION
Study limitations
This work can provide insights into relationships between species richness, productivity, and
soil nutrient resources; however, in order to provide a clear context for conclusions,
acknowledgment of a few study limitations is necessary before moving on to interpretation of
results. Sampling in each grid was conducted only once at, or shortly after, the height of the
growing season. The transient nature of spring ephemerals and other species with low
biomass, and human error, may have caused some species to be missed during counts. As
such species richness has probably been slightly underestimated. Also, samples of litter and
live biomass from areas with large bunchgrasses most likely underestimated total biomass,
live biomass and litter, because the bases of the large bunchgrasses were not collected
(Figure 2.5).
While measurements of total nutrients can reveal broad patterns, it is important to recognize
that much of the nutrients in the soil may be present in insoluble forms which are unavailable
for plant absorption. Leaves were measured for carbon and nitrogen content; however, roots
are known to be a major repository (~90%) of vegetative carbon and nitrogen in grasses
(Schuman et al. 1999). Additionally, biomass samples were oven dried at 80 C° for 48 hours
before elemental analysis of total carbon and nitrogen which may have caused some of the
nitrogen to volatilize in the form of ammonia. Nitrogen volatilization from cut grass can
occur at temperatures as low as 10 °C and occurs more rapidly at higher temperatures
(Whitehead et al. 1988). Bias may have been introduced into the leaf carbon and nitrogen
results because rates of volatilization may depend, in part, on initial concentrations, and
potentially on specific characteristics of the vegetation itself.
Plots from the same grid cannot be considered completely independent samples. In many of
the regressions with total biomass, live biomass and litter (but not species richness) there
were clear groupings of points which likely reflect this lack of independence. In regressions
of these response variables with soil carbon to nitrogen ratio, phosphorus, potassium,
magnesium and manganese, these groupings were largely missed by fitted curves but

82
2

sometimes still returned high R values. Care was taken to assess and report whether fitted
lines were actually a good fit to the data as, in these instances, regression analysis is not
appropriate.
Generally, it is not considered good practice to compare R2 values between models with
different data transformations or for model selection; however, this rule is usually referred to
in the context of model selection where the outcome of dropping one variable from a model
is being weighed against its retention. Here, comparison is used only to convey an
impression of model fit and not to build complex models. The limitations that accompany
aggregation of plots to investigate scale are examined in more detail in the 'Scale' section
near the end of the discussion.
Species richness and biomass relationships
The relationship between species richness and total biomass was expected to be unimodal as
predicted by the HBM (Al-Mufti et al. 1977, Grime 1979). In the regressions that had total
biomass and litter as explanatory variables and species richness as the response variable, the
expected unimodal curve was apparent but had relatively low R2 values both for the full 14grid dataset and the 4-grid soil dataset. These results are not consistent with the findings of
Adler et al. (2011) as they concluded that there was no clear relationship between biomass
and species richness at any scale; fine scale, regional, or global. Interestingly, the
relationship between live biomass and species richness was consistently negative linear and
accounted for very little of the variation in species richness, only as much as 4% at the 1 m2
scale. This draws attention to the potential difference and importance of the choice to
include, or exclude, litter when collecting samples to test the HBM. In this study at the 1 m2
scale, the form of the significant relationship was different between litter and live biomass in
regressions with species richness, the first principal component from the soil nutrient PCA,
soil carbon, soil nitrogen, soil phosphorus, and the first principal component from the PCA of
all soil nutrients with leaf carbon, leaf nitrogen and leaf carbon to nitrogen ratio. In five out
of six of these cases live biomass had significant linear relationships while litter gave
significant concave down relationships. Four of the five linear cases for live biomass were
positive linear relationships. The case where live biomass produced a negative linear

83
relationship occurred in regressions with species richness. Total biomass did not consistently
take the same form as either live biomass or litter. Thus, litter could be an important
component of the productivity proxy in resolving the unimodal curve predicted by the HBM,
as pointed out by Fridley et al. (2012), and may explain some of the inconsistencies in the
results of different studies, such as those of Adler et al. (2011) and others (e.g. Moore and
Keddy 1989, Gough et al. 1994; for meta-analyses see: Mittelbach et al. 2001; Gillman and
Wright 2006; Pärtel, Laanisto, and Zobel 2007). Certainly, there is potential for the
significant form to differ between including and excluding litter. The results from
regressions of total biomass with species richness from this study correspond with others that
find support for the HBM (e.g. Al-Mufti et al. 1977, Wheeler and Giller 1982, Walker and
Peet 1983, Tilman 1986, Austin 1987, Day et al. 1988, Wilson and Shay 1990, Shipley et al.
1991, Wheeler and Shaw 1991). Where relationships were significant, forms were consistent
across increasing scales for both the 14-grid and 4-grid datasets.
Patterns in the PCA of the soil nutrient data were consistent with those that would be
expected to coincide with the HBM. The first principal component appeared to represent
productivity; regressions with PC1 as the explanatory variable and litter, live biomass and
total biomass as the response variables support this observation with strong R2 values (0.82,
0.67, and 0.76, respectively). Although there is evidence of curvature in the litter and total
biomass relationships with PC1, the majority of the fitted curve is fairly straight and the
maximum occurs at high values of the PC1 axis (Figure 2.9). It may be that there is
proportionally less litter towards the high biomass end of the PC1 axis because of higher
decomposition rates and grazing in high productivity sites; this may reduce the build-up of
the litter layer in spite of the high level of productivity. In low productivity sites breakdown
of litter could be slower because of the drier nature of these sites. In regressions with PC1 as
the explanatory variable, the form of the relationship with species richness resulted in a
classic humped-shape curve which explained 32% of the variation in the data. Regressions
of species richness, total biomass, live biomass and litter with the second principal
component indicated that PC2 may represent species richness. Of the response variables, this
axis was able to explain a considerable amount, 35%, of variation in species richness with a
negative linear relationship (Figure 2.9). This indicates that species richness decreases from

84
the bottom of the PCA biplot to the top (Figure 2.7). The relationships of the biomass
variables with PC2 were all concave up and explained ~20% of the variation in these
variables, the lowest R2 values overall for regressions with both PC1 and PC2. Given that the
principal component analysis was based entirely on the nutrient data, the apparent
representation of biomass and species richness by PC1 and PC2 emphasizes the innate
structuring of herbaceous communities on soil nutrients. Soil resources have impacts on
patterns of vegetation and likewise the vegetation that grows feeds back to influence future
soil nutrient profiles.
Soil nutrients
Carbon
As predicted, soil carbon explained a high proportion of the variation in both total biomass
(72% at 1 m2) and live biomass (61% at 1 m2) in positive linear relationships. These findings
are in accordance with texts and literature and are intuitive given that greater production
results in higher levels of litter being laid down and eventually incorporated into the soil.
This leads to greater soil organic carbon (and nitrogen) which in turn has many benefits for
plant growth including soil moisture retention, ion exchange capacity, and slow release of
nutrients (Batjes 1996, Brady and Weil 1996, Wolkovich et al. 2010). Soil carbon was
strongly related to litter (80% at 1 m2) in a concave down curve; however, the maximum of
this curve did not occur inside the range of the data and the fitted curve is more or less linear
for the majority of its range (Figure 2.10). Still, it appears that the increasing curvature at
high litter levels with increasing soil carbon is a reflection of greater heterogeneity in soil
carbon at high productivity levels which results in elongation of the cloud points of litter
values along the soil carbon axis.
Soil nutrients are not homogenously distributed through space. Different species have
different nutrient requirements so soil nutrient heterogeneity is important to species richness
(Willems et al. 1993, Janssens et al. 1998, Aarssen 2001). Increased heterogeneity of
environmental conditions is also thought to contribute to increased productivity (Šímová et
al. 2013). Heterogeneity has been suggested to play a role in the scale dependence of the
species richness productivity relationship because the degree of environmental heterogeneity

85
often varies with scale (Chesson 1998, Chase and Leibold 2002, Chalcraft et al. 2004). In
small plots the distribution of soil nutrients is likely to be relatively homogenous, however,
large plots are more likely to capture spatial heterogeneity by including patches with various
nutrient quantities. At large scales species turnover and richness increase because of the
aggregation of different patches of resources. So far, studies evaluating the effect of
heterogeneity on species richness and productivity have produced mixed results (Šímová et
al. 2013). Newman (1973) and Tilman (1988) state that heterogeneity varies in a humpedshape pattern across habitats of increasing fertility. Perhaps, the curve detected at the extent
of the biomass range in this study (~1850 g/m2) is indicative of a humped-shape relationship
in soil heterogeneity with increasing soil nutrients.
In the distance biplot of PC1 and PC2 from the soil nutrients PCA, soil carbon was indicated
to be an important variable as it contributed more than average to the ordination space. As
predicted, soil carbon was tightly grouped with soil nitrogen indicating a positive correlation
between these two soil nutrients; soil phosphorus was also in close proximity. This is logical
because soil nitrogen and soil phosphorus are both commonly limiting nutrients and they,
like carbon, are tightly linked to biomass production. Plant available nitrogen and the
composition of soil organic matter are key factors in nutrient cycling rates and primary
productivity (Brady and Weil 1996). The patterns shown for soil carbon, soil nitrogen, soil
phosphorus and soil potassium in the soil nutrient PCA are consistent with those expected to
coincide with the HBM as PC1 seems to represent productivity, PC2 seems to represent
inverted species richness, and soil carbon, soil nitrogen, soil phosphorus, and soil potassium
are oriented towards the high productivity end of PC1.
Soil carbon produced a concave down relationship in the regression with species richness as
the response variable at the 1 m2 scale, as predicted. Although this relationship was
(perhaps) somewhat weaker than expected, explaining only 15% of the variation in species
richness, this concave down relationship had a clear maximum in the midrange of soil carbon
values and was quite curved, producing a unimodal curve as expected to coincide with the
HBM.

86
2

In regressions at the 1 m scale, carbon always explained over 60% of the variation in total
biomass, live biomass and litter. With increasing scale these relationships were consistently
positive linear for total biomass and live biomass up to 16 m2 and went from being concave
down to positive linear for litter between 2 m2 and 4 m2. The minimum amount of variation
in species richness that was explained by soil carbon was 15%; these relationships were
consistently concave down at scales increasing up to 4 m2 and were insignificant at greater
scales. No significant relationships were found at the 64 m2 scale for regressions with any of
the nutrients with only one exception (potassium) which will be discussed in due course.
These results correspond well with the observation by Waide et al. (1999) that unimodal
relationships commonly occur across community boundaries or when plots are from multiple
community types.
Nitrogen
The prediction that soil nitrogen would positively relate to total biomass and live biomass
was supported as was the expectation that species richness would be related to soil nitrogen
by a unimodal curve. At all scales, patterns that emerged for soil nitrogen were identical to
those of soil carbon; the values of individual results were also extremely similar. This
supports the prediction that soil carbon and nitrogen would be highly positively correlated
and could be expected because of the role of soil nitrogen in plant growth that causes it to be
tightly associated with biomass production and, therefore, also highly correlated to soil
carbon in natural systems. The strong positive correlation between soil nitrogen and biomass
variables suggests that nitrogen probably is limiting in these study sites. Litter produced a
curved relationship with soil nitrogen (as it did with carbon) where a positive linear one was
expected. The explanation for this follows the same logic as for the curved relationship
between litter and soil carbon. Soil nitrogen patterns were consistent with those expected to
coincide with the HBM, results from the Rothemsted Park Grass experiment (Crawley et al.
2005) and other literature (Kirchner 1977, Goldberg and Miller 1990, Bobbink 1991, Wilson
and Tilman 1993, Chapin et al. 1995, Wedin and Tilman 1996, Gough et al. 2000, Baer et al.
2003, Cornwell and Grubb 2003).

87
Soil carbon to nitrogen ratio
At the 1 m2 scale, soil carbon to nitrogen ratio was not related to total biomass, live biomass
and litter by a positive linear relationship as was expected to coincide with the HBM; instead,
a significant concave down curve resulted explaining 29%, 20% and 42% of the variation
respectively. As predicted, and in accordance with the HBM, soil carbon to nitrogen ratio
was related to species richness by a concave down curve and explained a similar amount of
the variation in the data (24% at 1 m2) to regressions between soil carbon to nitrogen ratio
and productivity variables; however, this fitted line appears to be a more true fit of the data
than the fitted lines from regressions with biomass variables (Figure 2.12). Although results
for soil carbon, nitrogen and carbon to nitrogen ratio were not completely predicted, they do
not contradict information presented by Brady and Weil (1996) or Chapin et al. (1993). With
increasing scale the concave down forms became positive linear for all variables (species
richness, total biomass, live biomass and litter). In the PCA of all soil nutrients and leaf
nutrients, soil carbon to nitrogen ratio aligned well with PC1 which seemed to represent
productivity and was perpendicular to PC2 which seems to represent inverted species
richness.
Given the similarity of the soil carbon and nitrogen regression results and the closeness of
these nutrients in the PCA biplots, it was interesting that the form of relationships between
soil carbon and nitrogen in regressions with the productivity variables varied from those of
soil carbon to nitrogen ratio in regressions with the productivity variables. With total and
live biomass, soil carbon and nitrogen gave positive linear forms as opposed to concave
down forms produced in regressions with soil carbon to nitrogen ratio. At the 1 m2 scale, soil
carbon and nitrogen explained more of the variation in the productivity variables, between
61% - 81% compared to between 20% - 42%, explained by soil carbon to nitrogen ratio.
Phosphorus
Soil phosphorus was predicted to have a positive linear relationship with productivity
variables because it is the second most commonly limiting nutrient in natural systems and is
often tightly linked to biomass production. This hypothesis was supported for live biomass

88
2

2

2

2

at the 1 m , 2 m and 4 m scales; however, this hypothesis was not supported at the 1 m

scale for total biomass or at the 1 m2 and 2 m2 scales for litter where concave down forms
were significant. Maxima for these curves were also at the end of the range of measured
values and increasing productivity was associated with an increase in the variation of soil
phosphorus. Again, an expected humped-shape relationship in soil heterogeneity as
predicted by the environmental heterogeneity hypothesis (Newman 1973, Tilman 1988) may
help to explain this observation, as in the cases of soil carbon and nitrogen. For total biomass
and litter at the 2 m2 and 4 m2 and at the 4 m2 and 16 m2 scales, respectively, the relationship
became positive linear, corresponding with predictions, and was not significant at larger
scales.
Although the concave down curve between litter and soil phosphorus gave relatively strong
R2 values, it was a poor fit to the data; the fitted line for soil phosphorus and species richness
also gave similar R2 values and appears to be a more true fit of the data (Figure 2.13). The
prediction that soil phosphorus would show a concave down relationship with species
richness, as predicted by the HBM and as found by Janssens et al. (1998), was not supported;
nor was the somewhat commonly reported negative linear relationship found (Janssens et al.
1998, Venterink et al. 2001, Lambers et al. 2010). In regressions between soil phosphorus
and species richness a positive linear form was evident from 1 m2 - 16 m2. Although our
results do not support previous studies, it is quite difficult to draw conclusions based on total
phosphorus measurements or to compare them with studies based on extractable phosphorus
given that only ~0.01% of the total phosphorus present in soils is actually available for use by
plants.
Measuring plant available phosphorus in the soil would likely have been more telling in
terms of the questions raised in this study. It could be that other nutrients, such as nitrogen,
are more limiting and phosphorus therefore exerts little control over vegetation dynamics
such as productivity and species richness in this system. Or maybe phosphorus is relatively
limiting and sampling a greater range of biomass would reveal that the pattern observed here
is only the increasing phase of a humped-shape relationship between phosphorus and species
richness. Because insoluble precipitates form when iron and phosphate interact (Dalton et al.
1983) the orientation of phosphorus in the opposite direction of iron in the soil nutrient PCA

89
may be an indication that phosphorus is not readily available, especially at lower productivity
levels, and provide some support for the latter suggestion. As it is, results do not fully
correspond with those expected to coincide with the HBM.
Potassium
It was predicted that soil potassium may show a positive linear relationship with biomass
variables because it is the third most commonly limiting nutrient in natural systems and, like
soil phosphorus and nitrogen, is often tightly correlated with biomass production. This
hypothesis was not supported at the 1 m2 scale for live biomass or at the 1 m2 or 2 m2 scales
for total biomass and litter where the form of relationship was concave up. The relationship
became positive linear, as predicted by the HBM, only at intermediate scales (2 m2 - 4 m2).
The regressions between potassium and litter were not significant at 16 m2 but showed a
significant concave up curve at the 64 m2 scale and returned a perfect R2 value of 1.00 (Table
2.10). This is very likely a spurious result of fitting regression lines to only four data points.
The figures of fitted regression lines for soil potassium and litter across scales support this
conclusion (Figure G.5).
Potassium was predicted to potentially show a humped-shape curve with species richness in
accordance with the HBM because of its potential positive linear relationship with
productivity variables. This hypothesis was not supported as regressions between soil
potassium and species richness were consistently negative linear in form at the 1 m2, 2 m2
and 4 m2 scales.
Although regressions of soil potassium with productivity variables gave stronger R2 values
than regressions with species richness, the fitted lines were a poor fit for two groups of
points, one at low and one at high productivity, that were scattered over the lower half of the
range of soil potassium values. The fitted lines from regressions of soil potassium and
species richness were a more convincing fit to the data points (Figure 2.14).
Given that soil potassium normally has less influence over community diversity than soil
phosphorus (because it is usually less limiting) and that in this system either phosphorus is

90
limiting over a wider range of biomass than was sampled or is not as limiting as nitrogen and
therefore is not limiting enough to exert control over diversity, it is unlikely that potassium
exerts strong control over vegetation dynamics such as productivity and species richness in
the study area. Like phosphorus, in the soil nutrient PCA potassium was aligned slightly
better with PC2 than with PC1 and was oriented towards the high biomass end of PC1 but
towards the low species richness end of PC2. This may provide some support that the
regressions between species richness and soil potassium are a more true fit to the data than
those with total biomass, live biomass and litter.
Boron
Soil boron explained high levels of variation in live biomass, a minimum of 52%, in a
concave down curve at 1 m2, 2 m2, and 4 m2 scales and in a positive linear relationship at
16 m2; and explained moderate levels of the variation in total biomass and litter. Soils that
have less than 10 ppm are considered to be low in soil boron and those with greater levels,
high in soil boron (Power and Woods 1997). Powers and Woods were not clear as to
whether 10 ppm referred to total or available boron but they do state that most soils are low
in boron and that high soil boron tends to be the result of volcanic activity. It is interesting
that all plots with soil boron levels greater than ~11 ppm had high values for productivity
variables, though, conclusions are difficult to draw because they are also all from the same
grid. A minimum of 15% of the variation in species richness was explained by soil boron
and the form of the relationship switched from being concave up at 1 m2 and 2 m2 to
negative linear at the 4 m2 scale. In the PCA of the soil nutrients soil boron was about
equally aligned with PC1 and PC2 and oriented towards the high productivity end of PC1
and the low species richness end of PC2.
Iron
Relationships between soil iron and total biomass, live biomass and litter were very strong,
accounting for at least 79% of variation at the 1 m2 scale with concave up relationships. This
form was apparent across scales up to 16 m2, with the exception of litter in which case the
form of relationship switched from concave up to negative linear at the 16 m2 scale.

