Functional Plant Ecology
Abiotic and biotic controls on local spatial distribution and performance of Boechera stricta KUSUM J NAITHANI, Brent E. Ewers, Jonathan D. Adelman and David H. Siemens
Journal Name:
Frontiers in Plant Science
ISSN:
1664-462X
Article type:
Original Research Article
Received on:
07 Mar 2014
Accepted on:
28 Jun 2014
Provisional PDF published on:
28 Jun 2014
www.frontiersin.org:
www.frontiersin.org
Citation:
Naithani KJ, Ewers BE, Adelman JD and Siemens DH(2014) Abiotic and biotic controls on local spatial distribution and performance of Boechera stricta. Front. Plant Sci. 5:348. doi:10.3389/fpls.2014.00348
Copyright statement:
© 2014 Naithani, Ewers, Adelman and Siemens. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
This Provisional PDF corresponds to the article as it appeared upon acceptance, after rigorous peer-review. Fully formatted PDF and full text (HTML) versions will be made available soon.
1
Abiotic and biotic controls on local spatial distribution and performance of
2
Boechera stricta
3 4
K. J. Naithani, 1,2,4,†, B. E. Ewers1,2, J. D. Adelman2, D. H. Siemens3
5
1
Program in Ecology, University of Wyoming, Laramie, WY 82071 USA
6
2
Department of Botany, University of Wyoming, Laramie, WY 82071 USA
7
3
Department of Biology, Black Hills State University, Spearfish, SD 57799 USA
8
4
Present address: Department of Geography, The Pennsylvania State University, University Park,
9
PA 16802 USA
10
† Email: [email protected]
11 12
1
1
Abstract
2
This study investigates the relative influence of biotic and abiotic factors on community
3
dynamics using an integrated approach and highlights the influence of space on genotypic and
4
phenotypic traits in plant community structure. We examined the relative influence of
5
topography, environment, spatial distance, and intra- and interspecific interactions on spatial
6
distribution and performance of Boechera stricta (rockcress), a close perennial relative of model
7
plant Arabidopsis. First, using Bayesian kriging, we mapped the topography and environmental
8
gradients and explored the spatial distribution of naturally occurring rockcress plants and two
9
neighbors, Taraxacum officinale (dandelion) and Solidago missouriensis (goldenrod) found in
10
close proximity within a typical diverse meadow community across topographic and
11
environmental gradients. We then evaluated direct and indirect relationships among variables
12
using Mantel path analysis and developed a network displaying abiotic and biotic interactions in
13
this community. We found significant spatial autocorrelation among rockcress individuals,
14
either because of common microhabitats as displayed by high density of individuals at lower
15
elevation and high soil moisture area, or limited dispersal as shown by significant spatial
16
autocorrelation of naturally occurring inbred lines, or a combination of both. Goldenrod and
17
dandelion density around rockcress does not show any direct relationship with rockcress
18
fecundity, possibly due to spatial segregation of resources. However, dandelion density around
19
rockcress shows an indirect negative influence on rockcress fecundity via herbivory, indicating
20
interspecific competition. Overall, we suggest that common microhabitat preference and limited
21
dispersal are the main drivers for spatial distribution. However, intra-specific interactions and
22
insect herbivory are the main drivers of rockcress performance in the meadow community.
2
1
Key words:
2
Bayesian kriging, competition, correlogram, Mantel tests, path analysis, spatial interaction,
3
spatial pattern
4
Introduction
5
Spatial patterns are a crucial, but often overlooked, component to understanding the factors and
6
processes that structure plant communities (Levin, 1992; Jeltsch et al., 1999; McIntire and
7
Fajardo, 2009). Spatial distribution and performance (i.e. growth and reproduction) of any plant
8
species depends on the ability to cope with environment, most notably topography, soil
9
properties, and moisture availability (Goslee et al., 2005), intraspecific genotype variation of
10
plant species (Crutsinger et al. 2006; Lankau & Strauss 2007), intra- and interspecific plant-plant
11
interactions (Callaway and Walker, 1997; Holzapfel and Mahall, 1999; Pugnaire and Luque,
12
2001; Brooker et al., 2008; Genung et al., 2012), and insect herbivory (Becerra, 2007; Bloom et
13
al., 2003; Marquis, 1992). Investigating the relative importance of these controlling factors is
14
critical to understanding the underlying processes that structure plant communities. This study
15
describes the first application of an integrated approach using molecular, ecological, and
16
statistical tools to quantify the relative influence of biotic and abiotic factors on the spatial
17
distribution and performance of Boechera stricta (rockcress), an emerging ecological model
18
plant species (Rushworth et al. 2011). Such species show great promise for understanding
19
genetic controls on ecologically important traits (Song and Mitchell-Olds, 2011) and provide
20
opportunity to explore underlying mechanisms in natural populations, compared to artificial
21
experimental settings. Rockcress is widely distributed in the western United States (Song and
22
Mitchell-Olds, 2011) and shows local adaptations in diverse ecological habitats (Mitchell-Olds,
3
1
2001; Knight et al., 2006; Song et al., 2006), making it an ideal species to study the biotic and
2
abiotic controls on species distribution and growth in natural settings.