91
Additionally, for litter, unlike for total biomass and live biomass, the minima of the concave
up curves did not occur within the range of the data. Soil iron was also able to explain a
considerable amount of the variation in species richness, a minimum of 29%, and concave
down relationships emerged across scales up to 16 m2; in this case there was a clear
maximum nearly in the center of the range of data (Figure 2.16).
The plots that had the greatest concentrations of iron also had the lowest concentrations of
soil phosphorus and the lowest levels of total biomass, live biomass, and litter. Although
iron toxicity is not certain, the results of the current study do not contradict those of Ward et
al. (2008) which showed that when soil phosphorus is deficient (because there was very little
to begin with or due to the formation of precipitates with iron) there is greater incidence of
iron toxicity. In the correlation biplot of the soil nutrient PCA, iron, carbon, and nitrogen
were slightly more aligned with PC1 than PC2, and phosphorus was oriented towards the
high productivity end of PC1. Iron was oriented in the opposite direction from the others,
indicating negative correlation between iron and these soil nutrients. Productivity decreases
and species richness is unimodal with increasing soil iron concentrations suggesting that
decreasing soil iron concentrations could also potentially be substituted for increasing
productivity variables in the HBM.
Magnesium
There were no initial predictions about what patterns of soil magnesium should coincide with
the HBM. The relationships between soil magnesium and total biomass and litter were
concave up at scales of 4 m2 or smaller and explained 10% of the variation or less at the 1 m2
scale. The concave up relationship with live biomass switched to positive linear at the 2 m2
scale. Relationships between soil magnesium and species richness were also concave up and
were considerably stronger, explaining 49% of the variation in the data at the 1 m2 scale.
Fitted lines for species richness were also a truer fit to the data than fitted lines for
magnesium with the productivity variables. Over most of the measured range of soil
magnesium, increasing magnesium was associated with decreasing species richness, but there
does appear to be a slight increase in species richness at the high end of the range (Figure
2.17). The soil nutrient PCA is in agreement with the regression findings as magnesium was

92
fairly well aligned with PC2 and oriented in the direction that corresponds with lower species
richness and very slightly oriented towards the high productivity side of PC1. Given that
magnesium is commonly added as a liming agent along with calcium, and that one of the
main reasons to limit soil acidity through liming is to prevent aluminum and manganese
toxicity (Brady and Weil 1996), it makes sense that magnesium is oriented in the opposite
direction to soil aluminum and manganese in the PCA of soil nutrients (Figure 2.8). In terms
of the HBM, if one presumes causation (which may not be the case) it seems that variation in
soil magnesium has the potential to influence the height of the unimodal curve such that high
magnesium corresponds with lower species richness.
Manganese
There were no a priori assumptions about what patterns in soil manganese should coincide
with the HBM. Soil manganese explained fairly little of the variation in the total biomass,
live biomass and litter, as much as 12% at the 1 m2 and 2 m2 scales, after which relationships
became insignificant. These relationships were all concave up except for with litter at the
2 m2 scale which was positive linear; generally the fitted lines for these relationships went
between an upper and a lower cloud of points (Figure 2.18). Fitted lines for regressions
between manganese and species richness were a truer fit to the data. Relationships between
soil manganese and species richness were all positive linear at scales up to 16 m2 and gave
higher R2 values than relationships with the productivity variables explaining 25% of the
variation in the data at the 1 m2 scale. The PCA of the nutrient data also reflected this pattern
as manganese was nearly parallel to PC2, oriented in the direction of higher species richness
and away from soil magnesium. It appears that soil manganese may also have the potential
to influence the height of the unimodal curve such that high manganese corresponds with
high species richness.
Leaf nutrients
Leaf carbon and nitrogen content were predicted to increase with increasing productivity and
with increasing soil nitrogen and carbon content due to increasing soil fertility and turnover
of species. This prediction was not supported by the regressions of leaf carbon with soil
carbon, and leaf nitrogen with soil nitrogen, as leaf carbon and nitrogen decreased with

93
increasing productivity (soil carbon and nitrogen were positively correlated with
productivity, and leaf carbon and nitrogen decreased with increasing soil carbon and
nitrogen). These results contradicted those of Wedin and Tilman (1996) and Poorter et al.
(1990) as well as information reviewed by Chapin (1980). The PCA of the leaf nutrients
with all soil nutrients did not support this prediction either, as leaf carbon and nitrogen were
oriented away from soil carbon and nitrogen and in the direction of low productivity on the
PC1 axis. Leaf nitrogen and carbon were also oriented in the direction of lower species
richness on the PC2 axis. Leaf carbon to nitrogen ratio was oriented almost exactly in the
opposite direction of leaf carbon and leaf nitrogen content which were tightly grouped
indicating they are highly positively correlated, as predicted. The PCA of only leaf carbon,
nitrogen and carbon to nitrogen ratio with soil carbon, nitrogen and carbon to nitrogen ratio
also supported the prediction that leaf carbon and nitrogen content would be highly positively
correlated as these variables were tightly grouped in the correlation biplot of PC1 and PC2;
however, the prediction that leaf carbon to nitrogen ratio would be negatively related to soil
carbon to nitrogen ratio and productivity was not supported. Instead, a positive linear
relationship was found. The simplest explanation for the discrepancies between my results
and predictions for leaf carbon, nitrogen and carbon to nitrogen ratio is that oven-drying the
biomass prior to elemental analysis caused some of the nitrogen to volatilize from samples at
varying rates based on plant characteristics and initial nitrogen concentrations.
The results of regressions with the axes of the soil nutrient PCA with leaf nitrogen, carbon
and carbon to nitrogen ratio showed similar patterns to that of the PCA of only soil nutrients.
Again the first principal component seemed to represent productivity as, in regressions, PC1
was able to explain over 71% of the variation in the productivity variables. A positive linear
relationship explained 76% of the variation in litter. The significant concave up curves that
occurred for total biomass and live biomass had minimums well within the first half of the
range of PC1 so that over the majority of the plot the fitted line is increasing. Regressions
with PC1 and species richness did not return significant relationships; however, with PC2, a
negative linear relationship emerged accounting for 34% of the variation in the data. Unlike
the soil nutrient PCA, the second principal component explained similar amounts of the
variation the productivity variables to species richness with concave up curves. The

94
similarity between patterns found in the PCA of soil nutrients and the PCA with leaf carbon,
nitrogen, carbon to nitrogen ratio and soil nutrients is not surprising since the majority of the
input data is the same. Differences likely arise more because of the difference in the number
of plots that were sampled and less due to contributions by leaf nutrients and leaf carbon to
nitrogen ratio. Again, the apparent representation of productivity by PC1 and of species
richness by PC2, in combination with the strengths and forms of relationships that occurred
in the regressions, indicates that there are patterns (structure) in the soil nutrients that align
with those expected to coincide with the HBM.
Scale
Assessment of the prediction that increasing scale would weaken and potentially break the
unimodal relationship between species richness and productivity was inconclusive. Multiple
R2 values often increased at larger scales, suggesting better model fit. In opposition,
significant relationships often went from curved forms to linear forms before becoming
insignificant at the largest scales. This pattern probably does not reflect a real pattern that
exists in nature; instead, it is likely attributable to decreasing sample size with increasing
scale of investigation. The reduction in the number of degrees of freedom results in larger
p values, and therefore fewer significant results, at large scales. One less parameter is
estimated (allowing one more degree of freedom) in a linear model than in a quadratic model
which may explain why the models selected tended to switch from quadratic to linear before
becoming insignificant.
Objective three, as stated in the introduction, cannot be adequately addressed with this
dataset; however, the regularity with which concave curves became linear relationships
before becoming insignificant draws attention to an interesting possibility. Perhaps a cause
of the positive linear forms often reported in the literature at large scales (Pianka 1966,
Currie 1991, Chase and Leibold 2002) is, in part, that studies at large scales typically have
fewer samples than those at small scales. This results in loss of power to distinguish
relationships rather than detection of a change in the relationship itself.

95
Summary
Species richness was related to total biomass with a unimodal curve as predicted by the
HBM. Soil nutrients relating strongly to productivity included carbon, nitrogen and iron and
related to species richness as would be expected to coincide with the HBM. Soil phosphorus
and potassium had less clear relationships potentially because nitrogen exerts more control
over community structure as it may be more limiting in this system. Leaf nitrogen and
carbon were negatively related to productivity, counter to expectations, but this was probably
due to nitrogen volatilization prior to elemental analysis. Soil magnesium and manganese
had opposite relationships with species richness such that high magnesium corresponded to
low species richness and high manganese corresponded with high species richness. It is
possible that these nutrients contribute to determination of the height of the species richness
curve. Regression analyses and principal component analyses were in consistent agreement.
The principal component analyses based on soil nutrients revealed biomass and species
richness as the first two axes, indicating strong connections between community species
richness-productivity dynamics and soil nutrient resources. Regressions between species
richness, total biomass, and live biomass, and between species richness and the first two
principal components, were also in broad agreement with the HBM. It appeared that
relationships were breaking down with increasing scales but this was attributable in large part
to a reduction in degrees of freedom with plot aggregation at larger scales. It was not
possible to resolve scale relationships within the limitations of the study design; however, it
became apparent that the emergence of positive linear relationships in the literature for
studies at larger scales may be partially due to smaller sample sizes.

96
CHAPTER 3: CONCLUSION

Context and general findings
Biodiversity is crucial to ecosystem functioning because of its control of ecological
processes; so much so, that the study of biodiversity in ecosystem function has become a
field of research unto itself (Cardinale et al. 2011). Interest in this area of work has been
driven by the massive, global, unprecedented losses of biological diversity in recent decades,
and by the dependence of people on biodiversity for the ecosystem services it provides. The
vegetation in plant communities acts as the base of the entire food web and feeds back to
influence the environment by contributing to soil formation and nutrient levels. A systems'
level of biodiversity determines how effectively nutrients and other limiting resources (e.g.
light, water) are transmitted into biomass and the extent to which ecosystem services may be
provided (Cardinale et al. 2011).
Species diversity has an important role in determining the functioning of ecosystems as a
whole because the characteristics of individual species influence what processes occur and to
what extent (Chapin et al. 2000). Higher levels of biodiversity usually result in greater
ecosystem stability and can support greater diversity at higher trophic levels (Haddad et al.
2001). In the face of continuously intensifying land use, maintaining high diversity of
species and representation of different functional groups is necessary to preserve ecosystem
function (Loreau et al. 2001).
The patterns found in this study are in line with what was already known, that species
richness, primary productivity and resource availability are closely connected in natural
communities. The relationship between species richness and total biomass in these study
sites is unimodal as predicted by the HBM; however, given the wealth of other research on
the subject, this finding does not contribute significantly towards resolving the debate
surrounding the model. Nutrients such as carbon and nitrogen were strongly positively
related to productivity and also showed humped-shape relationships with species richness.
These results were also expected and do not advance science notably. Magnesium,
manganese, and phosphorus appeared to correlate more with the height of the species

97
richness curve, and these findings present interesting opportunities for future research. In
spite of effort to isolate the influence of scale on the relationship between species richness
and productivity, this work has not helped to clarify the forms associated with specific scales.
Alternatively, it suggests that some of the confusion surrounding scale in the literature may
be related to sample size. Conclusions about the HBM, the role of soil nutrient resources in
structuring communities, and the scales at which these relationships apply, have important
implications for ecology and management and there are several directions future research
could take.
Management implications
On many landscapes, people have the power to affect disturbance, productivity, and land use,
all of which are among the most influential drivers of global loss of species richness (Sala et
al. 2000). As such, studies looking at nutrient resources in relation to species richness and
productivity have important messages for management efforts. Knowledge of the importance
of species diversity and how different levels of disturbance (such as cattle grazing) can
influence species numbers, gives the ability to optimize agriculture and species richness. The
same is true of fertilizer application with regards to species richness; some can be beneficial,
but driving lands to be very highly productive will likely come at a cost to biodiversity.
These lessons extend to conservation and reclamation as well. Preserving biodiversity to
keep ecosystem services is a major goal of conservation and an understanding of what
combination of conditions will promote high levels of species richness continues to be
fundamental in directing efforts to conserve species and in restoration of damaged habitats.
Future directions
As with all research, the work presented here began by building on a foundation of numerous
previous studies and ends by drawing attention to several areas for future work. Because up
to 90% of vegetation in temperate grasslands occurs below ground in the form of roots
rhizomes and shoot-bases (Pärtel et al. 2012) and because roots are the repository of the
majority (~90%) of vegetative carbon and nitrogen in grasses (Schuman et al. 1999), studies
investigating the below ground species richness, root-biomass and root-nutrient content will
continue to provide further evaluations of the extent to which the HBM applies. Future work

98
of this type should also focus on the amount of plant available nutrients as well as total
nutrients present in the soil. This would help to resolve the amount of nutrients actually
available for plant uptake and conversion into biomass versus the amount that may be
trapped in insoluble forms or released slowly over time. Collection of additional information
such as soil pH would also be advisable as pH holds strong influence over availability of soil
nutrients. Manipulative nutrient addition experiments investigating the influence of
magnesium and manganese on species richness would be useful to determine the role these
nutrients have in determining diversity. To address the problems of independence and
replication with regard to the investigation of scale, work should be done in which there is
high replication of independent soil nutrient, biomass and species richness sampling. In
doing this, care should be taken to keep sample size equal and adequate between each scale
investigated. Lastly, because sample size may be playing an important role in the form of
relationships that have been found in studies conducted at different scales, a meta-analysis
looking into the type of pattern resolved with respect to both scale and sample number could
be a significant step in explaining discrepancies in the literature.

99
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APPENDIX A: MORAN'S I CORRELOGRAMS
Species Richness - L2

Species Richness - L3

Species Richness - L4

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Species Richness - U1

Species Richness - U2

Species Richness - U3

Species Richness - U4

Species Richness - U5

4

5

6

7

8

9

0.6
0.4
0.0

0.2

Moran's I Statistic

0.4
0.3
0.2
0.1

Moran's I Statistic

0.0
-0.1

-0.6
3

9

0.5

0.2
0.0
-0.4

-0.2

Moran's I Statistic

-0.2
-0.4

0.2

Moran's I Statistic

0.0

0.4

0.6

Distance Classes (m)

0.0

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Species Richness - P1

Species Richness - P2

Species Richness - P3

Species Richness - P4

9

2

3

4

5

6

7

8

9

Distance Classes (m)

0.0

Moran's I Statistic

0.0
-0.4

-0.4

-0.2

Moran's I Statistic

0.0
-0.2
-0.4

-0.4

-0.2

0.0

Moran's I Statistic

0.2

0.2

0.2

0.2

0.4

0.4

Distance Classes (m)

-0.2

Moran's I Statistic

3

Distance Classes (m)

-0.8

-0.6

-0.6

Moran's I Statistic

0.0
-0.4

-0.3
2

Distance Classes (m)

-0.2

2

-0.2

Moran's I Statistic

0.0
-0.1

Moran's I Statistic

-0.2

0.0
-0.1
-0.2

Moran's I Statistic

-0.3
-0.4

-0.3
2

0.1

0.1

0.2

0.3
0.2
0.1
0.0
-0.1

Moran's I Statistic

-0.2

0.2
0.0
-0.2
-0.4

Moran's I Statistic

Species Richness - L5

0.2

0.2

Species Richness - L1

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Figure A.1. Correlograms of Moran's I Statistic plotted against distance classes for species richness in each
grid. Red filled points indicate significant correlation, hollow points indicate non-significant values.

113

5

6

7

8

9

3

4

5

6

7

8

9

0.2
-0.2

0.0

Moran's I Statistic

0.1
0.0
-0.1

Moran's I Statistic

-0.2
-0.3

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Total Biomass - U1

Total Biomass - U2

Total Biomass - U3

Total Biomass - U4

Total Biomass - U5

5

6

7

8

9

2

3

4

5

6

7

8

9

3

4

5

6

7

8

9

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Total Biomass - P1

Total Biomass - P2

Total Biomass - P3

Total Biomass - P4

5

6

7

8

9

0.00
-0.05

3

4

5

6

7

0.0
-0.6

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

-0.2

Moran's I Statistic

0.0
-0.5

Moran's I Statistic

2

-0.4

0.5

0.4
0.3
0.2
0.1
0.0

Moran's I Statistic

-0.2

-0.1

0.2
0.0
-0.2
-0.4
-0.6

4

9

0.2

Distance Classes (m)

3

-0.10

Moran's I Statistic

-0.20
2

Distance Classes (m)

Distance Classes (m)

-0.15

0.1
0.0
-0.1

Moran's I Statistic
2

-0.2

-0.15

-0.4
4

9

0.05

0.2

0.15
0.10
0.05
-0.05 0.00

Moran's I Statistic

0.1
0.0
-0.1
-0.3

-0.2

Moran's I Statistic

0.3
0.2
0.1
0.0
-0.2

3

0.10

Distance Classes (m)

0.2

Distance Classes (m)

-0.8

2

0.4

0.3
2

0.4

2

Total Biomass - L5

0.2

0.1
0.0
-0.2

-0.15
4

Total Biomass - L4

-0.1

0.00
-0.05
-0.10

Moran's I Statistic

Moran's I Statistic

0.05

0.3
0.2
0.1
0.0

Moran's I Statistic

-0.1
-0.2

3

-0.1

Moran's I Statistic

Total Biomass - L3

Distance Classes (m)

0.4

0.5

2

Moran's I Statistic

Total Biomass - L2

0.10

Total Biomass - L1

8

9

Distance Classes (m)

Figure A.2. Correlograms of Moran's I Statistic plotted against distance classes for total biomass in each
grid. Red filled points indicate significant correlation, hollow points indicate non-significant values.

9

114

4

5

6

7

8

9

3

4

5

6

7

8

-0.1

Moran's I Statistic

0.0

0.1

0.2
0.1
0.0
-0.1
-0.4

-0.3

-0.3

-0.2

Moran's I Statistic

0.10

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Live Biomass - U1

Live Biomass - U2

Live Biomass - U3

Live Biomass - U4

Live Biomass - U5

3

4

5

6

7

8

9

0.2

0.2
3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Live Biomass - P1

Live Biomass - P2

Live Biomass - P3

Live Biomass - P4

9

0.0

2

3

4

5

6

7

8

9

Distance Classes (m)

0.0
-0.2
-0.4
-1.0

-0.8

-0.6

Moran's I Statistic

0.2

0.5
0.0

Moran's I Statistic

-0.5

0.2
0.0
-0.4

-0.2

Moran's I Statistic

0.0
-0.2

0.4

Distance Classes (m)

-0.4

-0.2

Moran's I Statistic
2

Distance Classes (m)

-0.6

-0.4

0.1
0.0
-0.2

-0.2
2

-0.1

Moran's I Statistic

0.1
0.0

Moran's I Statistic

-0.1

0.0
-0.1
-0.3

-0.2

-0.2

0.0

Moran's I Statistic

0.1

0.2

9

0.2

Distance Classes (m)

0.2

Distance Classes (m)

-0.4

Moran's I Statistic

0.05
-0.10

2

Live Biomass - L5

Distance Classes (m)

0.2

2

Moran's I Statistic

0.00

Moran's I Statistic

-0.1
-0.2

Moran's I Statistic

-0.3
-0.4
3

-0.05

0.0

0.3
0.2
0.1
0.0

Moran's I Statistic

-0.1
-0.2

2

Live Biomass - L4

-0.2

Live Biomass - L3

0.3

Live Biomass - L2
0.15

Live Biomass - L1

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Figure A.3. Correlograms of Moran's I Statistic plotted against distance classes for live biomass in each grid.
Red filled points indicate significant correlation, hollow points indicate non-significant values.

115

5

6

7

8

9

2

3

4

5

6

7

8

0.6
0.4

Moran's I Statistic

0.2
0.0

0.1

Moran's I Statistic
3

4

5

6

7

8

9

-0.2
2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Litter - U1

Litter - U2

Litter - U3

Litter - U4

Litter - U5

4

5

6

7

8

9

2

3

4

5

6

7

8

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Litter - P1

Litter - P2

Litter - P3

Litter - P4

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

9

9

0.05

2

3

4

5

6

7

8

0.2

0.4

Distance Classes (m)

-0.2

0.0

Moran's I Statistic

0.2
0.0

Moran's I Statistic

-0.4

-0.2
3

-0.2

0.2
0.1
0.0

Moran's I Statistic

0.0
-0.2
-0.4
-0.6

-0.1

0.2

0.3

0.4

Distance Classes (m)

Distance Classes (m)

0.00

Moran's I Statistic

-0.10

-0.2

9

-0.05

0.3
0.2
0.1
0.0

Moran's I Statistic

-0.1

0.10
0.05
0.00
-0.10

-0.05

Moran's I Statistic

0.0
-0.1
-0.3

-0.2

Moran's I Statistic

0.4
0.3
0.2
0.1
0.0

3

9

0.10

Distance Classes (m)

-0.8

2

-0.2
2

Distance Classes (m)

0.4

2

-0.1

-0.1

9

0.2

0.3
4

-0.2

Moran's I Statistic

-0.3

-0.3
3

-0.1

Moran's I Statistic

Litter - L5

Distance Classes (m)

0.5

2

Moran's I Statistic

Litter - L4

0.0

0.1
0.0
-0.1

Moran's I Statistic

-0.2

0.15
0.10
0.05
0.00
-0.10 -0.05

Moran's I Statistic

Litter - L3

0.0

Litter - L2

0.20

Litter - L1

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Figure A.4. Correlograms of Moran's I Statistic plotted against distance classes for litter in each grid. Red
filled points indicate significant correlation, hollow points indicate non-significant values.

9

116
Soil Carbon - P1

Soil Carbon - P2

5

6

7

8

9

2

3

4

5

6

7

8

9

0.0
-0.2
-0.6

-0.4

Moran's I Statistic

0.4
0.2
0.0
-0.4

-0.8

-0.6

-0.6
4

-0.2

Moran's I Statistic

0.2
0.0
-0.2

Moran's I Statistic

-0.4

0.0
-0.1

3

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Soil Nitrogen - L4

Soil Nitrogen - L5

Soil Nitrogen - P1

Soil Nitrogen - P2

9

3

4

5

6

7

8

9

0.0
-0.2
-0.4
-0.6
-0.8

-0.6

-0.6
2

Moran's I Statistic

0.2
-0.2

0.0

Moran's I Statistic

-0.4

0.0
-0.2

Moran's I Statistic

-0.4

-0.1
-0.2
-0.3
-0.4

Moran's I Statistic

0.0

0.2

0.4

0.2

0.1

2

0.2

0.4

Soil Carbon - L5

-0.2

Moran's I Statistic

0.1

Soil Carbon - L4

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Soil Carbon to Nitrogen Ratio - L4

Soil Carbon to Nitrogen Ratio - L5

Soil Carbon to Nitrogen Ratio - P1

Soil Carbon to Nitrogen Ratio - P2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

5

6

7

8

0.2
0.0

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Soil Phosphorus - L4

Soil Phosphorus - L5

Soil Phosphorus - P1

Soil Phosphorus - P2

4

5

6

7

8

9

2

3

4

5

6

7

8

0.4
0.3
0.2
0.1

Moran's I Statistic

-0.1

0.0

0.2
0.0
-0.4

-0.2
3

-0.2

Moran's I Statistic

0.2
0.1
0.0
-0.1

0.0

0.1

Moran's I Statistic

0.3

0.2

0.4

0.4

Distance Classes (m)

-0.1

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Soil Potassium - L4

Soil Potassium - L5

Soil Potassium - P1

Soil Potassium - P2

6

7

8

9

2

3

4

5

6

7

8

9

0.2
0.1
0.0
-0.3

-1.0

-0.2

-0.1

Moran's I Statistic

0.0
-0.5

Moran's I Statistic

0.05

0.3

0.10
5

0.00

Moran's I Statistic
4

-0.20 -0.15 -0.10 -0.05

0.2
0.1
0.0
-0.1
-0.2

3

9

0.5

Distance Classes (m)

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Soil Boron - L4

Soil Boron - L5

Soil Boron - P1

Soil Boron - P2

2

3

4

5

6

7

8

Distance Classes (m)

9

-0.05
-0.15

Moran's I Statistic

0.0

Moran's I Statistic

-0.5

0.2
0.0
-0.2

-0.25

-0.20

-0.6

-0.10

Moran's I Statistic

0.4

0.5

0.6

9

0.05

Distance Classes (m)

-0.4

Moran's I Statistic

4

Distance Classes (m)

0.00 0.05 0.10 0.15

2

3

Distance Classes (m)

0.3

2

Moran's I Statistic

-0.2

0.2
0.1
0.0

Moran's I Statistic

-0.1

-0.6
-0.8

-0.5

2

Moran's I Statistic

Moran's I Statistic

0.3

0.4
0.2
0.0
-0.2
-0.4

Moran's I Statistic

0.0
-0.1
-0.2
-0.3
-0.4

Moran's I Statistic

0.1

0.4

Distance Classes (m)

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

117
Soil Iron - L5

Soil Iron - P1

3

4

5

6

7

8

9

3

4

5

6

7

8

9

0.4
0.2
0.0
-0.2

Moran's I Statistic

-0.6
2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

Distance Classes (m)

Distance Classes (m)

Distance Classes (m)

Soil Magnesium - L4

Soil Magnesium - L5

Soil Magnesium - P1

Soil Magnesium - P2

9

0.4
0.2
-0.2

0.0

Moran's I Statistic

0.0

Moran's I Statistic

-0.5

0.0
-0.2

Moran's I Statistic

0.2

0.5

0.6
0.4
0.2
0.0
-0.2
-0.4

Moran's I Statistic

-0.4

0.2
0.1
0.0

Moran's I Statistic

-0.2
2

Distance Classes (m)
0.4

2

-0.1

0.2
0.0
-0.4

-0.2

Moran's I Statistic

0.3

0.10
0.05
0.00
-0.05

Moran's I Statistic

Soil Iron - P2

0.4

0.4

Soil Iron - L4

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

4

5

6

7

8

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Distance Classes (m)

Soil Manganese - L4

Soil Manganese - L5

Soil Manganese - P1

Soil Manganese - P2

0.0
-0.1
-0.3

-0.2

Moran's I Statistic

0.1

0.2

0.4
0.2
0.0
-0.6

-0.2

-0.6

-0.4

-0.2

Moran's I Statistic

0.0
-0.2
-0.4

Moran's I Statistic

0.2
0.1
0.0

0.3

Distance Classes (m)

-0.1

Moran's I Statistic

3

Distance Classes (m)
0.2

2

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

Distance Classes (m)

9

2

3

4

5

6

7

8

9

Distance Classes (m)

Figure A.5. Correlograms of Moran's I Statistic plotted against distance classes for soil
nutrients for each grid that had soil samples taken. Carbon (row 1), nitrogen (row 2),
carbon to nitrogen ratio (row 3), phosphorus (row 4), potassium (row 5), boron (row 6),
iron (row 7), magnesium (row 8) and manganese (row 9). Red filled points indicate
significant correlation, hollow points indicate non-significant values.

118
APPENDIX B: SEMI-VARIOGRAMS
L1 - Species Richness & Total Biomass

L1 - Species Richness & Total Biomass
2

4

90

1.0

6

L2 - Species Richness & Total Biomass
8

L2 - Species Richness & Total Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

L3 - Species Richness & Total Biomass

8

10

2

4

6

8

Distance (m)

L3 - Species Richness & Total Biomass
2

4

90

1.0

6

6

8

10

Distance (m)

L4 - Species Richness & Total Biomass

L4 - Species Richness & Total Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

L5 - Species Richness & Total Biomass

8

10

2

4

6

8

Distance (m)

L5 - Species Richness & Total Biomass
2

4

90

1.0

6

6

8

10

Distance (m)

U1 - Species Richness & Total Biomass

U1 - Species Richness & Total Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

1.0

0.8

0.4

0.2

4

0.2

0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

U2 - Species Richness & Total Biomass

8

10

2

4

6

8

Distance (m)

U2 - Species Richness & Total Biomass
2

4

90

1.0

6

6

8

10

Distance (m)

U3 - Species Richness & Total Biomass

U3 - Species Richness & Total Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

U4 - Species Richness & Total Biomass

2

90

8

10

2

4

6

8

Distance (m)

U4 - Species Richness & Total Biomass

1.0

6

4

6

8

10

Distance (m)

U5 - Species Richness & Total Biomass

U5 - Species Richness & Total Biomass

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

4

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

2

0.4

0.6
0.2

0.4

0.2

2

4

6

8

10

Distance (m)

10

1.0

0.8
0.8

8

135

1.0

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

119
P1 - Species Richness & Total Biomass

P1 - Species Richness & Total Biomass
2

4

90

1.0

6

P2 - Species Richness & Total Biomass
8

P2 - Species Richness & Total Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P3 - Species Richness & Total Biomass

2

90

8

10

2

4

6

8

Distance (m)

P3 - Species Richness & Total Biomass

1.0

6

4

6

8

10

Distance (m)

P4 - Species Richness & Total Biomass

P4 - Species Richness & Total Biomass

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.1. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and log
transformed total biomass as the explanatory variable, for each grid (L1-5, U1-5, P1-4). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

120
L1 - Species Richness & Live Biomass

L1 - Species Richness & Live Biomass
2

4

90

1.0

6

L2 - Species Richness & Live Biomass
8

L2 - Species Richness & Live Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

L3 - Species Richness & Live Biomass

8

10

2

4

6

8

Distance (m)

L3 - Species Richness & Live Biomass
2

4

90

1.0

6

6

8

10

Distance (m)

L4 - Species Richness & Live Biomass

L4 - Species Richness & Live Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

L5 - Species Richness & Live Biomass

8

10

2

4

6

8

Distance (m)

L5 - Species Richness & Live Biomass
2

4

90

1.0

6

6

8

10

Distance (m)

U1 - Species Richness & Live Biomass

U1 - Species Richness & Live Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

U2 - Species Richness & Live Biomass

8

10

2

4

6

8

Distance (m)

U2 - Species Richness & Live Biomass
2

4

90

1.0

6

6

8

10

Distance (m)

U3 - Species Richness & Live Biomass

U3 - Species Richness & Live Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

U4 - Species Richness & Live Biomass

2

90

8

10

2

4

6

8

Distance (m)

U4 - Species Richness & Live Biomass

1.0

6

4

6

8

10

Distance (m)

U5 - Species Richness & Live Biomass

U5 - Species Richness & Live Biomass

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

4

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

2

0.4

0.6
0.2

0.4

0.2

2

4

6

8

10

Distance (m)

10

1.0

0.8
0.8

8

135

1.0

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

121
P1 - Species Richness & Live Biomass

P1 - Species Richness & Live Biomass
2

4

90

1.0

6

P2 - Species Richness & Live Biomass
8

P2 - Species Richness & Live Biomass

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P3 - Species Richness & Live Biomass

2

90

8

10

2

4

6

8

Distance (m)

P3 - Species Richness & Live Biomass

1.0

6

4

6

8

10

Distance (m)

P4 - Species Richness & Live Biomass

P4 - Species Richness & Live Biomass

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.2. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and log
transformed live biomass as the explanatory variable, for each grid (L1-5, U1-5, P1-4). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

122
L1 - Species Richness & Litter

L1 - Species Richness & Litter
2

4

90

1.0

L2 - Species Richness & Litter
6

8

L2 - Species Richness & Litter

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

L3 - Species Richness & Litter

8

10

2

4

6

8

Distance (m)

L3 - Species Richness & Litter
2

4

90

1.0

6

6

8

10

Distance (m)

L4 - Species Richness & Litter

L4 - Species Richness & Litter

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

L5 - Species Richness & Litter

8

10

2

4

6

8

Distance (m)

L5 - Species Richness & Litter
2

4

90

1.0

6

6

8

10

Distance (m)

U1 - Species Richness & Litter

U1 - Species Richness & Litter

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

U2 - Species Richness & Litter

8

10

2

4

6

8

Distance (m)

U2 - Species Richness & Litter
2

4

90

1.0

6

6

8

10

Distance (m)

U3 - Species Richness & Litter

U3 - Species Richness & Litter

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

U4 - Species Richness & Litter

2

90

8

10

2

4

6

8

Distance (m)

U4 - Species Richness & Litter

1.0

6

4

6

8

10

Distance (m)

U5 - Species Richness & Litter

U5 - Species Richness & Litter

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

4

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

2

0.4

0.6
0.2

0.4

0.2

2

4

6

8

10

Distance (m)

10

1.0

0.8
0.8

8

135

1.0

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

123
P1 - Species Richness & Litter

P1 - Species Richness & Litter
2

4

90

1.0

P2 - Species Richness & Litter
6

8

P2 - Species Richness & Litter

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P3 - Species Richness & Litter

2

90

8

10

2

4

6

8

Distance (m)

P3 - Species Richness & Litter

1.0

6

4

6

8

10

Distance (m)

P4 - Species Richness & Litter

P4 - Species Richness & Litter

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.3. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and log
transformed litter as the explanatory variable, for each grid (L1-5, U1-5, P1-4). The second
and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

124
L4 - Species Richness & Soil Carbon

L4 - Species Richness & Soil Carbon
2

4

90

1.0

6

L5 - Species Richness & Soil Carbon
8

L5 - Species Richness & Soil Carbon

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Carbon

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Carbon
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Species Richness & Soil Carbon

P2 - Species Richness & Soil Carbon

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.4. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
carbon as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

L4 - Species Richness & Soil Nitrogen

L4 - Species Richness & Soil Nitrogen
2

4

90

1.0

6

L5 - Species Richness & Soil Nitrogen
8

L5 - Species Richness & Soil Nitrogen

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Nitrogen

2

90

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Nitrogen

1.0

6

4

6

8

10

Distance (m)

P2 - Species Richness & Soil Nitrogen

P2 - Species Richness & Soil Nitrogen

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.5. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
nitrogen as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

125
L4 - Species Richness & Soil Carbon to Nitrogen Ratio

L4 - Species Richness & Soil Carbon to Nitrogen Ratio
2

4

90

1.0

6

8

L5 - Species Richness & Soil Carbon to Nitrogen Ratio

L5 - Species Richness & Soil Carbon to Nitrogen Ratio

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

0.8

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Carbon to Nitrogen Ratio

45

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Carbon to Nitrogen Ratio
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Species Richness & Soil Carbon to Nitrogen Ratio

P2 - Species Richness & Soil Carbon to Nitrogen Ratio

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.6. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
carbon to nitrogen ratio as the explanatory variable, for each grid that involved soil sampling
(L4, L5, P1 and P2). The second and fourth columns show directional semi-variograms at 0,
45, 90, and 135º.