3
Combinations of complementary mathematical and statistical techniques have been used
4
in recent studies to investigate links between observed spatial patterns and underlying ecological
5
processes (e.g., process models and geostatistics (Loranty et al., 2008); multiple ordination and
6
geostatistics (Wagner, 2003); Structural Equation Modeling and Bayesian statistics (Arhonditsis
7
et al., 2006); mixed models and Bayesian kriging (Smithwick et al., 2012); and Mantel tests and
8
path analysis (Goslee et al., 2005)). The integration of these tools can provide information about
9
spatial structure of variables and potential underlying ecological processes. Here, we integrated
10
Bayesian kriging (Diggle et al., 1998; Diggle and Ribeiro, 2002), a novel data-model fusion
11
approach for spatial interpolation of topography and environmental data across the local
12
landscape, and Mantel path analysis (Mantel, 1967; Leduc et al., 1992; Goslee et al., 2005) to
13
infer the relative importance of microhabitat preference, limited dispersal, competition, and
14
herbivory in determining the spatial distribution and performance on a local scale.
15
First, we examined the spatial distribution of rockcress individuals and the density of
16
inter-specific neighbors across the topography of the local landscape, which included gradients
17
of soil moisture, vapor pressure deficit, and topology (measured as elevation). Second, we
18
determined the spatial structure of environmental and intra- and interspecific variables (see
19
methods for detailed description of these variables) using piecewise Mantel correlograms
20
(Goslee and Urban, 2007). The Mantel correlogram is particularly useful for studying ecological
21
patterns in count data because it provides the spatial information in terms of distance apart rather
22
than geographical location using dissimilarity-based analysis (Urban et al., 2002). Third, we
23
evaluated plausible hypotheses on underlying processes using Mantel path analysis in the
4
1
presence and absence of space (Goslee et al., 2005). We asked: 1) what governs the spatial
2
distribution and performance of rockcress on a local scale? and 2) what is the relative importance
3
of factors governing the spatial distribution and performance at this scale?
4
Materials and Methods
5
Study Site
6
We studied spatial distribution and performance of rockcress (Boechera stricta (previously
7
Arabis drummondii (Al-Shehbaz, 2003)) plants occurring within a conspicuous highly populated
8
local area in the northern Black Hills, South Dakota, USA, (Lat: 44.403611, Long: -103.938403,
9
elevation 1365 m) during the summer of 2004. Rockcress plants grew within a 40 m x 50 m
10
meadow area surrounded by ponderosa pine (Pinus ponderosa), aspen (Populus tremuloides),
11
birch (Betula spp.) and burr oak (Quercus macrocarpa). Other common plant species that
12
inhabited the meadow were goldenrod (Solidago missouriensis), dandelion (Taraxacum
13
officinale), mouse-ear chickweed (Cerastium vulgatum), snowberry (Symphoricarpos albus) and
14
sedge (Carex spp.). The relief between the highest and the lowest measured point across the
15
study area was 9.55 m.
16
Environmental data
17
A hand-held probe (Theta Probe, Delta-T Devices) was used to measure surface (0-6 cm) soil
18
moisture and a hand-held sling psychrometer (Bacharach 12-7012; Bacharach, Inc. New
19
Kensington, PA) was used for vapor pressure deficit. These measurements were taken at 71
20
randomly selected locations once to represent the spatial gradient of environmental variables
21
across the meadow. 5
1
Sampling
2
Every rockcress individual (n = 234) in the study area was geolocated and sampled for growth
3
(diameter of basal rosette, rosette diameter) and reproductive fitness (number of reproductive
4
stalks, stalk number; reproductive stalk diameter, stalk diameter; and number of fruits, fruit
5
number). In addition, amount of herbivore damage (percent area consumed) on basal rosette
6
leaves (rosette herbivory) and reproductive stalk leaves (stalk herbivory) were recorded.
7
Herbivory was quantified for each plant by counting the number of holes ( 1 mm) that the flea
8
beetles chewed on the leaves of basal rosette and reproductive stalks. To determine the influence
9
of neighboring species on rockcress growth and performance two plant species, goldenrod and
10
dandelion were selected due to their abundance in the landscape in close proximity to rockcress
11
as compared to other species. The number of goldenrod (goldenrod density) and dandelion
12
(dandelion density) plants within a 15 cm radius of each rockcress plant was recorded. The 15
13
cm radius was an appropriate distance because of the small size and high density of the meadow
14
plants.
15
Additionally, to distinguish between environmental and genetic causes for spatial
16
patterns, we genotyped 142 randomly selected rockcress plants using 7 polymorphic
17
microsatellite loci and STRUCTURE software (Pritchard et al., 2000), available at
18
http://pritchardlab.stanford.edu/structure.html. Briefly, this technique identifies groups of
19
relatives, which in this case are self-fertilizing (inbred) lineages (hereafter, line), or in other
20
words, overlapping-generation dependents from common ancestors. Please see detailed
21
description of this technique in Siemens et al. (2009).