L4 - Species Richness & Soil Phosphorus

L4 - Species Richness & Soil Phosphorus
2

4

90

1.0

6

L5 - Species Richness & Soil Phosphorus
8

L5 - Species Richness & Soil Phosphorus

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Phosphorus

2

90

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Phosphorus

1.0

6

4

6

8

10

Distance (m)

P2 - Species Richness & Soil Phosphorus

P2 - Species Richness & Soil Phosphorus

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.7. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
phosphorus as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

126
L4 - Species Richness & Soil Potassium

L4 - Species Richness & Soil Potassium
2

4

90

1.0

6

L5 - Species Richness & Soil Potassium
8

L5 - Species Richness & Soil Potassium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Potassium

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Potassium
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Species Richness & Soil Potassium

P2 - Species Richness & Soil Potassium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.8. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
potassium as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

L4 - Species Richness & Soil Boron

L4 - Species Richness & Soil Boron
2

4

90

1.0

6

L5 - Species Richness & Soil Boron
8

L5 - Species Richness & Soil Boron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Boron

2

90

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Boron

1.0

6

4

6

8

10

Distance (m)

P2 - Species Richness & Soil Boron

P2 - Species Richness & Soil Boron

10

2

135

90

1.0

4

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.9. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
boron as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

127
L4 - Species Richness & Soil Iron

L4 - Species Richness & Soil Iron
2

4

90

1.0

L5 - Species Richness & Soil Iron
6

8

L5 - Species Richness & Soil Iron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Iron

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Iron
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Species Richness & Soil Iron

P2 - Species Richness & Soil Iron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.10. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
iron as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

L4 - Species Richness & Soil Magnesium

L4 - Species Richness & Soil Magnesium
2

4

90

1.0

6

L5 - Species Richness & Soil Magnesium
8

L5 - Species Richness & Soil Magnesium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Magnesium

2

90

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Magnesium

1.0

6

4

6

8

10

Distance (m)

P2 - Species Richness & Soil Magnesium

P2 - Species Richness & Soil Magnesium

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.11. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
magnesium as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

128
L4 - Species Richness & Soil Manganese

L4 - Species Richness & Soil Manganese
2

4

90

1.0

6

L5 - Species Richness & Soil Manganese
8

L5 - Species Richness & Soil Manganese

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Species Richness & Soil Manganese

8

10

2

4

6

8

Distance (m)

P1 - Species Richness & Soil Manganese
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Species Richness & Soil Manganese

P2 - Species Richness & Soil Manganese

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.12. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with square root transformed species richness as the response variable and soil
manganese as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1
and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

L4 - Total Biomass & Soil Carbon

L4 - Total Biomass & Soil Carbon
2

4

90

1.0

L5 - Total Biomass & Soil Carbon
6

8

L5 - Total Biomass & Soil Carbon

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Carbon

2

90

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Carbon

1.0

6

4

6

8

10

Distance (m)

P2 - Total Biomass & Soil Carbon

P2 - Total Biomass & Soil Carbon

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.13. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil carbon as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

129
L4 - Total Biomass & Soil Nitrogen

L4 - Total Biomass & Soil Nitrogen
2

4

90

1.0

L5 - Total Biomass & Soil Nitrogen
6

8

L5 - Total Biomass & Soil Nitrogen

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Nitrogen

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Nitrogen
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Total Biomass & Soil Nitrogen

P2 - Total Biomass & Soil Nitrogen

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.14. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil nitrogen as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Total Biomass & Soil Carbon to Nitrogen Ratio

L4 - Total Biomass & Soil Carbon to Nitrogen Ratio
2

4

90

1.0

6

8

L5 - Total Biomass & Soil Carbon to Nitrogen Ratio

L5 - Total Biomass & Soil Carbon to Nitrogen Ratio

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

1.0

0.8

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Carbon to Nitrogen Ratio

45

0.4

0.2

4

0.2

0

0.6
0.2

0.4

2

0.4

2

90

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Carbon to Nitrogen Ratio

1.0

6

4

6

8

10

Distance (m)

P2 - Total Biomass & Soil Carbon to Nitrogen Ratio

P2 - Total Biomass & Soil Carbon to Nitrogen Ratio

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.15. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil carbon to
nitrogen ratio as the explanatory variable, for each grid that involved soil sampling (L4, L5,
P1 and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90,
and 135º.

130
L4 - Total Biomass & Soil Phosphorus

L4 - Total Biomass & Soil Phosphorus
2

4

90

1.0

6

L5 - Total Biomass & Soil Phosphorus
8

L5 - Total Biomass & Soil Phosphorus

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Phosphorus

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Phosphorus
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Total Biomass & Soil Phosphorus

P2 - Total Biomass & Soil Phosphorus

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.16. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil phosphorus
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Total Biomass & Soil Potassium

L4 - Total Biomass & Soil Potassium
2

4

90

1.0

6

L5 - Total Biomass & Soil Potassium
8

L5 - Total Biomass & Soil Potassium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

1.0

0.8

0.4

0.2

4

0.2

0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Potassium

2

90

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Potassium

1.0

6

4

6

8

10

Distance (m)

P2 - Total Biomass & Soil Potassium

P2 - Total Biomass & Soil Potassium

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.17. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil potassium as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

131
L4 - Total Biomass & Soil Boron

L4 - Total Biomass & Soil Boron
2

4

90

1.0

L5 - Total Biomass & Soil Boron
6

8

L5 - Total Biomass & Soil Boron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Boron

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Boron
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Total Biomass & Soil Boron

P2 - Total Biomass & Soil Boron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.18. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil boron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Total Biomass & Soil Iron

L4 - Total Biomass & Soil Iron
2

4

90

1.0

L5 - Total Biomass & Soil Iron
6

8

L5 - Total Biomass & Soil Iron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Iron

2

90

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Iron

1.0

6

4

6

8

10

Distance (m)

P2 - Total Biomass & Soil Iron

P2 - Total Biomass & Soil Iron

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.19. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil iron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

132
L4 - Total Biomass & Soil Magnesium

L4 - Total Biomass & Soil Magnesium
2

4

90

1.0

6

L5 - Total Biomass & Soil Magnesium
8

L5 - Total Biomass & Soil Magnesium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Magnesium

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Magnesium
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Total Biomass & Soil Magnesium

P2 - Total Biomass & Soil Magnesium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.20. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil magnesium
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Total Biomass & Soil Manganese

L4 - Total Biomass & Soil Manganese
2

4

90

1.0

6

L5 - Total Biomass & Soil Manganese
8

L5 - Total Biomass & Soil Manganese

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

1.0

0.8

0.4

0.2

4

0.2

0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Total Biomass & Soil Manganese

2

90

8

10

2

4

6

8

Distance (m)

P1 - Total Biomass & Soil Manganese

1.0

6

4

6

8

10

Distance (m)

P2 - Total Biomass & Soil Manganese

P2 - Total Biomass & Soil Manganese

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.21. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed total biomass as the response variable and soil manganese
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

133
L4 - Live Biomass & Soil Carbon

L4 - Live Biomass & Soil Carbon
2

4

90

1.0

L5 - Live Biomass & Soil Carbon
6

8

L5 - Live Biomass & Soil Carbon

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Carbon

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Carbon
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Live Biomass & Soil Carbon

P2 - Live Biomass & Soil Carbon

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.22. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil carbon as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Live Biomass & Soil Nitrogen

L4 - Live Biomass & Soil Nitrogen
2

4

90

1.0

L5 - Live Biomass & Soil Nitrogen
6

8

L5 - Live Biomass & Soil Nitrogen

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Nitrogen

2

90

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Nitrogen

1.0

6

4

6

8

10

Distance (m)

P2 - Live Biomass & Soil Nitrogen

P2 - Live Biomass & Soil Nitrogen

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.23. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil nitrogen as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

134
L4 - Live Biomass & Soil Carbon to Nitrogen Ratio

L4 - Live Biomass & Soil Carbon to Nitrogen Ratio
2

4

90

1.0

6

8

L5 - Live Biomass & Soil Carbon to Nitrogen Ratio

L5 - Live Biomass & Soil Carbon to Nitrogen Ratio

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

0.8

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Carbon to Nitrogen Ratio

45

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Carbon to Nitrogen Ratio
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Live Biomass & Soil Carbon to Nitrogen Ratio

P2 - Live Biomass & Soil Carbon to Nitrogen Ratio

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.24. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil carbon to
nitrogen ratio as the explanatory variable, for each grid that involved soil sampling (L4, L5,
P1 and P2). The second and fourth columns show directional semi-variograms at 0, 45, 90,
and 135º.

L4 - Live Biomass & Soil Phosphorus

L4 - Live Biomass & Soil Phosphorus
2

4

90

1.0

6

L5 - Live Biomass & Soil Phosphorus
8

L5 - Live Biomass & Soil Phosphorus

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Phosphorus

2

90

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Phosphorus

1.0

6

4

6

8

10

Distance (m)

P2 - Live Biomass & Soil Phosphorus

P2 - Live Biomass & Soil Phosphorus

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.25. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil phosphorus
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

135
L4 - Live Biomass & Soil Potassium

L4 - Live Biomass & Soil Potassium
2

4

90

1.0

6

L5 - Live Biomass & Soil Potassium
8

L5 - Live Biomass & Soil Potassium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Potassium

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Potassium
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Live Biomass & Soil Potassium

P2 - Live Biomass & Soil Potassium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.26. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil potassium as
the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.
L4 - Live Biomass & Soil Boron

L4 - Live Biomass & Soil Boron
2

4

90

1.0

L5 - Live Biomass & Soil Boron
6

8

L5 - Live Biomass & Soil Boron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Boron

2

90

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Boron

1.0

6

4

6

8

10

Distance (m)

P2 - Live Biomass & Soil Boron

P2 - Live Biomass & Soil Boron

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.27. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil boron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

136
L4 - Live Biomass & Soil Iron

L4 - Live Biomass & Soil Iron
2

4

90

1.0

L5 - Live Biomass & Soil Iron
6

8

L5 - Live Biomass & Soil Iron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Iron

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Iron
2

6

8

10

Distance (m)

P2 - Live Biomass & Soil Iron

4

90

1.0

6

P2 - Live Biomass & Soil Iron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.28. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil iron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.
L4 - Live Biomass & Soil Magnesium

L4 - Live Biomass & Soil Magnesium
2

4

90

1.0

6

L5 - Live Biomass & Soil Magnesium
8

L5 - Live Biomass & Soil Magnesium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Magnesium

2

90

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Magnesium

1.0

6

4

6

8

10

Distance (m)

P2 - Live Biomass & Soil Magnesium

P2 - Live Biomass & Soil Magnesium

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.29. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil magnesium
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

137
L4 - Live Biomass & Soil Manganese

L4 - Live Biomass & Soil Manganese
2

4

90

1.0

6

L5 - Live Biomass & Soil Manganese
8

L5 - Live Biomass & Soil Manganese

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Live Biomass & Soil Manganese

8

10

2

4

6

8

Distance (m)

P1 - Live Biomass & Soil Manganese
2

4

90

1.0

6

6

8

10

Distance (m)

P2 - Live Biomass & Soil Manganese

P2 - Live Biomass & Soil Manganese

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.30. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed live biomass as the response variable and soil manganese
as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2).
The second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.
L4 - Litter & Soil Carbon

L4 - Litter & Soil Carbon
2

L5 - Litter & Soil Carbon

4

90

1.0

6

8

L5 - Litter & Soil Carbon

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Carbon

2

90

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Carbon

1.0

6

4

6

8

10

Distance (m)

P2 - Litter & Soil Carbon

P2 - Litter & Soil Carbon

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.31. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil carbon as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

138
L4 - Litter & Soil Nitrogen

L4 - Litter & Soil Nitrogen
2

4

90

1.0

L5 - Litter & Soil Nitrogen
6

8

L5 - Litter & Soil Nitrogen

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Nitrogen

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Nitrogen
2

6

8

10

Distance (m)

P2 - Litter & Soil Nitrogen

4

90

1.0

6

P2 - Litter & Soil Nitrogen

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.32. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil nitrogen as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Litter & Soil Carbon to Nitrogen Ratio

L4 - Litter & Soil Carbon to Nitrogen Ratio
2

4

90

1.0

6

L5 - Litter & Soil Carbon to Nitrogen Ratio
8

L5 - Litter & Soil Carbon to Nitrogen Ratio

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Carbon to Nitrogen Ratio

2

90

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Carbon to Nitrogen Ratio

1.0

6

4

6

8

10

Distance (m)

P2 - Litter & Soil Carbon to Nitrogen Ratio

P2 - Litter & Soil Carbon to Nitrogen Ratio

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.33. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil carbon to nitrogen
ratio as the explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and
P2). The second and fourth columns show directional semi-variograms at 0, 45, 90, and
135º.

139
L4 - Litter & Soil Phosphorus

L4 - Litter & Soil Phosphorus
2

4

90

1.0

L5 - Litter & Soil Phosphorus
6

8

L5 - Litter & Soil Phosphorus

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Phosphorus

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Phosphorus
2

6

8

10

Distance (m)

P2 - Litter & Soil Phosphorus

4

90

1.0

6

P2 - Litter & Soil Phosphorus

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.34. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil phosphorus as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Litter & Soil Potassium

L4 - Litter & Soil Potassium
2

L5 - Litter & Soil Potassium

4

90

1.0

6

8

L5 - Litter & Soil Potassium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Potassium

2

90

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Potassium

1.0

6

4

6

8

10

Distance (m)

P2 - Litter & Soil Potassium

P2 - Litter & Soil Potassium

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.35. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil potassium as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

140
L4 - Litter & Soil Boron

L4 - Litter & Soil Boron
2

L5 - Litter & Soil Boron
4

90

1.0

6

8

L5 - Litter & Soil Boron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Boron

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Boron
2

4

6

8

10

Distance (m)

P2 - Litter & Soil Boron

90

1.0

6

P2 - Litter & Soil Boron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.36. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil boron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Litter & Soil Iron

L4 - Litter & Soil Iron
2

L5 - Litter & Soil Iron
4

90

1.0

6

8

L5 - Litter & Soil Iron

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Iron

2

90

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Iron

1.0

6

4

6

8

10

Distance (m)

P2 - Litter & Soil Iron

P2 - Litter & Soil Iron

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.37. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil iron as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

141
L4 - Litter & Soil Magnesium

L4 - Litter & Soil Magnesium
2

4

90

1.0

L5 - Litter & Soil Magnesium
6

8

L5 - Litter & Soil Magnesium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Magnesium

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Magnesium
2

6

8

10

Distance (m)

P2 - Litter & Soil Magnesium

4

90

1.0

6

P2 - Litter & Soil Magnesium

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

6

8

10

2

4

6

8

Distance (m)

10

Distance (m)

Figure B.38. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil magnesium as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

L4 - Litter & Soil Manganese

L4 - Litter & Soil Manganese
2

L5 - Litter & Soil Manganese

4

90

1.0

6

8

L5 - Litter & Soil Manganese

10

2

135

4

90

1.0

6

8

10

135

1.0

1.0

0.8

0.8
0.8

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

0.4

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

0.8

0.6

0.4

0.6
0.2

6

8

10

45

0.8

0.4

0.2

4

0.2

0
1.0

0.6
0.2

0.4

2

0.4

0.2

2

4

6

8

Distance (m)

10

2

4

Distance (m)

P1 - Litter & Soil Manganese

2

90

8

10

2

4

6

8

Distance (m)

P1 - Litter & Soil Manganese

1.0

6

4

6

8

10

Distance (m)

P2 - Litter & Soil Manganese

P2 - Litter & Soil Manganese

10

2

135

90

1.0

4

6

0.4

0.2

0

45

1.0

0.8

0.6

Semivariance (Normalized)

0.6

Semivariance (Normalized)

Semivariance (Normalized)

Semivariance (Normalized)

0.8
0.8

0.6

0.4

0.6

0.4

0.6
0.2

6

Distance (m)

8

10

0.2

0

45

1.0

0.8

0.4

0.2

4

0.4

0.6
0.2

0.4

2

10

1.0

0.8
0.8

8

135

1.0

0.2

2

4

6

8

10

Distance (m)

2

4

6

Distance (m)

8

10

2

4

6

8

10

Distance (m)

Figure B.39. Normalized semi-variograms of the standardized residuals computed for linear
regressions, with log transformed litter as the response variable and soil manganese as the
explanatory variable, for each grid that involved soil sampling (L4, L5, P1 and P2). The
second and fourth columns show directional semi-variograms at 0, 45, 90, and 135º.