22
Statistical procedures
6
1
Bayesian Kriging
2
Maps of environmental variables were generated using spatial interpolation in a Bayesian
3
framework. A fully probabilistic Gaussian spatial process model (Diggle et al., 1998; Diggle and
4
Ribeiro, 2002) was used for Bayesian kriging, which assumes that conditional on a Gaussian
5
underlying process, S the observed data, Yi: i = 1, …n are independent with a distribution in the
6
exponential family. A brief summary of the modeling approach is given below; detailed
7
information can be found in (Diggle and Ribeiro, 2002). The model can be expressed in a
8
hierarchical framework as follows:
9
Level 1: Yi|S ~ N(β(xi) + S(xi), τ2)
10
Level 2: S(xi) ~ N(0, σ2R(h; ϕ))
11
Level 3: prior(β, σ2, ϕ, τ2)
12
The first level describes a spatial linear trend (β = trend parameter) based on spatially referenced
13
explanatory variables. τ2 (nugget) represents measurement variability and/or spatial variation
14
below the sampling grain. The second level describes a stationary Gaussian spatial process
15
(S(xi)) with mean = 0, variance = σ2 and correlation function R(h;ϕ), where ϕ is correlation
16
parameter (range of spatial autocorrelation = 3ϕ) and h is lag distance (vector distance between
17
two locations), and the third level specifies the prior for the model parameters. We chose an
18
exponential correlation function to quantify spatial autcorrelation:
19
R(h;ϕ) = exp(-h/ϕ)
20
The mean and variance of topography and environmental data were estimated at individual
21
locations from the predictive distribution using the krige.bayes function of geoR library (Ribeiro
22
Jr and Diggle, 2001) in R version 2.15.2 (R Development Core Team, 2012). This algorithm
23
samples a parameter value from a discrete posterior distribution computed from joint distribution
(1)
(2)
7
1
of parameters and priors. We assumed a constant trend mean model and chose a sensible
2
interval of values for each parameter considering the study site to generate a multidimensional
3
parameter (ϕ, σ2, and τ2.rel (relative nugget = τ2/σ2)) grid. Please refer to Appendix 1 for exact
4
intervals for individual parameters. Flat priors (see Fig. S1a-c for an example of prior and
5
posterior distributions) were chosen for ϕ, and τ2.rel, and a reciprocal prior for σ2. The sampled
6
parameter value is then attached to [β | Y, ϕ, σ2, τ2.rel] and a realization is obtained from the
7
predictive distribution at an unsampled location. A large sample size was generated by repeating
8
this process several times which allowed a stable estimation of the underlying distribution. The
9
mean and the variance of the predictive distribution were computed at unsampled spatial
10
locations using 100,000 posterior draws. Leave-One-Out cross-validation (Figure S1 in
11
supplements) was used for model validation. The maps of environmental variables were used to
12
obtain data at individual plant’s location to conduct the Mantel correlation analysis.
13
The piecewise Mantel correlogram and Mantel test
14
A correlogram in this context is a plot of the spatial autocorrelation with lag distance, and the
15
Mantel test can be used to test the significance of the correlations. A simple Mantel test
16
((Mantel, 1967; Goslee and Urban, 2007) was performed using Euclidean distance to explore
17
variation in spatial structure of topography (local vertical relief measured as elevation),
18
environmental drivers (soil moisture and vapor pressure deficit), fitness parameters (growth
19
(rosette diameter) and reproduction (stalk numbers, stalk diameter, fruit number), and line) of
20
rockcress, density of neighboring plants (goldenrod density and dandelion density), and
21
herbivory on rockcress leaves (rosette herbivory and stalk herbivory). Data were standardized
22
before calculating Euclidean distances (as recommended by Goslee (2010)) and the error was
23
computed using 10,000 permutations. Autocorrelation range was determined by looking at the 8
1
significance value (P ≤ 0.05) of the individual bins of lag distance at every 2.5 m in the
2
correlograms. A pairwise correlation between all the variables was determined using simple
3
Mantel test that guided the path analysis.
4
Mantel path analysis
5
Path analysis is a regression technique to explore causal connections among relevant factors. We
6
used Mantel path analysis to quantify direct and indirect influence of various biotic and abiotic
7
factors on spatial distribution and performance of rockcress population. Partial Mantel tests were
8
conducted to evaluate the plausible hypotheses (generated by combining the information from
9
correlograms and pairwise Mantel tests) on underlying ecological processes by looking at the
10
relationship between two variables and keeping all other variables constant. For example, given
11
the a priori hypothesis that A effects B and B effects C, the partial Mantel test can be used to test
12
if C effects A in the absence of B, C~ A|B. If A and/or C displayed significant spatial
13
autocorrelation then space was added as an additional partial, C~A|Space + B, in the partial
14
Mantel test (See Table S1 in supplements for all the hypotheses). The direction of relationships
15
was predetermined based on the common ecological knowledge. For instance, local relief
16
influences soil moisture and not the other way. Similarly, the number of reproductive stalks
17
influences the number of seeds and not vice versa. When the direction could not be determined
18
using this approach then it was left as a simple correlation between two variables. The R
19
package “ecodist” (Goslee and Urban 2007) was used to calculate the Mantel correlogram and
20
conduct Mantel path analysis.
21
Results
22
What governs the spatial distribution and performance of a rockcress population? 9
1
Microhabitat preference
2
Rockcress plants were not evenly distributed across the local landscape, occurring at highest
3
densities at the lower end of the N-facing slope and at relatively high soil moisture levels (Fig.
4
1a-f). All variables displayed significant spatial autocorrelation except soil moisture (Fig. 2a-c).
5
Elevation displayed significant spatial autocorrelation (Fig. 2a) and a negative relationship with
6
soil moisture (Mantel tests, P ≤ 0.05, Fig 3a), which was also present after accounting for the
7
spatial structure (partial Mantel tests, Fig. 4). In general, rockcress size and reproduction showed
8
a negative relationship with elevation, a positive relationship between soil moisture and no
9
relationship with vapor pressure deficit. Thus rockcress occurred more often in lower, moist
10
areas and in these areas growth and reproduction were also higher. These patterns were reflected
11
in correlograms showing significant (P ≤ 0.05) spatial autocorrelation among rockcress
12
individuals (Fig. 2b) and Mantel tests showing significant negative correlation between elevation
13
and rockcress (rosette diameter, stalk number and fruit number) as well as a positive relationship
14
between soil moisture and rockcress (stalk number) (Fig. 3a). The relationship between soil
15
moisture and stalk number was not significant after accounting for space (Fig. 4). Vapor
16
pressure deficit had no influence on rockcress size or fecundity. Dandelion density around
17
rockcress was highest towards mid-elevations (Fig. 1d) and no influence of vapor pressure deficit
18
was detected. The density of goldenrod plants around rockcress was positively correlated with
19
high vapor pressure deficit (Fig. 3a) but this relationship was not significant after accounting for
20
space.
21
Intra-specific Interactions
10
1
Rockcress growth (rosette diameter), reproduction (stalk number, fruit number), and line were
2
significantly spatially autocorrelated (Fig. 2b) with varying ranges from 6.4 m (line) to 20.8 m
3
(rosette diameter). Genetically similar individuals were found in close proximity of one
4
another (spatially autocorrelated, Fig. 2b) and rosette diameter had positive influence on
5
reproduction with and without space (Fig. 3b, 4). Spatial distribution patterns of rockcress had
6
both genetic (2b) and environmental (Fig. 3a, 4) components.
7
Insect herbivory on rockcress
8
Herbivory on rockcress rosette and reproductive stalk leaves showed significant (P ≤ 0.05)
9
spatial autocorrelation (rosette herbivory (range = 12.6 m), stalk herbivory (range = 8.4 m)) (Fig
10
2c). Spatial cross-correlation (Mantel tests, Fig. 3c) and cross-correlations after removing
11
multiple correlation and space (Partial Mantel tests, Fig.4, Table S1 in supplements) showed
12
positive relationship between rosette herbivory and stalk herbivory. Interspecific neighbor
13
density (dandelion density) around rockcress was positively correlated with rosette herbivory
14
(Fig 3c, 4), and herbivory on the leaves of reproductive stalks (stalk herbivory) was negatively
15
correlated with fruit production (fruit number) (Fig. 3c, 4), indicating negative impact of rosette
16
herbivory on rockcress reproductive performance.
17
Inter-specific interactions
18
Mantel correlograms showed significant (P ≤ 0.05) spatial autocorrelation in neighboring
19
densities of goldenrod (range = 12.6 m) and dandelion (range = 12.6 m) (Fig. 2c). Partial Mantel
20
tests did not indicate any relationship between rockcress and neighboring densities of goldenrod
21
and dandelion.
11
1
What is the relative importance of factors governing the spatial distribution and performance of
2
a rockcress population?
3
The spatial distribution of rockcress individuals across the landscape was greatly influenced by
4
the spatial distance (significant spatial autocorrelation, Fig. 2b) and local relief (Fig. 3).
5
Rockcress plants were generally crowded in N-facing slopes at lower elevations where there is
6
shade by trees (Fig. 1). Soil moisture and vapor pressure deficit did not show any significant
7
influence on spatial distribution of rockcress plants. Range of autocorrelation for genotypic
8
diversity (line) was the lowest among intra-specific traits that indicates greater intra-specific
9
diversity of rockcress plants within short distances. Inter-specific interactions showed some
10
indirect influence on rockcress distribution mediated through increased herbivory (Fig. 4).
11
Overall space and elevation and has the greatest influence on spatial distribution of rockcress
12
individuals.
13
Elevation, soil moisture and vapor pressure deficit did not display any significant
14
influence on rockcress performance. Intra-specific interactions and insect herbivory are the main
15
drivers of rockcress performance. Additionally, indirect influence of inter-specific interactions
16
on rockcress performance were evident (Fig. 3, 4).