142

APPENDIX C: POISSON REGRESSIONS
Table C.1. Poisson regressions using data from all 14 grids with species richness as the response variable. Form codes are as follows:
CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG = negative linear
model. For quadratic models degrees of freedom for the null and residual deviance respectively are 895 and 893 at 1 m2, 447 and 445
at 2 m2, 223 and 221 at 4 m2, 55 and 53 at 16 m2, 13 and 11 at 64 m2; and for linear models are 895 and 894 at 1 m2, 447 and 446 at
2 m2, 223 and 222 at 4 m2, 55 and 54 at 16 m2, and 13 and 12 at 64 m2. Grey highlights show regressions at the 1 m2 scale. Nonsignificant results are left blank.
Exp. Variable
(g) (Log10)

Total Biomass

Live Biomass

Litter

Scale
(m2)

1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

CD
CD
CD
CD

t Statistic
8.41
7.56
5.64
3.37

p Value
4.25E-17
3.91E-14
1.73E-08
7.39E-04

Model
Null
Res.
Exp.
t Statistic p Value Disp. Dev.
Dev.
Dev.
-8.69
3.50E-18 0.84 848.27 752.13 11.33
-7.76
8.40E-15 1.00 519.58 445.32 14.29
-5.81
6.33E-09 1.11 293.26 245.86 16.16
-3.45
5.53E-04 1.11 75.85 59.09 22.09

NEG
NEG
NEG

-3.69
-3.25
-3.39

2.29E-04
1.17E-03
6.94E-04

0.93
1.14
1.27

848.27 834.57
519.58 508.93
293.26 281.58

1.61
2.05
3.98

4284.07
2329.96
1238.88

CD
CD
CD

8.21
7.79
5.45

2.25E-16
6.48E-15
4.91E-08

0.84
0.99
1.12

848.27 746.01
519.58 438.53
293.26 247.06

12.05
15.60
15.75

4197.52
2261.56
1206.36

-8.85
-8.16
-5.75

9.02E-19
3.46E-16
8.98E-09

AIC
4203.63
2268.35
1205.16
324.24

143
2

Scale  4 m

2

2

2

Scale  16 m

Scale  64 m

25

Species Richness

20

20
15

Species Richness

15

Species Richness

10

15
10

Species Richness

10

15

5

5

10

5

Species Richness

30

20

15

25

20

Scale  2 m

35

2

Scale  1 m

5

6

7

5.0

5.5

Total Biomass (g) (Log10)

6.0

6.5

7.0

7.5

8.0

6.0

Total Biomass (g) (Log10)

2

Scale  2 m

7.0

7.5

8.0

8.5

7.5

2

Scale  4 m

8.0

8.5

9.0

9.5

10.0

9.0

Total Biomass (g) (Log10)

2

10.0

10.5

11.0

2

2

Scale  64 m

25

25

Species Richness

20

20
15

Species Richness

15

Species Richness

10

15
10

Species Richness

10

15

5

5

10

5

Species Richness

30

20

15

9.5

Total Biomass (g) (Log10)

Scale  16 m

20

Scale  1 m

6.5

Total Biomass (g) (Log10)

35

4

5

6

7

4.5

5.0

Live Biomass (g) (Log10)

5.5

6.0

6.5

7.0

7.5

8.0

5.5

Live Biomass (g) (Log10)

2

Scale  2 m

6.5

7.0

7.5

8.0

8.5

7.0

7.5

Live Biomass (g) (Log10)

2

Scale  4 m

8.0

8.5

9.0

9.5

8.5

2

9.5

10.0

10.5

11.0

Live Biomass (g) (Log10)

2

2

Scale  16 m

Scale  64 m

25

25

Species Richness

20

20
15

Species Richness

15

Species Richness

10

15
10

Species Richness

10

15

5

5

10

5

Species Richness

30

20

15

9.0

Live Biomass (g) (Log10)

20

Scale  1 m

6.0

35

4

2

3

4

5

Litter (g) (Log10)

6

7

3

4

5

6

Litter (g) (Log10)

7

4

5

6

Litter (g) (Log10)

7

8

6

7

8

Litter (g) (Log10)

9

7.5

8.0

8.5

9.0

9.5

10.0

10.5

Litter (g) (Log10)

Figure C.1. Linear and quadratic fitted curves from Poisson regressions with species richness as the response variable and log
transformed total biomass (top row), live biomass (center row), and litter (bottom row) as the explanatory variables using the 14-grid
dataset across scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The significant model
in each plot is shown in bold.

144
Table C.2. Poisson regressions using data from the four soil grids with species richness as the response variable. Form codes are as
follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG = negative
linear model. For quadratic models degrees of freedom for the null and residual deviance respectively are 255 and 253 at 1 m2, 127
and 125 at 2 m2, 63 and 61 at 4 m2, 15 and 13 at 16 m2, 3 and 1 at 64 m2; and for linear models are 255 and 254 at 1 m2, 127 and 126
at 2 m2, 63 and 62 at 4 m2, 15 and 16 at 16 m2, and 3 and 2 at 64 m2. Grey highlights show regressions at the 1 m2 scale. Nonsignificant results are left blank.
Exp. Variable
(g) (Log10)

Total Biomass

Live Biomass

Litter

Scale
(m2)

1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

Form

Term 1

Term 2

CD
CD
CD
CD

t Statistic
4.88
4.33
3.94
2.98

p Value
1.04E-06
1.52E-05
8.10E-05
2.91E-03

Model
Null
Res.
Exp.
t Statistic p Value Disp. Dev.
Dev.
Dev.
-4.99
6.01E-07 0.98 277.75 248.41 10.56
-4.40
1.10E-05 1.20 172.51 150.10 12.99
-3.98
6.78E-05 1.34 98.98 81.47 17.69
-2.98
2.87E-03 1.26 25.44 16.39 35.59

NEG
NEG

-3.68
-3.11

2.34E-04
1.85E-03

1.04
1.29

277.75 264.18
172.51 162.78

4.88
5.64

1204.85
662.74

CD
CD
CD
CD

6.57
6.81
6.06
3.79

5.20E-11
9.73E-12
1.35E-09
1.49E-04

0.91
0.98
0.97
0.79

277.75 229.11
172.51 122.18
98.98 59.21
25.44 10.31

17.51
29.18
40.18
59.48

1171.77
624.14
325.98
87.14

-6.62
-6.84
-6.07
-3.78

3.51E-11
7.79E-12
1.24E-09
1.55E-04

AIC
1191.07
652.06
348.23
93.21

145
2

Scale  2 m

2

Scale  4 m

2

2

2

Scale  16 m

Scale  64 m

7.0

14

7.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

6.0

Total Biomass (g) (Log10)

2

Scale  2 m

2

7.0

7.5

Scale  4 m

8.0

8.5

7.5

8.0

8.5

9.0

9.5

10.0

9.0

Total Biomass (g) (Log10)

2

2

22

24
22

Species Richness

18
16
14

Species Richness

16

12
10

14

6
5.5

6.0

6.5

7.0

4.5

Live Biomass (g) (Log10)

5.0

5.5

6.0

6.5

7.0

8

4
5.0

7.5

5.5

Live Biomass (g) (Log10)

2

Scale  2 m

6.0

6.5

7.0

7.5

8.0

7.0

Live Biomass (g) (Log10)

2

Scale  4 m

7.5

8.0

8.5

9.0

8.5

2

2

22

24

Species Richness

16

16

12

14

Species Richness

18

22

20

16
14
12
10

Species Richness

8
6

10

14

6
7

3

4

5

6

Litter (g) (Log10)

7

8

4
6

10.5

2

4
5

10.0

Scale  64 m

14
10
8

Species Richness

12

12
10
8

Species Richness

6

4

Litter (g) (Log10)

9.5

Live Biomass (g) (Log10)

Scale  16 m

4
2

3

9.0

Live Biomass (g) (Log10)

18

14

Scale  1 m

2

11.0

20

16
14
12
10

Species Richness

8
6
4.5

10.5

2

4
4.0

10.0

Scale  64 m

14
10
8

Species Richness

12

12
10
8
6

Species Richness

4
2

3.5

9.5

Total Biomass (g) (Log10)

Scale  16 m

18

14

Scale  1 m

6.5

Total Biomass (g) (Log10)

20

6.5

18

6.0

20

5.5

18

5.0

Total Biomass (g) (Log10)

8

4
4.5

18

Species Richness

16

10

6
4
2
4.0

20

22

20
16
14
12

Species Richness

18

14
12

4

6

8

10

Species Richness

10
8

Species Richness

10
8
6

Species Richness

12

12

16

24

14

22

18

14

Scale  1 m

4

5

6

Litter (g) (Log10)

7

8

6

7

8

Litter (g) (Log10)

9

7.5

8.0

8.5

9.0

9.5

10.0

10.5

Litter (g) (Log10)

Figure C.2. Linear and quadratic fitted curves from Poisson regressions with species richness as the response variable and log
transformed total biomass (top row), live biomass (center row), and litter (bottom row) as the explanatory variables using the four soil
grids dataset across scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

146
Table C.3. Poisson regressions with soil nutrient PCA axes using data from the four soil grids with species richness as the response
variable. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear
model, and NEG = negative linear model. For quadratic models degrees of freedom for the null and residual deviance respectively are
255 and 253; and for linear models are 255 and 254. Non-significant results are left blank.
Scale
(m2)

1
1
1

CD
CD
NEG

Term 1

Model
Null
Res.
Exp.
p Value t Statistic p Value Disp. Dev.
Dev.
Dev.
2.02E-02
-9.18
4.17E-20 0.72 277.75 181.47 34.66
2.63E-22
-3.32
9.04E-04 0.68 277.75 171.74 38.17
8.79E-06
1.02 277.75 258.26 7.02

t Statistic
2.32
-9.71
-4.45

2

2

2

-0.4

-0.2

0.0

0.2

PC1

0.4

0.6

0.8

12
10

Species Richness

12
10
8

2

4

6
4
2

2

4

6

8

10

Species Richness

12

14

Scale  1 m

14

Scale  1 m

14

Scale  1 m

Species Richness

Term 2

8

PC1
PC2
PC3

Form

6

Explanatory
Variable

-0.6

-0.4

-0.2

0.0

PC2

0.2

0.4

0.6

-0.4

-0.2

0.0

0.2

0.4

PC3

Figure C.3. Linear and quadratic fitted curves from Poisson regressions with species richness as the response
variable and PC1, PC2, and PC3 from the soil nutrient PCA. The dotted line is the fitted linear model and
the dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.

AIC
1124.14
1114.40
1198.92

147
Table C.4. Poisson regressions of soil nutrients as the explanatory variable with species richness as the response variable. Form codes
are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS = positive linear model, and NEG =
negative linear model. For quadratic models degrees of freedom for the null and residual deviance respectively are 255 and 253 at
1 m2, 127 and 125 at 2 m2, 63 and 61 at 4 m2, 15 and 13 at 16 m2, 3 and 1 at 64 m2; and for linear models are 255 and 254 at 1 m2, 127
and 126 at 2 m2, 63 and 62 at 4 m2, 15 and 16 at 16 m2, and 3 and 2 at 64 m2. Grey highlights show regressions at the 1 m2 scale.
Non-significant results are left blank.
Explanatory
Variable

Soil Carbon

Soil Nitrogen

Soil C:N

Soil Phosphorus

Scale
(m2) Form

1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4

Term 1

Term 2

Model
Null
Res.
Exp.
t Statistic p Value Disp. Dev.
Dev.
Dev.
-5.23
1.67E-07 0.93 277.75 234.50 15.57
-5.23
1.67E-07 0.93 277.75 234.50 15.57
-4.94
7.95E-07 1.09 172.51 136.51 20.87
-4.12
3.80E-05 1.22 98.98 74.22 25.01

CD
CD
CD
CD

t Statistic
6.00
6.00
5.54
4.59

p Value
2.01E-09
2.01E-09
3.11E-08
4.43E-06

AIC
1177.16
1177.16
638.47
340.99

CD
CD
CD

5.75
5.30
4.35

9.19E-09
1.16E-07
1.38E-05

-5.08
-4.80
-3.95

3.68E-07
1.62E-06
7.68E-05

0.94
1.12
1.26

277.75 237.55
172.51 139.54
98.98 76.80

14.47
19.11
22.41

1180.22
641.50
343.56

CD
CD
POS
POS

4.85
3.79
5.52
3.04

1.21E-06
1.51E-04
3.30E-08
2.38E-03

-4.54
-3.51

5.66E-06
4.45E-04

0.81
0.93
1.05
1.09

277.75 205.86
172.51 115.97
98.98 65.37
25.44 15.19

25.88
32.78
33.95
40.28

1148.52
617.93
330.14
90.02

CD
CD
POS

4.03
3.71
6.16

5.62E-05
2.10E-04
7.30E-10

-3.23
-3.08

1.22E-03
2.09E-03

0.77
0.85
0.97

277.75 194.44
172.51 106.12
98.98 60.41

29.99
38.48
38.97

1137.11
608.08
325.17

148

Soil Potassium

Soil Boron

Soil Iron

Soil Magnesium

Soil Manganese

16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64
1
2
4
16
64

POS

3.67

2.39E-04

0.78

25.44

10.97

56.90

85.79

NEG
NEG
NEG

-6.14
-5.28
-4.19

8.41E-10
1.32E-07
2.73E-05

0.93
1.13
1.28

277.75 237.28
172.51 142.30
98.98 79.64

14.57
17.51
19.54

1177.94
642.26
344.41

CU
CU
CU

-4.78
-4.47
-3.55

1.74E-06
7.91E-06
3.81E-04

3.77
3.64
2.93

1.61E-04
2.70E-04
3.42E-03

0.90
1.05
1.18

277.75 226.92
172.51 130.93
98.98 72.22

18.30
24.10
27.03

1169.58
632.89
338.99

CD
CD
CD
CD

8.55
8.05
6.83
3.80

1.19E-17
8.05E-16
8.79E-12
1.46E-04

-8.72
-8.18
-6.92
-3.87

2.85E-18
2.92E-16
4.49E-12
1.10E-04

0.76
0.80
0.78
0.68

277.75 193.39
172.51 100.14
98.98 47.74
25.44
8.83

30.37
41.95
51.76
65.30

1136.06
602.10
314.51
85.65

CU
CU
CU
NEG

-7.02
-6.06
-4.74
-3.98

2.26E-12
1.35E-09
2.09E-06
6.89E-05

5.33
4.87
3.94

1.01E-07
1.12E-06
8.26E-05

0.55
0.55
0.47
0.59

277.75 139.69
172.51 68.61
98.98 28.87
25.44
8.21

49.71
60.23
70.83
67.72

1082.35
570.57
295.63
83.04

CD
CD
CD
POS

3.48
3.39
3.04
3.84

4.98E-04
6.94E-04
2.39E-03
1.23E-04

-3.12
-3.09
-2.79

1.80E-03
1.99E-03
5.28E-03

0.80
0.83
0.75
0.76

277.75 202.50
172.51 103.42
98.98 45.68
25.44 10.58

27.09
40.05
53.85
58.40

1145.16
605.38
312.45
85.41

149
2

Scale  2 m

2

Scale  4 m

2

2

2

Scale  16 m

Scale  64 m

14

1e+05

2e+04

4e+04

6e+04

8e+04

8

1e+05

20000

40000

Soil Carbon (ppm)

2

Scale  2 m

2

Scale  4 m

80000

10000

20000

30000

40000

50000

60000

70000

80000

10000

2

2

22

24

2

6000

8000

22
16

8
1000

2000

3000

2

5000

Scale  4 m

6000

7000

8000

1000

2000

3000

4000

5000

6000

7000

1000

2

2

4000

5000

6000

7000

2

22

Scale  64 m

22

Species Richness

18
16
14

16

Species Richness

12

12

6

8

10

Species Richness

14

20

16

24

14
10
8

Species Richness

12

12
10
8

Species Richness

6

10

14

6
8

9

10

11

Soil Carbon to Nitrogen Ratio

12

8

4

4
12

3000

Soil Nitrogen (ppm)

Scale  16 m

4

11

2000

Soil Nitrogen (ppm)

18

14

Scale  2 m

4000

Soil Nitrogen (ppm)

2

10

20

Species Richness

18
16
14

Species Richness

12

14
4000

Scale  1 m

9

70000

10

6
4
2000

Soil Nitrogen (ppm)

Soil Carbon to Nitrogen Ratio

60000

20

16
14
12
10

Species Richness

8
6
8000

Soil Nitrogen (ppm)

8

50000

2

4
6000

40000

Scale  64 m

14
10
8

Species Richness

12

12
10
8

Species Richness

6

4000

30000

Soil Carbon (ppm)

Scale  16 m

4
2

2000

20000

Soil Carbon (ppm)

18

14

Scale  1 m

60000

Soil Carbon (ppm)

18

8e+04

20

6e+04

Soil Carbon (ppm)

18

4e+04

18

Species Richness

16

10

6
4

4
2

2e+04

20

22

20
16
14
12

Species Richness

18

14
12

4

6

8

10

Species Richness

10
8

Species Richness

10
8
6

Species Richness

12

12

16

24

14

22

18

14

Scale  1 m

8.5

9.0

9.5

10.0

10.5

11.0

Soil Carbon to Nitrogen Ratio

11.5

8.5

9.0

9.5

10.0

10.5

Soil Carbon to Nitrogen Ratio

11.0

8.5

9.0

9.5

10.0

10.5

11.0

Soil Carbon to Nitrogen Ratio

Figure C.4. Linear and quadratic fitted curves from Poisson regressions with species richness as the response variable and soil carbon
(top row), soil nitrogen (center row), and soil carbon to nitrogen ratio (bottom row) as the explanatory variables using the four soil
grids dataset across scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

150
2

Scale  2 m

2

Scale  4 m

2

2

2

Scale  16 m

Scale  64 m

14
800

900

1000

1100

1200

1300

1400

8
800

900

Soil Phosphorus (ppm)

2

Scale  2 m

2

1100

1200

Scale  4 m

1300

1400

900

1000

1100

1200

900

Soil Phosphorus (ppm)

2

2

22

24
16

10

14

6
4500

5000

Soil Potassium (ppm)

5500

6000

6500

7000

8

4
8000

7500

5000

5500

Soil Potassium (ppm)

2

Scale  2 m

6000

6500

7000

7500

5000

5500

Soil Potassium (ppm)

2

Scale  4 m

6000

6500

7000

5500

Soil Potassium (ppm)

2

2

2

22

24

Species Richness

16
14

16

12

Species Richness

18

22

20

16
14
12
10

Species Richness

8
6

10

14

6
40

10

20

30

Soil Boron (ppm)

40

8

4

4
30

6500

Scale  64 m

14
10
8

Species Richness

12

12
10
8
6

Species Richness

4
2

20

Soil Boron (ppm)

6000

Soil Potassium (ppm)

Scale  16 m

18

14

Scale  1 m

10

20

Species Richness

16
14
12

Species Richness

18

22

20

16
14
12
10

Species Richness

8
6
7000

1200

2

4
6000

1100

Scale  64 m

14
10
8

Species Richness

12

12
10
8
6

Species Richness

4
2

5000

1000

Soil Phosphorus (ppm)

Scale  16 m

18

14

Scale  1 m

1000

Soil Phosphorus (ppm)

18

1400

20

1200

Soil Phosphorus (ppm)

18

1000

18

Species Richness

16

10

6
4

4
2

800

20

22

20
16
14
12

Species Richness

18

14
12

4

6

8

10

Species Richness

10
8

Species Richness

10
8
6

Species Richness

12

12

16

24

14

22

18

14

Scale  1 m

5

10

15

20

25

Soil Boron (ppm)

30

35

40

5

10

15

20

25

Soil Boron (ppm)

30

35

10

15

20

25

Soil Boron (ppm)

Figure C.5. Linear and quadratic fitted curves from Poisson regressions with species richness as the response variable and soil
phosphorus (top row), soil potassium (center row), and soil boron (bottom row) as the explanatory variables using the four soil grids
dataset across scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The significant model
in each plot is shown in bold.

151
2

Scale  2 m

2

Scale  4 m

2

2

2

Scale  16 m

Scale  64 m

14
25000

30000

35000

8

40000

30000

Soil Iron (ppm)

2

Scale  2 m

2

Scale  4 m

40000

30000

35000

40000

30000

Soil Iron (ppm)

2

2

2

22

24

Species Richness

16
14

16

12

Species Richness

18

22

20

16
14
12
10

Species Richness

8
6

10

14

6
20000

6000

8000

Soil Magnesium (ppm)

10000

12000

14000

16000

18000

8

4

4
15000

8000

Soil Magnesium (ppm)

2

Scale  2 m

10000

12000

14000

16000

8000

Soil Magnesium (ppm)

2

Scale  4 m

10000

12000

14000

7000

2

2

11000

12000

2

22

24

Species Richness

16
14

16

12

Species Richness

18

22

20

16
14
12
10

Species Richness

8
6

10

14

6
700

750

800

850

900

950

Soil Manganese (ppm)

1000

8

4

4
1000

10000

Scale  64 m

14
10
8

Species Richness

12

12
10
8

Species Richness

6

900

9000

Soil Magnesium (ppm)

Scale  16 m

4
2

800

Soil Manganese (ppm)

8000

Soil Magnesium (ppm)

18

14

Scale  1 m

700

40000

Scale  64 m

14
10
8

Species Richness

12

12
10
8
6

Species Richness

4
2

10000

35000

Soil Iron (ppm)

Scale  16 m

18

14

Scale  1 m

35000

Soil Iron (ppm)

20

45000

18

40000

20

35000

Soil Iron (ppm)

18

30000

18

Species Richness

16

10

6
4

4
2
25000

20

22

20
16
14
12

Species Richness

18

14
12

4

6

8

10

Species Richness

10
8

Species Richness

10
8
6

Species Richness

12

12

16

24

14

22

18

14

Scale  1 m

800

850

900

950

Soil Manganese (ppm)

1000

800

850

900

Soil Manganese (ppm)

950

1000

820

840

860

880

900

920

940

960

Soil Manganese (ppm)

Figure C.6. Linear and quadratic fitted curves from Poisson regressions with species richness as the response variable and soil iron
(top row), soil magnesium (center row), and soil manganese (bottom row) as the explanatory variables using the four soil grids dataset
across scales. The dotted line is the fitted linear model and the dashed line is the fitted quadratic model. The significant model in
each plot is shown in bold.

152
Table C.5. Poisson regressions with axes from the PCA of all soil and leaf nutrients as the explanatory variables and species richness
as the response variable. Form codes are as follows: CD = concave down quadratic model, CU = concave up quadratic model, POS =
positive linear model, and NEG = negative linear model. For quadratic models degrees of freedom for the null and residual deviance
respectively are 35 and 33, and for linear models are 35 and 34. Non-significant results are left blank.

PC1
PC2
PC3

1
1
1

Form

Term 1

Term 2

Model

CD
NEG

t Statistic
-0.54
-3.41

p Value t Statistic p Value
5.88E-01
-2.77
5.53E-03
6.53E-04

Disp.
0.89
0.76

2

2
12
10

8

Species Richness

10

12

Scale  1 m

-0.5

0.0

PC1

0.5

4
2

2

4

6

Species Richness

10
8
6

Species Richness

4
2
-1.0

Res.
Dev.
29.39
26.01

2

Scale  1 m

12

Scale  1 m

Null
Dev.
38.70
38.70

8

Scale
(m2)

6

Explanatory
Variable

-0.5

0.0

0.5

PC2

1.0

-0.4

-0.2

0.0

0.2

0.4

PC3

Figure C.7. Linear and quadratic fitted curves from Poisson regressions with species richness as the response
variable and PC1, PC2, and PC3 from the soil and leaf nutrient PCA. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.

Exp.
Dev.
24.05
32.81

AIC
166.27
160.88

153
2

2

-0.5

0.0

PC1

0.5

1.0

12
10
8
4
2

4
2
-1.0

6

8

Species Richness

10

12

Scale  1 m

6

Species Richness

10
8
6
2

4

Species Richness

2

Scale  1 m

12

Scale  1 m

-0.4

-0.2

0.0

0.2

PC2

0.4

0.6

0.8

-0.2

0.0

0.2

0.4

PC3

Figure C.8. Linear and quadratic fitted curves from Poisson regressions with species richness as the
response variable and PC1, PC2, and PC3 from the PCA of only soil carbon, nitrogen and carbon to
nitrogen ratio and leaf carbon, nitrogen and carbon to nitrogen ratio. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is shown in
bold.

154
APPENDIX D: SPECIES RICHNESS AND BIOMASS - SCALED REGRESSIONS
2

Scale  2 m

2

Scale  4 m

2

Scale  16 m

2

Scale  64 m
6.0

2

5.0

2.0

1.5

3.0

2.0

4.0

4.5

Species Richness

4.0

Species Richness

2.5

3.5

4.0
3.5
3.0

Species Richness

3.5

2.0

2.5

3.0

Species Richness

3.0
2.5

Species Richness

3.5

4.5

5.5

4.0

4.5

4.0

5.0

4.5

5.0

Scale  1 m

4

5

6

7

5.0

5.5

Total Biomass (g) (Log10)

6.5

7.0

7.5

8.0

6.0

Scale  2 m

6.5

7.0

7.5

8.0

8.5

7.5

Total Biomass (g) (Log10)

2

Scale  4 m

8.0

8.5

9.0

9.5

10.0

9.0

Total Biomass (g) (Log10)

2

Scale  16 m

10.0

10.5

Scale  64 m

11.0

2

6.0

5.0

4.5

5.0

2.0

1.5

3.0

2.0

4.0

4.5

Species Richness

4.0

Species Richness

2.5

3.5

4.0
3.5
3.0

Species Richness

3.5

2.0

2.5

3.0

Species Richness

3.0
2.5

Species Richness

3.5

4.5

5.5

4.0

4.5

4.0

9.5

Total Biomass (g) (Log10)

2

5.0

Scale  1 m

6.0

Total Biomass (g) (Log10)

2

4

5

6

7

4.5

5.0

Live Biomass (g) (Log10)

6.0

6.5

7.0

7.5

8.0

5.5

2

Scale  2 m

6.0

6.5

7.0

7.5

8.0

8.5

7.0

7.5

Live Biomass (g) (Log10)

2

Scale  4 m

8.0

8.5

9.0

9.5

8.5

9.0

Live Biomass (g) (Log10)

2

Scale  16 m

2

10.0

10.5

11.0

Scale  64 m

2

8.5

9.5

6.0

5.0

4.5

5.0

2.0

1.5

3.0

2.0

4.0

4.5

Species Richness

4.0

Species Richness

2.5

3.5

4.0
3.5
3.0

Species Richness

3.5

2.0

2.5

3.0

Species Richness

3.0
2.5

Species Richness

3.5

4.5

5.5

4.0

4.5

4.0

9.5

Live Biomass (g) (Log10)

5.0

Scale  1 m

5.5

Live Biomass (g) (Log10)

2

3

4

5

Litter (g) (Log10)

6

7

3

4

5

6

Litter (g) (Log10)

7

4

5

6

Litter (g) (Log10)

7

8

6

7

8

Litter (g) (Log10)

9

7.5

8.0

9.0

10.0

10.5

Litter (g) (Log10)

Figure D.1. Square root transformed species richness with fitted curves from linear regression models with log
transformed total biomass (top row) and log transformed live biomass (center panels) and log transformed litter
(bottom panels) as the explanatory variables, across scales, using the 14-grid dataset. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.

155
2

Scale  2 m

2

Scale  4 m

2

Scale  16 m

2

Scale  64 m

2

4.4
4.0

4.2

Species Richness

4.6

4.8

4.5
4.0
3.5

Species Richness

3.5
3.0

Species Richness

3.0
2.5

Species Richness

3.0
2.5
4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

5.0

Total Biomass (g) (Log10)

5.5

6.0

6.5

7.0

7.5

8.0

6.0

Total Biomass (g) (Log10)

2

Scale  2 m

6.5

7.0

7.5

8.0

8.5

7.5

Total Biomass (g) (Log10)

2

Scale  4 m

8.0

8.5

9.0

9.5

10.0

9.0

Total Biomass (g) (Log10)

2

Scale  16 m

9.5

10.0

10.5

11.0

Total Biomass (g) (Log10)

2

Scale  64 m

2

4.4
4.0

4.2

Species Richness

4.6

4.8

4.5
4.0
3.5

Species Richness

3.5
3.0

Species Richness

3.0
2.5

Species Richness

3.0
2.5

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

4.5

Live Biomass (g) (Log10)

5.5

6.0

6.5

7.0

7.5

5.5

Live Biomass (g) (Log10)

2

Scale  2 m

6.0

6.5

7.0

7.5

8.0

7.0

Live Biomass (g) (Log10)

2

Scale  4 m

7.5

8.0

8.5

9.0

8.5

9.0

Live Biomass (g) (Log10)

2

Scale  16 m

9.5

10.0

10.5

Live Biomass (g) (Log10)

2

Scale  64 m

2

4.4
4.0

4.2

Species Richness

4.6

4.8

4.5
4.0
3.5

Species Richness

3.5
3.0

Species Richness

3.0
2.5

Species Richness

3.0
2.5

2

3

4

5

Litter (g) (Log10)

6

7

3

4

5

6

Litter (g) (Log10)

7

3.6

2.0

1.5

3.0

2.0

3.8

2.5

2.0

Species Richness

3.5

4.0

3.5

5.0

Scale  1 m

5.0

3.6

2.0

1.5

3.0

2.0

3.8

2.5

2.0

Species Richness

3.5

4.0

3.5

5.0

Scale  1 m

3.6

2.0

1.5

3.0

2.0

3.8

2.5

2.0

Species Richness

3.5

4.0

3.5

5.0

Scale  1 m

4

5

6

Litter (g) (Log10)

7

8

6

7

8

Litter (g) (Log10)

9

7.5

8.0

8.5

9.0

9.5

10.0

10.5

Litter (g) (Log10)

Figure D.2. Square root transformed species richness with fitted curves from linear regression models with log
transformed total biomass (top row) and log transformed live biomass (center panels) and log transformed litter
(bottom panels) as the explanatory variables, across scales, using the 4-grid dataset. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is shown in bold.

156
APPENDIX E: KAISER-GUTTMAN AND PC3 BIPLOTS

Kaiser-Guttman Criterion

Eigenvalue

6
Average eigenvalue

5
4
3
2
1

PC14

PC13

PC12

PC11

PC10

PC9

PC8

PC7

PC6

PC5

PC4

PC3

PC2

PC1

0

Broken Stick Model

Percent

40

Eigenvalue
Broken stick model

30
20
10

PC14

PC13

PC12

PC11

PC10

PC9

PC8

PC7

PC6

PC5

PC4

PC3

PC2

PC1

0

Figure E.1. Kaiser-Guttman criterion (upper panel) and broken stick model (lower
panel) evaluation of the PCA axes on the soil nutrient data.

2

157

Cu
N
C

0

Zn
Mg
C
Ba
Fe

S

Mn

-2

P

Na

-6

-4

PC3

K

Al

-4

-2

0

2

4

PC1

Figure E.2. Distance biplot of PC1 and PC3 from the PCA of the soil nutrient data.
Each grid is indicated by points of a certain colour. The L4 (red points) and L5
(green points) grids were lower biomass grids while the P1 (blue points) and P2
(black points) grids were higher biomass grids.

0.5

1.0

1.5

158

Cu
NC

0.0

Mg
Ca
B

Fe

S

Mn

-0.5

K
P

Na

-1.5

-1.0

PC3

Zn

-2.0

Al

-2

-1

0

1

2

PC1

Figure E.3. Correlation biplot of PC1 and PC3 from the PCA on the soil nutrient
data. Each grid is indicated by points of a certain colour. The L4 (red points) and
L5 (green points) grids were lower biomass grids while the P1 (blue points) and P2
(black points) grids were higher biomass grids.

159

Eigenvalue

Kaiser-Guttman Criterion
Average eigenvalue

6
4
2

PC16
PC17
PC18

PC1
PC2
PC3
PC4
PC5
PC6
PC7
PC8
PC9
PC10
PC11
PC12
PC13
PC14
PC15

0

Broken Stick Model

Percent

40

Eigenvalue
Broken stick model

30
20
10

PC15
PC16
PC17
PC18

PC11
PC12
PC13
PC14

PC7
PC8
PC9
PC10

PC4
PC5
PC6

PC1
PC2
PC3

0

Figure E.4. Plots of the Kaiser-Guttman criterion and broken stick models of the
PCA on the soil and leaf nutrient data. The Kaiser-Guttman plot shows the first
four principal component axes contain relevant information while the more
conservative broken stick model indicates only two axes need be considered.

2

160

Zn

1

Cu

Leaf N
Leaf C

Mg

Ca Mn

N
C

0

BK

PC3

S
Fe

Leaf C:N
P

-1

C:N

-3

-2

Na

Al

-2

-1

0

1

2

PC1

Figure E.5. Distance biplot of PC1 and PC3 from the PCA on the soil and leaf nutrient
data. Each grid is indicated by points of a certain colour. The L4 (red points) and L5
(green points) grids were lower biomass grids while the P1 (blue points) and P2 (black
points) grids were higher biomass grids.

0.5

1.0

1.5

161

Zn

Cu
Mg

N
C

Ca Mn
BK

0.0

PC3

Leaf N
Leaf C

S
Fe

Leaf C:N
P
C:N

-0.5

Na

-1.5

-1.0

Al

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

PC1

Figure E.6. Correlation biplot of PC1 and PC3 from the PCA on the soil and leaf nutrient
data. Each grid is indicated by points of a certain colour. The L4 (red points) and L5
(green) grids were lower biomass grids while the P1 (blue points) and P2 (black points)
grids were higher biomass grids.

162

Eigenvalue

Kaiser-Guttman Criterion
4

Average eigenvalue

3
2
1

PC6

PC5

PC4

PC3

PC2

PC1

0

70
60
50
40
30
20
10
0

PC6

PC5

PC4

PC3

PC2

Eigenvalue
Broken stick model

PC1

Percent

Broken Stick Model

Figure E.7. Plots of the Kaiser-Guttman criterion and broken stick models of the
PCA on the soil and leaf carbon, nitrogen and carbon to nitrogen ratio nutrient
data. The Kaiser-Guttman plot suggests the first two PCA axes contain relevant
information while the more conservative broken stick model indicates only PC1
need be considered.

163
APPENDIX F: PCA REGRESSIONS
2

0.4

0.6

0.8

-0.4

-0.2

2

0.2

0.4

-0.4

0.4

0.6

0.8

-0.2

0.0

0.2

0.4

0.6

-0.4

2

-0.2

0.0

0.2

0.6

7.0
6.5
6.0

2

-0.2

0.6

0.8

7

2

5
4

Litter (g) (Log10)

6

7
5
4

2

3

Litter (g) (Log10)
0.4

0.0

Scale  1 m

2

PC1

5.5
-0.4

6

7
6
5
4
3

0.2

6.5

7.0
0.4

PC3

Scale  1 m

2

0.0

0.4

2

3.5
-0.6

PC2

Scale  1 m

-0.2

Scale  1 m

5.0

Live Biomass (g) (Log10)

6.0
5.5
5.0
4.5

0.8

0.2

6.0

2

6.5

7.0

0.4

0.0

PC3

Scale  1 m

PC1

-0.4

-0.2

3

0.2

5.5
-0.4

3.5
0.0

0.4

5.0

0.6

4.0

4.5

5.0

5.5

6.0

Live Biomass (g) (Log10)

6.5

7.0

2

4.0

-0.2

0.2

2

7.5
-0.4

PC2

3.5
-0.4

0.4

4.0
-0.6

PC1
Scale  1 m

0.2

4.5

5.0

5.5

6.0

6.5

7.0

Total Biomass (g) (Log10)

7.5
0.2

0.0

Scale  1 m

4.0
0.0

-0.2

2

4.5

Total Biomass (g) (Log10)

7.5
7.0
6.5
6.0
5.5
5.0
4.5

-0.2

3.0

0.6

PC3

Scale  1 m

4.0

Total Biomass (g) (Log10)

0.0

PC2

Scale  1 m

-0.4

2.5

Species Richness

1.5
-0.6

4.5

0.2

4.0

0.0

2

2.0

3.0
2.5

Species Richness

1.5
-0.2

PC1

Live Biomass (g) (Log10)

Scale  1 m

2.0

3.5
3.0
2.5

Species Richness

2.0
1.5
-0.4

Litter (g) (Log10)

2

3.5

Scale  1 m
3.5

Scale  1 m

-0.6

-0.4

-0.2

0.0

PC2

0.2

0.4

0.6

-0.4

-0.2

0.0

0.2

0.4

PC3

Figure F.1. Square root transformed species richness, log transformed total biomass, log
transformed live biomass, and log transformed litter with the soil nutrient PCA axes. Fitted
curves from linear regression models at 1 m2 having PC1 (left panels) PC2 (center panels)
and PC3 (right panels) as the explanatory variables are shown. The dotted line is the fitted
linear model and the dashed line is the fitted quadratic model. The significant model in each
plot is shown in bold.