17
Discussion
18
Microhabitat preference
19
Spatial autocorrelation for plant performance and genetic variation indicate spatial aggregation
20
among related plants for general fitness, which is most likely a consequence of limited dispersal
21
and habitat heterogeneity. Facilitation among con-specific plants is a less likely explanation,
22
given inter-plant spacing among rockcress individuals was typically much greater than the reach 12
1
of canopies or root systems; the nearest neighbors of the rockcress plants were often other
2
species of plants. Genetic similarities decreased at shorter distances (
Abiotic and biotic controls on local spatial distribution and performance of Boechera stricta KUSUM J NAITHANI, Brent E. Ewers, Jonathan D. Adelman and David H. Siemens
Journal Name:
Frontiers in Plant Science
ISSN:
1664-462X
Article type:
Original Research Article
Received on:
07 Mar 2014
Accepted on:
28 Jun 2014
Provisional PDF published on:
28 Jun 2014
www.frontiersin.org:
www.frontiersin.org
Citation:
Naithani KJ, Ewers BE, Adelman JD and Siemens DH(2014) Abiotic and biotic controls on local spatial distribution and performance of Boechera stricta. Front. Plant Sci. 5:348. doi:10.3389/fpls.2014.00348
Copyright statement:
© 2014 Naithani, Ewers, Adelman and Siemens. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
This Provisional PDF corresponds to the article as it appeared upon acceptance, after rigorous peer-review. Fully formatted PDF and full text (HTML) versions will be made available soon.
1
Abiotic and biotic controls on local spatial distribution and performance of
2
Boechera stricta
3 4
K. J. Naithani, 1,2,4,†, B. E. Ewers1,2, J. D. Adelman2, D. H. Siemens3
5
1
Program in Ecology, University of Wyoming, Laramie, WY 82071 USA
6
2
Department of Botany, University of Wyoming, Laramie, WY 82071 USA
7
3
Department of Biology, Black Hills State University, Spearfish, SD 57799 USA
8
4
Present address: Department of Geography, The Pennsylvania State University, University Park,
9
PA 16802 USA
10
† Email: [email protected]
11 12
1
1
Abstract
2
This study investigates the relative influence of biotic and abiotic factors on community
3
dynamics using an integrated approach and highlights the influence of space on genotypic and
4
phenotypic traits in plant community structure. We examined the relative influence of
5
topography, environment, spatial distance, and intra- and interspecific interactions on spatial
6
distribution and performance of Boechera stricta (rockcress), a close perennial relative of model
7
plant Arabidopsis. First, using Bayesian kriging, we mapped the topography and environmental
8
gradients and explored the spatial distribution of naturally occurring rockcress plants and two
9
neighbors, Taraxacum officinale (dandelion) and Solidago missouriensis (goldenrod) found in
10
close proximity within a typical diverse meadow community across topographic and
11
environmental gradients. We then evaluated direct and indirect relationships among variables
12
using Mantel path analysis and developed a network displaying abiotic and biotic interactions in
13
this community. We found significant spatial autocorrelation among rockcress individuals,
14
either because of common microhabitats as displayed by high density of individuals at lower
15
elevation and high soil moisture area, or limited dispersal as shown by significant spatial
16
autocorrelation of naturally occurring inbred lines, or a combination of both. Goldenrod and
17
dandelion density around rockcress does not show any direct relationship with rockcress
18
fecundity, possibly due to spatial segregation of resources. However, dandelion density around
19
rockcress shows an indirect negative influence on rockcress fecundity via herbivory, indicating
20
interspecific competition. Overall, we suggest that common microhabitat preference and limited
21
dispersal are the main drivers for spatial distribution. However, intra-specific interactions and
22
insect herbivory are the main drivers of rockcress performance in the meadow community.
2
1
Key words:
2
Bayesian kriging, competition, correlogram, Mantel tests, path analysis, spatial interaction,
3
spatial pattern
4
Introduction
5
Spatial patterns are a crucial, but often overlooked, component to understanding the factors and
6
processes that structure plant communities (Levin, 1992; Jeltsch et al., 1999; McIntire and
7
Fajardo, 2009). Spatial distribution and performance (i.e. growth and reproduction) of any plant
8
species depends on the ability to cope with environment, most notably topography, soil
9
properties, and moisture availability (Goslee et al., 2005), intraspecific genotype variation of
10
plant species (Crutsinger et al. 2006; Lankau & Strauss 2007), intra- and interspecific plant-plant
11
interactions (Callaway and Walker, 1997; Holzapfel and Mahall, 1999; Pugnaire and Luque,
12
2001; Brooker et al., 2008; Genung et al., 2012), and insect herbivory (Becerra, 2007; Bloom et
13
al., 2003; Marquis, 1992). Investigating the relative importance of these controlling factors is
14
critical to understanding the underlying processes that structure plant communities. This study
15
describes the first application of an integrated approach using molecular, ecological, and
16
statistical tools to quantify the relative influence of biotic and abiotic factors on the spatial
17
distribution and performance of Boechera stricta (rockcress), an emerging ecological model
18
plant species (Rushworth et al. 2011). Such species show great promise for understanding
19
genetic controls on ecologically important traits (Song and Mitchell-Olds, 2011) and provide
20
opportunity to explore underlying mechanisms in natural populations, compared to artificial
21
experimental settings. Rockcress is widely distributed in the western United States (Song and
22
Mitchell-Olds, 2011) and shows local adaptations in diverse ecological habitats (Mitchell-Olds,
3
1
2001; Knight et al., 2006; Song et al., 2006), making it an ideal species to study the biotic and
2
abiotic controls on species distribution and growth in natural settings.