164
2

0.0

0.5

3.5
3.0
2.0
1.5
-0.5

0.0

2

1.0

-0.4

2

0.0

0.5

7.0
0.5

-0.2

2

0.2

0.4

5.5
5.0

1.0

-0.4

-0.2

0.0

PC3
2

4

Litter (g) (Log10)

2

2

5

6

2

3

5

6

Scale  1 m

4

Litter (g) (Log10)

0.4

6.5
0.5

3

6
5
4
3

0.2

2

4.5

Live Biomass (g) (Log10)
0.0

Scale  1 m

0.5

0.4

4.0
-0.5

2

2

0.0

0.2

6.0

6.5
5.5
5.0
4.5

Live Biomass (g) (Log10)

4.0
0.5

0.0

Scale  1 m

PC2

Scale  1 m

PC1

6.0

-0.4

6.0

6.5
6.0
5.5
5.0

0.0

-0.5

5.5

1.0

PC3

Scale  1 m

PC1

-1.0

5.0

Total Biomass (g) (Log10)

2

4.5

-0.5

2

4.5
0.0

PC2

4.0
-1.0

0.4

4.0
-0.5

PC1
Scale  1 m

0.2

6.5

7.0
6.5
6.0
5.5
4.5
4.0
-0.5

0.0

Scale  1 m

5.0

Total Biomass (g) (Log10)

6.5
6.0
5.5
5.0
4.0
-1.0

-0.2

PC3

Scale  1 m

4.5

Total Biomass (g) (Log10)

0.5

PC2

7.0

Scale  1 m

2

2.5

Species Richness

3.0
2.0
1.5
-0.5

PC1

Live Biomass (g) (Log10)

Scale  1 m

2.5

Species Richness

3.0
2.5

Species Richness

2.0
1.5
-1.0

Litter (g) (Log10)

2

3.5

Scale  1 m

3.5

Scale  1 m

-0.5

0.0

0.5

PC2

1.0

-0.4

-0.2

0.0

PC3

Figure F.2. Square root transformed species richness, log transformed total
biomass, log transformed live biomass, and log transformed litter with the soil and
leaf nutrient PCA axes. Fitted curves from linear regression models at 1 m2
having PC1 (left panels) PC2 (center panels) and PC3 (right panels) as the
explanatory variables are shown. The dotted line is the fitted linear model and the
dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold.

165

0.0

0.5

1.0

-0.2

0.0

2

0.8

-0.2

2

0.0

0.2

0.4

0.6

0.0

5.5

6.0

6.5
0.0

0.2

0.4

0.6

0.8

-0.2

0.0

0.2

0.4

PC3
2

4
2

2

5

6

2

3

4

5

Litter (g) (Log10)

6

Scale  1 m

3

Litter (g) (Log10)

6
5

2

4.0
-0.2

Scale  1 m

1.0

0.4

5.0

Live Biomass (g) (Log10)

6.5
6.0
5.5
5.0
-0.4

2

0.5

0.2

Scale  1 m

PC2

4

0.0

PC1

6.0

2

4.0
1.0

3

-0.5

5.5

-0.2

4.5

Live Biomass (g) (Log10)

6.5
6.0
5.5
5.0

0.5

2
-1.0

5.0

0.8

PC3

Scale  1 m

PC1
Scale  1 m

6.5

7.0
-0.2

2

0.0

2

4.0
-0.4

PC2

4.5

-0.5

0.4

4.5

Total Biomass (g) (Log10)

6.5
6.0
5.5
5.0

1.0

0.2

Scale  1 m

7.0
0.5

4.0
-1.0

0.0

PC3

4.0
0.0

Scale  1 m

3.0

3.5
0.6

4.5

Total Biomass (g) (Log10)

6.5
6.0
5.5
5.0

Total Biomass (g) (Log10)

4.5

-0.5

PC1

Live Biomass (g) (Log10)

0.4

Scale  1 m

4.0
-1.0

Litter (g) (Log10)

0.2

PC2

7.0

Scale  1 m

2.5

Species Richness
-0.4

PC1

4.5

-0.5

1.5

1.5
-1.0

Scale  1 m

2

2.0

2.5

Species Richness

3.0

3.5

Scale  1 m

2

2.0

3.0
2.5
2.0
1.5

Species Richness

3.5

Scale  1 m

2

-0.4

-0.2

0.0

0.2

PC2

0.4

0.6

0.8

-0.2

0.0

0.2

0.4

PC3

Figure F.3. Square root transformed species richness, log transformed total
biomass, log transformed live biomass, and log transformed litter with the soil and
leaf carbon, nitrogen and carbon to nitrogen ratio PCA axes. Fitted curves from
linear regression models at 1 m2 having PC1 (left panels) PC2 (center panels) and
PC3 (right panels) as the explanatory variables are shown. The dotted line is the
fitted linear model and the dashed line is the fitted quadratic model. The
significant model in each plot is shown in bold.

166
APPENDIX G: SOIL NUTRIENTS - SCALED REGRESSIONS
2

4e+04

6e+04

2

6e+04

8e+04

6
5
4

Litter (g) (Log10)

3

6e+04

8e+04

Scale  2 m

1e+05

2

6
4

5

Litter (g) (Log10)

7

7.0
6.5
6.0

3
2e+04

4e+04

6e+04

8e+04

1e+05

2e+04

Soil Carbon (ppm)

2

2

6e+04

Scale  4 m

8e+04

1e+05

8

2

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0

4e+04

Soil Carbon (ppm)

8.0

Scale  4 m

6.5

4

Total Biomass (g) (Log10)

3.5

4e+04

Soil Carbon (ppm)

5.5

1e+05

6.0

4.0

Scale  4 m

3.0

2e+04

2.0

Species Richness

4e+04

Soil Carbon (ppm)

2.5

1e+05

2

4.5
2e+04

Soil Carbon (ppm)
Scale  4 m

8e+04

5.0

Live Biomass (g) (Log10)

7.5
7.0
6.5
6.0

1e+05

6e+04

7

8e+04

4e+04

Scale  2 m

5.0
6e+04

6.5

2e+04

Soil Carbon (ppm)

5.5

Total Biomass (g) (Log10)

3.5
3.0

Species Richness

2.5

4e+04

6.0

1e+05

2

7.5

Scale  2 m

2.0

2e+04

7

7.0

8e+04

Soil Carbon (ppm)

8.0

Scale  2 m

5.5

2
2e+04

2

6

1e+05

Soil Carbon (ppm)

5

8e+04

2

5.5

6e+04

Scale  1 m

3.5

4.0
4e+04

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5

2e+04

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

20000

40000

60000

80000

20000

Soil Carbon (ppm)
2

Scale  16 m

80000

20000

2

60000

Scale  16 m

80000

20000

40000

60000

80000

Soil Carbon (ppm)

2

Scale  16 m

2

2

Scale  64 m

50000

70000

50000

70000

10000

2

70000

2

10.0

10.5

10.5
70000

50000

Scale  64 m

Litter (g) (Log10)

8.0
7.5

8.5
50000

30000

Soil Carbon (ppm)

10.0

Live Biomass (g) (Log10)

11.0
10.5

30000

Soil Carbon (ppm)

8

9
30000

Scale  64 m

10.0
10000

7

Litter (g) (Log10)

6

2

9.0
30000

Soil Carbon (ppm)

9.0
10000

Soil Carbon (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8
3.6
10000

8.5

70000

9.5

50000

9.0

30000

Soil Carbon (ppm)

5.0

Scale  64 m

8.0
7.0

10000

8.5

70000

9.5

50000

Soil Carbon (ppm)

9.0

30000

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

10000

Species Richness

40000

Soil Carbon (ppm)

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

60000

10.0

Scale  16 m

40000

Soil Carbon (ppm)

10000

30000

50000

Soil Carbon (ppm)

70000

10000

30000

50000

70000

Soil Carbon (ppm)

Figure G.1. Fitted curves from linear regressions with soil carbon as the explanatory variable
and square root transformed species richness (first column), log transformed total biomass
(second column), log transformed live biomass (third column) and log transformed litter
(fourth column) as response variables across scales. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold.

167
2

2000

4000

6000

6
5
4

Litter (g) (Log10)

3

6000

Scale  2 m

8000

2

6
4

5

Litter (g) (Log10)

7

7.0
6.5
6.0
5.5

3

8000

2000

4000

6000

8000

2000

Soil Nitrogen (ppm)

2

2

6000

Scale  4 m

8000

8

2

7
6

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0
6.5

4000

Soil Nitrogen (ppm)

8.0

Scale  4 m

4

6.0

Total Biomass (g) (Log10)

4000

Soil Nitrogen (ppm)

5

4000

Scale  4 m

4.0

2000

4.5

2

3.5

8000

2

5.0

Live Biomass (g) (Log10)

8.0
7.5
7.0
6.5
6.0

2000

Soil Nitrogen (ppm)

3.0

6000

Scale  2 m

5.0
8000

2.5

4000

Soil Nitrogen (ppm)

2.0

Species Richness

6.5

2000

5.5

Total Biomass (g) (Log10)

3.5

Species Richness

3.0

6000

Soil Nitrogen (ppm)
Scale  4 m

6.0

8000

2

7.5

Scale  2 m

2.5

4000

7

7.0

6000

Soil Nitrogen (ppm)

2

2.0

2000

5.5

2

8000

Soil Nitrogen (ppm)
Scale  2 m

2

5.5

6000

Scale  1 m

3.5

4.0
4000

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5

2000

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

1000

3000

5000

7000

1000

3000

Soil Nitrogen (ppm)

Scale  16 m

1000

5000

Scale  16 m

7000

1000

3000

5000

7000

Soil Nitrogen (ppm)

2

Scale  16 m

2

3000

4000

5000

6000

2

Scale  64 m

3000

4000

5000

Soil Nitrogen (ppm)

6000

7000

4000

5000

6000

7000

1000

2

4000

5000

6000

7000

1000

3000

4000

5000

Scale  64 m

6000

7000

10.0

10.5

2

Litter (g) (Log10)

8.0

8.5
3000

Soil Nitrogen (ppm)

2000

Soil Nitrogen (ppm)

10.5

Live Biomass (g) (Log10)

11.0
10.5

2000

8

9
3000

Scale  64 m

10.0
1000

7

Litter (g) (Log10)

6
2000

2

9.0
2000

9.0
1000

Soil Nitrogen (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8
3.6
1000

8.5

7000

Soil Nitrogen (ppm)

9.5

2000

5.0

Scale  64 m

8.0
7.0

1000

9.0

7000

8.5

6000

7.5

5000

10.0

4000

9.5

3000

Soil Nitrogen (ppm)

9.0

2000

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

1000

Species Richness

3000

Soil Nitrogen (ppm)

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

7000

2

10.0

Scale  16 m

5000

Soil Nitrogen (ppm)

2

2000

3000

4000

5000

Soil Nitrogen (ppm)

6000

7000

1000

2000

3000

4000

5000

6000

7000

Soil Nitrogen (ppm)

Figure G.2. Fitted curves from linear regressions with soil nitrogen as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold.

168
2

8

9

11

11

6
5
4
3

11

12

2

6
4

5

Litter (g) (Log10)

7

7.0
6.5
6.0

3
8

9

10

11

12

8

9

Soil Carbon to Nitrogen Ratio

2

2

11

Scale  4 m

12

8

2

Litter (g) (Log10)

7.5
7.0
6.5

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0

10

Soil Carbon to Nitrogen Ratio

8.0

Scale  4 m

6.5

4

Total Biomass (g) (Log10)

Scale  2 m

5.5

12

6.0

4.0

10

7

10

Scale  4 m

3.5

9

Soil Carbon to Nitrogen Ratio

6

2

3.0

8

2.0

Species Richness

12

4.5
9

Soil Carbon to Nitrogen Ratio

2.5

11

2

5.0

Live Biomass (g) (Log10)

7.5
7.0
6.5
8

Soil Carbon to Nitrogen Ratio
Scale  4 m

Litter (g) (Log10)
Scale  2 m

6.0

12

10

5

11

9

Soil Carbon to Nitrogen Ratio

5.0
10

6.5

8

5.5

Total Biomass (g) (Log10)

3.5
3.0

Species Richness

2.5

9

6.0

12

2

7.5

Scale  2 m

2.0
8

7

7.0

10

Soil Carbon to Nitrogen Ratio

2

8.0

Scale  2 m

5.5

2

12

Soil Carbon to Nitrogen Ratio

6.0

11

2

5.5

10

Scale  1 m

3.5

4.0
9

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5

8

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

8.5

9.0

9.5

10.0 10.5 11.0

11.5

8.5

Soil Carbon to Nitrogen Ratio

10.0 10.5 11.0

Scale  16 m

11.5

8.5

9.5

10.0 10.5 11.0

Scale  16 m

11.5

8.5

9.0

9.5

10.0 10.5 11.0

11.5

Soil Carbon to Nitrogen Ratio

2

Scale  16 m

2

10.0

10.5

2

Scale  64 m

9.5

10.0

10.5

11.0

10.0

10.5

11.0

8.5

2

10.0

10.5

11.0

9.5

10.0

Scale  64 m

10.5

11.0

10.0

10.5

2

Litter (g) (Log10)

8.0

8.5
9.5

9.0

Soil Carbon to Nitrogen Ratio

10.5

Live Biomass (g) (Log10)

11.0
10.5

9.0

Soil Carbon to Nitrogen Ratio

8

9
9.5

Scale  64 m

10.0
8.5

7

Litter (g) (Log10)

6
9.0

2

9.0
9.0

Soil Carbon to Nitrogen Ratio

9.0
8.5

Soil Carbon to Nitrogen Ratio

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8
3.6
8.5

8.5

11.0

9.5

9.5

9.0

9.0

Soil Carbon to Nitrogen Ratio

5.0

Scale  64 m

8.0
7.0

8.5

8.5

11.0

7.5

10.5

10.0

10.0

9.5

9.5

Soil Carbon to Nitrogen Ratio

9.0

9.0

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

8.5

Species Richness

9.0

Soil Carbon to Nitrogen Ratio

2

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

9.5

10.0

Scale  16 m

9.0

Soil Carbon to Nitrogen Ratio

2

8.5

9.0

9.5

10.0

10.5

Soil Carbon to Nitrogen Ratio

11.0

8.5

9.0

9.5

10.0

10.5

11.0

Soil Carbon to Nitrogen Ratio

Figure G.3. Fitted curves from linear regressions with soil carbon to nitrogen ratio as the
explanatory variable and square root transformed species richness (first column), log
transformed total biomass (second column), log transformed live biomass (third column) and
log transformed litter (fourth column) as response variables across scales. The dotted line is
the fitted linear model and the dashed line is the fitted quadratic model. The significant
model in each plot is shown in bold.

169
2

1000

6
5
4
3

Litter (g) (Log10)

Scale  2 m

6
4

5

Litter (g) (Log10)

7

7.0
6.5
6.0
5.5

1400

3
800

900

1000

1200

1400

800

Soil Phosphorus (ppm)

2

2

1000

1200

Scale  4 m

1400

8

2

7

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0

900

Soil Phosphorus (ppm)

8.0

Scale  4 m

6.5

4

Total Biomass (g) (Log10)

1400

2

6

1200

6.0

4.0

1200

7.5
1000

Scale  4 m

3.5

1000

Soil Phosphorus (ppm)

4.5

2

3.0

800

2.0

Species Richness

900

Soil Phosphorus (ppm)

2.5

1400

2

5.0

Live Biomass (g) (Log10)

8.0
7.5
7.0
6.5
800

Soil Phosphorus (ppm)
Scale  4 m

1200

Scale  2 m

6.0

1400

1000

Soil Phosphorus (ppm)

5.0
1200

6.5
800

2

5.5

Total Biomass (g) (Log10)

3.5

Species Richness

3.0

1000

6.0

1400

Scale  2 m

2.5

900

7

7.0

1200

Soil Phosphorus (ppm)

2.0
800

5.5

2
800

2

5

1400

Soil Phosphorus (ppm)
Scale  2 m

2

5.5

1200

Scale  1 m

3.5

4.0
1000

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5
800

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

900

1000 1100 1200 1300 1400

800

Soil Phosphorus (ppm)

Scale  16 m

800

1000 1100 1200 1300 1400

800

Soil Phosphorus (ppm)
Scale  16 m

900

1000 1100 1200 1300 1400

Soil Phosphorus (ppm)

2

Scale  16 m

2

Scale  64 m

1200

1200

900

2

1200

1100

Scale  64 m

1200

10.0

10.5

2

Litter (g) (Log10)

8.0

8.5
1100

1000

Soil Phosphorus (ppm)

10.5

Live Biomass (g) (Log10)

11.0
10.5

1000

Soil Phosphorus (ppm)

8
6

1100

Scale  64 m

10.0

900

7

Litter (g) (Log10)

9

9.0

2

9.0
1100

1000

Soil Phosphorus (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8

1000

Soil Phosphorus (ppm)

8.5

900

9.5

2

3.6

900

8.0

1200

9.0

1100

8.5

1000

Soil Phosphorus (ppm)

5.0

Scale  64 m

7.0
900

7.5

1200

10.0

1100

9.5

1000

Soil Phosphorus (ppm)

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

900

Species Richness

900

2

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

1000 1100 1200 1300 1400

Soil Phosphorus (ppm)

10.0

Scale  16 m

900

2

9.0

800

900

1000

1100

Soil Phosphorus (ppm)

1200

900

1000

1100

1200

Soil Phosphorus (ppm)

Figure G.4. Fitted curves from linear regressions with soil phosphorus as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold.

170
2

6000

4

5000

6000

7000

8000

6
5
3

4.5

4

5.5

6.0

6.5

Litter (g) (Log10)

7

7.0

7.5

Soil Potassium (ppm)
2
Scale  2 m

4500 5000 5500 6000 6500 7000 7500

4500 5000 5500 6000 6500 7000 7500

Soil Potassium (ppm)

2

Scale  4 m

Soil Potassium (ppm)

2

Scale  4 m
8

2

7
6

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0
6.5

2.0

4

6.0

Total Biomass (g) (Log10)

8000

8.0

Scale  4 m

4.0

7000

5.0

Live Biomass (g) (Log10)

8.0
7.5
7.0
6.5
6.0
5.0
2

3.5

6000

Soil Potassium (ppm)
2
Scale  2 m

Soil Potassium (ppm)

3.0

3

Litter (g) (Log10)
5000

4500 5000 5500 6000 6500 7000 7500

Soil Potassium (ppm)

2.5

5

6

6.5
6.0

8000

5.5

Total Biomass (g) (Log10)

3.5
3.0
2.5
2.0

Species Richness

7

7.0

7000

Soil Potassium (ppm)
2
Scale  2 m

4500 5000 5500 6000 6500 7000 7500

Species Richness

5.5

2
5000

5

8000

Soil Potassium (ppm)
2
Scale  2 m

Scale  4 m

2

5.5

7000

Scale  1 m

3.5

4.0
6000

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5

5000

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

5000

5500

6000

6500

7000

7500

5000

Soil Potassium (ppm)

6500

Scale  16 m

7000

7500

5000

6000

6500

Scale  16 m

7000

7500

5000

5500

6000

6500

7000

7500

Soil Potassium (ppm)

2

Scale  16 m

2

6500

Scale  64 m

6500

7000

5000

2

6000

6500

7000

2

10.0

10.5

10.5

Scale  64 m

Litter (g) (Log10)

8.5
6500

5500

Soil Potassium (ppm)

10.0

Live Biomass (g) (Log10)

11.0
10.5

6000

Soil Potassium (ppm)

8
6

6000

Scale  64 m

10.0

5500

7

Litter (g) (Log10)

9

9.0

2

9.0
6500

5500

Soil Potassium (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8

6000

Soil Potassium (ppm)

8.5
5000

9.5

2

3.6

5500

8.0

7000

9.0

6000

8.5

5500

Soil Potassium (ppm)

5.0

Scale  64 m

7.0
5000

8.0

7000

7.5

6500

9.5

6000

9.0

5500

Soil Potassium (ppm)

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

5000

Species Richness

5500

Soil Potassium (ppm)

2

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

6000

10.0

Scale  16 m

5500

Soil Potassium (ppm)

2

5500

6000

Soil Potassium (ppm)

6500

5500

6000

6500

Soil Potassium (ppm)

Figure G.5. Fitted curves from linear regressions with soil potassium as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold.