3
Combinations of complementary mathematical and statistical techniques have been used
4
in recent studies to investigate links between observed spatial patterns and underlying ecological
5
processes (e.g., process models and geostatistics (Loranty et al., 2008); multiple ordination and
6
geostatistics (Wagner, 2003); Structural Equation Modeling and Bayesian statistics (Arhonditsis
7
et al., 2006); mixed models and Bayesian kriging (Smithwick et al., 2012); and Mantel tests and
8
path analysis (Goslee et al., 2005)). The integration of these tools can provide information about
9
spatial structure of variables and potential underlying ecological processes. Here, we integrated
10
Bayesian kriging (Diggle et al., 1998; Diggle and Ribeiro, 2002), a novel data-model fusion
11
approach for spatial interpolation of topography and environmental data across the local
12
landscape, and Mantel path analysis (Mantel, 1967; Leduc et al., 1992; Goslee et al., 2005) to
13
infer the relative importance of microhabitat preference, limited dispersal, competition, and
14
herbivory in determining the spatial distribution and performance on a local scale.
15
First, we examined the spatial distribution of rockcress individuals and the density of
16
inter-specific neighbors across the topography of the local landscape, which included gradients
17
of soil moisture, vapor pressure deficit, and topology (measured as elevation). Second, we
18
determined the spatial structure of environmental and intra- and interspecific variables (see
19
methods for detailed description of these variables) using piecewise Mantel correlograms
20
(Goslee and Urban, 2007). The Mantel correlogram is particularly useful for studying ecological
21
patterns in count data because it provides the spatial information in terms of distance apart rather
22
than geographical location using dissimilarity-based analysis (Urban et al., 2002). Third, we
23
evaluated plausible hypotheses on underlying processes using Mantel path analysis in the
4
1
presence and absence of space (Goslee et al., 2005). We asked: 1) what governs the spatial
2
distribution and performance of rockcress on a local scale? and 2) what is the relative importance
3
of factors governing the spatial distribution and performance at this scale?
4
Materials and Methods
5
Study Site
6
We studied spatial distribution and performance of rockcress (Boechera stricta (previously
7
Arabis drummondii (Al-Shehbaz, 2003)) plants occurring within a conspicuous highly populated
8
local area in the northern Black Hills, South Dakota, USA, (Lat: 44.403611, Long: -103.938403,
9
elevation 1365 m) during the summer of 2004. Rockcress plants grew within a 40 m x 50 m
10
meadow area surrounded by ponderosa pine (Pinus ponderosa), aspen (Populus tremuloides),
11
birch (Betula spp.) and burr oak (Quercus macrocarpa). Other common plant species that
12
inhabited the meadow were goldenrod (Solidago missouriensis), dandelion (Taraxacum
13
officinale), mouse-ear chickweed (Cerastium vulgatum), snowberry (Symphoricarpos albus) and
14
sedge (Carex spp.). The relief between the highest and the lowest measured point across the
15
study area was 9.55 m.
16
Environmental data
17
A hand-held probe (Theta Probe, Delta-T Devices) was used to measure surface (0-6 cm) soil
18
moisture and a hand-held sling psychrometer (Bacharach 12-7012; Bacharach, Inc. New
19
Kensington, PA) was used for vapor pressure deficit. These measurements were taken at 71
20
randomly selected locations once to represent the spatial gradient of environmental variables
21
across the meadow. 5
1
Sampling
2
Every rockcress individual (n = 234) in the study area was geolocated and sampled for growth
3
(diameter of basal rosette, rosette diameter) and reproductive fitness (number of reproductive
4
stalks, stalk number; reproductive stalk diameter, stalk diameter; and number of fruits, fruit
5
number). In addition, amount of herbivore damage (percent area consumed) on basal rosette
6
leaves (rosette herbivory) and reproductive stalk leaves (stalk herbivory) were recorded.
7
Herbivory was quantified for each plant by counting the number of holes ( 1 mm) that the flea
8
beetles chewed on the leaves of basal rosette and reproductive stalks. To determine the influence
9
of neighboring species on rockcress growth and performance two plant species, goldenrod and
10
dandelion were selected due to their abundance in the landscape in close proximity to rockcress
11
as compared to other species. The number of goldenrod (goldenrod density) and dandelion
12
(dandelion density) plants within a 15 cm radius of each rockcress plant was recorded. The 15
13
cm radius was an appropriate distance because of the small size and high density of the meadow
14
plants.