171
2

10

20

30

6
5
4

Litter (g) (Log10)

3

30

Scale  2 m

40

2

6
4

5

Litter (g) (Log10)

7

7.0
6.5
6.0
5.5

3

40

10

20

30

40

10

Soil Boron (ppm)

2

Scale  4 m

2

Scale  4 m

40

8

2

7

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

30

4

5.5

8.5
8.0
7.5
7.0
6.5
6.0

20

Soil Boron (ppm)

8.0

Scale  4 m
Total Biomass (g) (Log10)

20

Soil Boron (ppm)

6

2

4.0

10

4.5
20

Soil Boron (ppm)

3.5

40

2

5.0

Live Biomass (g) (Log10)

8.0
7.5
7.0
6.5
6.0

10

3.0

30

Scale  2 m

5.0
40

2.5

20

Soil Boron (ppm)

2.0

Species Richness

6.5

10

5.5

Total Biomass (g) (Log10)

3.5

Species Richness

3.0

30

Soil Boron (ppm)
Scale  4 m

6.0

40

2

7.5

Scale  2 m

2.5

20

7

7.0

30

Soil Boron (ppm)

2

2.0

10

5.5

2

40

Soil Boron (ppm)
Scale  2 m

2

5

30

Scale  1 m

3.5

4.0
20

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5

10

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

5

10

15

20

25

30

35

40

5

10

Soil Boron (ppm)

25

Scale  16 m

30

35

40

5

15

20

25

30

35

40

5

10

Soil Boron (ppm)
Scale  16 m

15

20

25

30

35

40

Soil Boron (ppm)

2

Scale  16 m

2

15

20

25

30

2

Scale  64 m

20

25

20

25

30

35

5

2

25

15

20

25

Scale  64 m

30

35

10.0

10.5

2

Litter (g) (Log10)

8.0

8.5
20

10

Soil Boron (ppm)

10.5

Live Biomass (g) (Log10)

11.0
10.5

15

Soil Boron (ppm)

8

9
15

Scale  64 m

10.0

10

7

Litter (g) (Log10)

6
10

2

9.0
15

Soil Boron (ppm)

9.0
5

Soil Boron (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8
3.6

10

8.5

35

Soil Boron (ppm)

9.5

10

5.0

Scale  64 m

8.0
7.0

5

9.0

35

8.5

30

7.5

25

10.0

20

9.5

15

Soil Boron (ppm)

9.0

10

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

5

Species Richness

10

2

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

20

10.0

Scale  16 m

15

Soil Boron (ppm)

2

10

15

20

Soil Boron (ppm)

25

10

15

20

25

Soil Boron (ppm)

Figure G.6. Fitted curves from linear regressions with soil boron as the explanatory variable
and square root transformed species richness (first column), log transformed total biomass
(second column), log transformed live biomass (third column) and log transformed litter
(fourth column) as response variables across scales. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold.

172
2

30000

40000

6
5
4

Litter (g) (Log10)

3

35000

40000

45000

6
5
3

4

Litter (g) (Log10)

7

7.0
6.5
6.0
25000

30000

35000

40000

25000

30000

Soil Iron (ppm)

2

2

Scale  4 m

40000

8

2

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0

35000

Soil Iron (ppm)

8.0

Scale  4 m

6.5

4

Total Biomass (g) (Log10)

30000

Soil Iron (ppm)
2
Scale  2 m

5.5

40000

6.0

4.0

25000

7

35000

Scale  4 m

3.5

45000

7.5
30000

2

3.0

40000

4.5
25000

Soil Iron (ppm)

2.5

35000

2.0

Species Richness

30000

5.0

Live Biomass (g) (Log10)

8.0
7.5
7.0
6.5
6.0

40000

Soil Iron (ppm)
Scale  4 m

6.5
25000

5.0
35000

6.0

45000

Soil Iron (ppm)
2
Scale  2 m

5.5

Total Biomass (g) (Log10)

3.5
3.0

Species Richness

2.5

30000

7

7.0

35000

Soil Iron (ppm)
2
Scale  2 m

2.0
25000

5.5

2
25000

6

45000

Soil Iron (ppm)
2
Scale  2 m

5

40000

2

5.5

35000

Scale  1 m

3.5

4.0
30000

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5
25000

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

30000

35000

40000

35000

40000

30000

40000

30000

35000

40000

Soil Iron (ppm)

Soil Iron (ppm)

2

2

2

Scale  16 m

Scale  16 m

Scale  64 m

40000

30000

2

40000

2

Litter (g) (Log10)

10.0

10.0

10.5

10.5

Scale  64 m

8.0
7.5

8.5
40000

35000

Soil Iron (ppm)

9.5

Live Biomass (g) (Log10)

11.0
10.5

35000

Soil Iron (ppm)

8

9

Scale  64 m

10.0

30000

7

Litter (g) (Log10)

6

2

9.0
40000

35000

Soil Iron (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8

35000

Soil Iron (ppm)

9.0

30000

9.5

2

3.6

30000

8.5

40000

9.0

35000

Soil Iron (ppm)

5.0

Scale  64 m

8.0
7.0

30000

8.5

40000

Soil Iron (ppm)

9.0

35000

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

8.0

3.5

4.0

Total Biomass (g) (Log10)

4.5

10.0

Scale  16 m

3.0

30000

Species Richness

35000

Soil Iron (ppm)

2

Scale  16 m

Species Richness

30000

Soil Iron (ppm)

30000

35000

Soil Iron (ppm)

40000

30000

35000

40000

Soil Iron (ppm)

Figure G.7. Fitted curves from linear regressions with soil iron as the explanatory variable
and square root transformed species richness (first column), log transformed total biomass
(second column), log transformed live biomass (third column) and log transformed litter
(fourth column) as response variables across scales. The dotted line is the fitted linear model
and the dashed line is the fitted quadratic model. The significant model in each plot is shown
in bold.

173
2

10000

4
3

Litter (g) (Log10)

7
6
5

Litter (g) (Log10)

4
3
6000

8000 10000

14000

18000

6000

Soil Magnesium (ppm)

2

2

Scale  4 m

18000

8

2

7
6

Litter (g) (Log10)

7.5
7.0
6.5
6.0

Live Biomass (g) (Log10)

14000

4

5.5

8.5
8.0
7.5
7.0

8000 10000

Soil Magnesium (ppm)

8.0

Scale  4 m

6.5

Total Biomass (g) (Log10)

5

6

6.5
7.0
6.5
6.0
5.5

18000

6.0

4.0

20000

2

5

14000

Scale  4 m

3.5

15000

Scale  2 m

4.5
8000 10000

2

3.0

10000

Soil Magnesium (ppm)

2.0

Species Richness

20000

2

5.0

Live Biomass (g) (Log10)

8.0
7.5
7.0
6.5
6.0
6000

Soil Magnesium (ppm)

2.5

15000

Scale  2 m

5.0
18000

Soil Magnesium (ppm)
Scale  4 m

6.0

10000

Soil Magnesium (ppm)

5.5

Total Biomass (g) (Log10)

3.5

Species Richness

3.0

14000

5.5

20000

2

7.5

Scale  2 m

2.5

8000 10000

7

7.0

15000

Soil Magnesium (ppm)

2

2.0
6000

2

2

20000

Soil Magnesium (ppm)
Scale  2 m

Scale  1 m

3.5

4.0
15000

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5

10000

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

8000

10000

12000

14000

16000

8000

Soil Magnesium (ppm)

Scale  16 m

14000

16000

8000

12000

Scale  16 m

14000

16000

8000

10000

12000

14000

16000

Soil Magnesium (ppm)

2

Scale  16 m

2

2

Scale  64 m

9000

10000

11000

Soil Magnesium (ppm)

12000

12000

14000

8000

2

11000

12000

14000

2

10.0

10.5

10.5
10000

12000

Scale  64 m

Litter (g) (Log10)

8.0
7.5

8.5
9000

Soil Magnesium (ppm)

10000

Soil Magnesium (ppm)

10.0

Live Biomass (g) (Log10)

11.0
10.5

8000

8

9
10000

Scale  64 m

10.0
7000

7

Litter (g) (Log10)

6

2

9.0
8000

9.0

8000

Soil Magnesium (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8
3.6
7000

8.5

14000

9.5

12000

9.0

10000

Soil Magnesium (ppm)

8.5

8000

5.0

Scale  64 m

8.0
7.0

14000

9.5

12000

Soil Magnesium (ppm)

9.0

10000

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

8000

Species Richness

10000

Soil Magnesium (ppm)

2

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

12000

10.0

Scale  16 m

10000

Soil Magnesium (ppm)

2

7000

8000

9000

10000

11000

Soil Magnesium (ppm)

12000

7000

8000

9000

10000

11000

12000

Soil Magnesium (ppm)

Figure G.8. Fitted curves from linear regressions with soil magnesium as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold.

174
2

800

900

950

6
5
4
3

Litter (g) (Log10)
750

800

850

900

950

6

1000

700

750

Soil Manganese (ppm)

2

2

850

900

Scale  4 m

950

1000

8

2

Litter (g) (Log10)

7.5
7.0
6.5

Live Biomass (g) (Log10)

8.5
8.0
7.5
7.0

800

Soil Manganese (ppm)

8.0

Scale  4 m

6.5

4

Total Biomass (g) (Log10)

5
3

700

6.0

4.0

4

Litter (g) (Log10)

7

7.0
6.5
6.0
5.5

1000

7

850

Scale  4 m

3.5

1000

6

800

2

3.0

900

2.0

Species Richness

800

Soil Manganese (ppm)
2
Scale  2 m

7.5
750

Soil Manganese (ppm)

2.5

700

4.5
700

Soil Manganese (ppm)
Scale  4 m

1000

5.0

Live Biomass (g) (Log10)

7.5
7.0
6.5
6.0

1000

900

6.0

950

800

Soil Manganese (ppm)
2
Scale  2 m

8.0
900

6.5
700

5.0
850

6.0

1000

5.5

Total Biomass (g) (Log10)

3.5
3.0

Species Richness

2.5

800

7

7.0

900

Soil Manganese (ppm)
2
Scale  2 m

2.0

750

5.5

2
700

5

1000

Soil Manganese (ppm)
2
Scale  2 m

700

2

5.5

900

Scale  1 m

3.5

4.0
800

2

5.0

Live Biomass (g) (Log10)

7.0
6.5
6.0
5.5
5.0
4.5

Total Biomass (g) (Log10)

3.5
3.0
2.5

Species Richness

2.0
1.5
700

Scale  1 m

4.5

Scale  1 m

4.0

2

7.5

Scale  1 m

800

850

900

950

1000

800

Soil Manganese (ppm)

950

Scale  16 m

1000

800

900

950

Scale  16 m

1000

800

850

900

950

1000

Soil Manganese (ppm)

2

Scale  16 m

2

900

950

2

Scale  64 m

860

880

900

920

Soil Manganese (ppm)

940

960

950

1000

800

2

900

920

940

960

950

1000

2

10.0

10.5

10.5
880

900

Scale  64 m

Litter (g) (Log10)

8.0
7.5

8.5
860

Soil Manganese (ppm)

850

Soil Manganese (ppm)

10.0

Live Biomass (g) (Log10)

11.0
10.5

840

8

9
900

Scale  64 m

10.0
820

7

Litter (g) (Log10)

6
850

2

9.0
840

9.0

800

Soil Manganese (ppm)

9.5

Total Biomass (g) (Log10)

4.8
4.6
4.4
4.2
4.0
3.8
3.6
820

8.5

1000

9.5

850

Soil Manganese (ppm)

5.0

Scale  64 m

8.0
7.0

800

9.0

1000

8.5

950

9.5

900

Soil Manganese (ppm)

9.0

850

7.5

Live Biomass (g) (Log10)

9.5
9.0
8.5
7.5

800

Species Richness

850

Soil Manganese (ppm)

2

8.0

Total Biomass (g) (Log10)

4.5
4.0
3.5
3.0

Species Richness

900

10.0

Scale  16 m

850

Soil Manganese (ppm)

2

820

840

860

880

900

920

Soil Manganese (ppm)

940

960

820

840

860

880

900

920

940

960

Soil Manganese (ppm)

Figure G.9. Fitted curves from linear regressions with soil manganese as the explanatory
variable and square root transformed species richness (first column), log transformed total
biomass (second column), log transformed live biomass (third column) and log transformed
litter (fourth column) as response variables across scales. The dotted line is the fitted linear
model and the dashed line is the fitted quadratic model. The significant model in each plot is
shown in bold.

175
APPENDIX H: SPECIES IDENTIFIED
Table H.1. Plant species occurring in the study plots. Species presence in a grid (L1-5, U1-5, P1-4) is indicated by and "X". There
were 41 species that could not be identified, not shown here.
Species
Achillea millefolium
Achnatherum nelsonii
Achnatherum occidentale
Achnatherum richardsonii
Agoseris glauca var. dasycephala
Agropyron cristatum
Agrostis gigantea
Antennaria microphylla
Antennaria umbrinella
Arabis holboellii
Artemisia frigida
Astragalus collinus
Astragalus miser
Balsamorhiza sagittata
Bromus squarrosus
Bromus tectorum
Campanula rotundifolia
Cardamine pensylvanica
Carex petasata
Carex praticola
Carex utriculata
Castilleja thompsonii

L1
X
X
X

X

X

L2 L3 L4 L5 U1 U2 U3 U4 U5 P1 P2 P3
X X
X X X X X X X X
X
X
X X
X X
X X
X
X X
X
X
X
X X
X X X
X
X X
X X
X
X X
X X X X
X
X
X
X X
X X X
X
X
X

X

X

X
X

X

X
X

X
X
X
X

X

X

X

X

P4

X

X

X

X

X

X

176

Centaurea diffusa
Centaurea stoebe ssp. micranthos
Cerastium arvense
Chenopodium album
Collinsia parviflora
Comandra umbellata
Crepis atribarba
Danthonia intermedia
Delphinium nuttallianum
Lescurainia sophia
Eleocharis palustris
Elymus glaucus
Elymus repens
Elymus trachycaulus ssp. subsecundus
Epilobium ciliatum
Equisetum arvense
Erigeron compositus
Erigeron corymbosus
Erigeron filifolius var. filifolius
Erigeron flagellaris
Erigeron linearis
Erigeron pumilus var. intermedius
Eriogonum heracleoides
Festuca campestris
Linum lewisii ssp. lewisii
Fritillaria pudica
Gaillardia aristata

(L1 L2
X

L3

L4

L5 U1 U2 U3 U4 U5 P1 P2 P3 P4)
X

X

X
X
X

X
X
X

X

X
X
X
X
X
X
X

X

X

X
X
X
X

X
X
X
X

X
X

X
X

X

X

X
X
X

X

X

X
X

X
X

X
X

X
X

X
X

X

X

X

X

177

Galium boreale
Galium trifidum ssp. subbiflorum
Geranium viscosissimum var. viscosissimum
Geum triflorum
Symphyotrichum pilosum var. pilosum
Hesperostipa comata
Juncus balticus
Koeleria macrantha
Lactuca serriola
Linaria genistifolia ssp. dalmatica
Lithospermum ruderale
Lomatium macrocarpum
Lomatium dissectum
Lotus denticulatus
Medicago lupulina
Medicago sativa
Melilotus alba
Moehringia lateriflora
Muhlenbergia asperifolia
Opuntia fragilis
Orthocarpus luteus
Oxytropis campestris
Penstemon procerus
Phalaris arundinacea
Phleum pratense
Plantago major
Plantago patagonica

(L1 L2

L3

L4

X
X
X

X

X

X

X

X

X

X

L5 U1 U2 U3 U4 U5 P1 P2 P3 P4)
X
X
X
X X
X
X
X
X X X X
X X
X
X X X
X X X X X X
X X
X
X
X X
X

X
X
X
X

X

X

X
X

X
X

X
X
X
X

X

X

X
X
X

X
X

X
X
X
X

X

X
X

X
X

178

Poa palustris
Poa pratensis
Poa secunda
Polygonum douglasii
Potentilla gracilis
Pseudoroegneria spicata
Rhinanthus minor
Rumex crispus
Schoenocrambe linifolia
Scirpus microcarpus
Scutellaria galericulata
Sium suave
Sonchus arvensis
Sporobolus cryptandrus
Symphyotrichum ericoides
Taraxacum officinale
Tragopogon dubius
Trifolium pratense
Triglochin maritima
Verbascum thapsus
Vicia americana
Zigadenus venenosus

(L1 L2

L3

L4

X
X
X

X

X
X
X

X

X

X

X

X

L5 U1 U2 U3 U4 U5 P1 P2 P3 P4)
X X
X X X X X X X X
X
X X
X X
X X X X X
X X
X X X X X
X
X
X

X
X
X
X
X
X
X
X

X
X

X

X
X

X
X

X
X

X
X

X
X

X
X

X
X

X
X

X

X
X
X

X
X
X
X

X

X

X

X

X