15
Additionally, to distinguish between environmental and genetic causes for spatial
16
patterns, we genotyped 142 randomly selected rockcress plants using 7 polymorphic
17
microsatellite loci and STRUCTURE software (Pritchard et al., 2000), available at
18
http://pritchardlab.stanford.edu/structure.html. Briefly, this technique identifies groups of
19
relatives, which in this case are self-fertilizing (inbred) lineages (hereafter, line), or in other
20
words, overlapping-generation dependents from common ancestors. Please see detailed
21
description of this technique in Siemens et al. (2009).
22
Statistical procedures
6
1
Bayesian Kriging
2
Maps of environmental variables were generated using spatial interpolation in a Bayesian
3
framework. A fully probabilistic Gaussian spatial process model (Diggle et al., 1998; Diggle and
4
Ribeiro, 2002) was used for Bayesian kriging, which assumes that conditional on a Gaussian
5
underlying process, S the observed data, Yi: i = 1, …n are independent with a distribution in the
6
exponential family. A brief summary of the modeling approach is given below; detailed
7
information can be found in (Diggle and Ribeiro, 2002). The model can be expressed in a
8
hierarchical framework as follows:
9
Level 1: Yi|S ~ N(β(xi) + S(xi), τ2)
10
Level 2: S(xi) ~ N(0, σ2R(h; ϕ))
11
Level 3: prior(β, σ2, ϕ, τ2)
12
The first level describes a spatial linear trend (β = trend parameter) based on spatially referenced
13
explanatory variables. τ2 (nugget) represents measurement variability and/or spatial variation
14
below the sampling grain. The second level describes a stationary Gaussian spatial process
15
(S(xi)) with mean = 0, variance = σ2 and correlation function R(h;ϕ), where ϕ is correlation
16
parameter (range of spatial autocorrelation = 3ϕ) and h is lag distance (vector distance between
17
two locations), and the third level specifies the prior for the model parameters. We chose an
18
exponential correlation function to quantify spatial autcorrelation:
19
R(h;ϕ) = exp(-h/ϕ)
20
The mean and variance of topography and environmental data were estimated at individual
21
locations from the predictive distribution using the krige.bayes function of geoR library (Ribeiro
22
Jr and Diggle, 2001) in R version 2.15.2 (R Development Core Team, 2012). This algorithm
23
samples a parameter value from a discrete posterior distribution computed from joint distribution
(1)
(2)
7
1
of parameters and priors. We assumed a constant trend mean model and chose a sensible
2
interval of values for each parameter considering the study site to generate a multidimensional
3
parameter (ϕ, σ2, and τ2.rel (relative nugget = τ2/σ2)) grid. Please refer to Appendix 1 for exact
4
intervals for individual parameters. Flat priors (see Fig. S1a-c for an example of prior and
5
posterior distributions) were chosen for ϕ, and τ2.rel, and a reciprocal prior for σ2. The sampled
6
parameter value is then attached to [β | Y, ϕ, σ2, τ2.rel] and a realization is obtained from the
7
predictive distribution at an unsampled location. A large sample size was generated by repeating
8
this process several times which allowed a stable estimation of the underlying distribution. The
9
mean and the variance of the predictive distribution were computed at unsampled spatial
10
locations using 100,000 posterior draws. Leave-One-Out cross-validation (Figure S1 in
11
supplements) was used for model validation. The maps of environmental variables were used to
12
obtain data at individual plant’s location to conduct the Mantel correlation analysis.
13
The piecewise Mantel correlogram and Mantel test
14
A correlogram in this context is a plot of the spatial autocorrelation with lag distance, and the
15
Mantel test can be used to test the significance of the correlations. A simple Mantel test
16
((Mantel, 1967; Goslee and Urban, 2007) was performed using Euclidean distance to explore
17
variation in spatial structure of topography (local vertical relief measured as elevation),
18
environmental drivers (soil moisture and vapor pressure deficit), fitness parameters (growth
19
(rosette diameter) and reproduction (stalk numbers, stalk diameter, fruit number), and line) of
20
rockcress, density of neighboring plants (goldenrod density and dandelion density), and
21
herbivory on rockcress leaves (rosette herbivory and stalk herbivory). Data were standardized
22
before calculating Euclidean distances (as recommended by Goslee (2010)) and the error was
23
computed using 10,000 permutations. Autocorrelation range was determined by looking at the 8
1
significance value (P ≤ 0.05) of the individual bins of lag distance at every 2.5 m in the
2
correlograms. A pairwise correlation between all the variables was determined using simple
3
Mantel test that guided the path analysis.
4
Mantel path analysis
5
Path analysis is a regression technique to explore causal connections among relevant factors. We
6
used Mantel path analysis to quantify direct and indirect influence of various biotic and abiotic
7
factors on spatial distribution and performance of rockcress population. Partial Mantel tests were
8
conducted to evaluate the plausible hypotheses (generated by combining the information from
9
correlograms and pairwise Mantel tests) on underlying ecological processes by looking at the
10
relationship between two variables and keeping all other variables constant. For example, given
11
the a priori hypothesis that A effects B and B effects C, the partial Mantel test can be used to test
12
if C effects A in the absence of B, C~ A|B. If A and/or C displayed significant spatial
13
autocorrelation then space was added as an additional partial, C~A|Space + B, in the partial
14
Mantel test (See Table S1 in supplements for all the hypotheses). The direction of relationships
15
was predetermined based on the common ecological knowledge. For instance, local relief
16
influences soil moisture and not the other way. Similarly, the number of reproductive stalks
17
influences the number of seeds and not vice versa. When the direction could not be determined
18
using this approach then it was left as a simple correlation between two variables. The R
19
package “ecodist” (Goslee and Urban 2007) was used to calculate the Mantel correlogram and
20
conduct Mantel path analysis.
21
Results
22
What governs the spatial distribution and performance of a rockcress population? 9
1
Microhabitat preference
2
Rockcress plants were not evenly distributed across the local landscape, occurring at highest
3
densities at the lower end of the N-facing slope and at relatively high soil moisture levels (Fig.
4
1a-f). All variables displayed significant spatial autocorrelation except soil moisture (Fig. 2a-c).
5
Elevation displayed significant spatial autocorrelation (Fig. 2a) and a negative relationship with
6
soil moisture (Mantel tests, P ≤ 0.05, Fig 3a), which was also present after accounting for the
7
spatial structure (partial Mantel tests, Fig. 4). In general, rockcress size and reproduction showed
8
a negative relationship with elevation, a positive relationship between soil moisture and no
9
relationship with vapor pressure deficit. Thus rockcress occurred more often in lower, moist
10
areas and in these areas growth and reproduction were also higher. These patterns were reflected
11
in correlograms showing significant (P ≤ 0.05) spatial autocorrelation among rockcress
12
individuals (Fig. 2b) and Mantel tests showing significant negative correlation between elevation
13
and rockcress (rosette diameter, stalk number and fruit number) as well as a positive relationship
14
between soil moisture and rockcress (stalk number) (Fig. 3a). The relationship between soil
15
moisture and stalk number was not significant after accounting for space (Fig. 4). Vapor
16
pressure deficit had no influence on rockcress size or fecundity. Dandelion density around
17
rockcress was highest towards mid-elevations (Fig. 1d) and no influence of vapor pressure deficit
18
was detected. The density of goldenrod plants around rockcress was positively correlated with
19
high vapor pressure deficit (Fig. 3a) but this relationship was not significant after accounting for
20
space.
21
Intra-specific Interactions
10
1
Rockcress growth (rosette diameter), reproduction (stalk number, fruit number), and line were
2
significantly spatially autocorrelated (Fig. 2b) with varying ranges from 6.4 m (line) to 20.8 m
3
(rosette diameter). Genetically similar individuals were found in close proximity of one
4
another (spatially autocorrelated, Fig. 2b) and rosette diameter had positive influence on
5
reproduction with and without space (Fig. 3b, 4). Spatial distribution patterns of rockcress had
6
both genetic (2b) and environmental (Fig. 3a, 4) components.
7
Insect herbivory on rockcress
8
Herbivory on rockcress rosette and reproductive stalk leaves showed significant (P ≤ 0.05)
9
spatial autocorrelation (rosette herbivory (range = 12.6 m), stalk herbivory (range = 8.4 m)) (Fig
10
2c). Spatial cross-correlation (Mantel tests, Fig. 3c) and cross-correlations after removing
11
multiple correlation and space (Partial Mantel tests, Fig.4, Table S1 in supplements) showed
12
positive relationship between rosette herbivory and stalk herbivory. Interspecific neighbor
13
density (dandelion density) around rockcress was positively correlated with rosette herbivory
14
(Fig 3c, 4), and herbivory on the leaves of reproductive stalks (stalk herbivory) was negatively
15
correlated with fruit production (fruit number) (Fig. 3c, 4), indicating negative impact of rosette
16
herbivory on rockcress reproductive performance.
17
Inter-specific interactions
18
Mantel correlograms showed significant (P ≤ 0.05) spatial autocorrelation in neighboring
19
densities of goldenrod (range = 12.6 m) and dandelion (range = 12.6 m) (Fig. 2c). Partial Mantel
20
tests did not indicate any relationship between rockcress and neighboring densities of goldenrod
21
and dandelion.
11
1
What is the relative importance of factors governing the spatial distribution and performance of
2
a rockcress population?
3
The spatial distribution of rockcress individuals across the landscape was greatly influenced by
4
the spatial distance (significant spatial autocorrelation, Fig. 2b) and local relief (Fig. 3).
5
Rockcress plants were generally crowded in N-facing slopes at lower elevations where there is
6
shade by trees (Fig. 1). Soil moisture and vapor pressure deficit did not show any significant
7
influence on spatial distribution of rockcress plants. Range of autocorrelation for genotypic
8
diversity (line) was the lowest among intra-specific traits that indicates greater intra-specific
9
diversity of rockcress plants within short distances. Inter-specific interactions showed some
10
indirect influence on rockcress distribution mediated through increased herbivory (Fig. 4).
11
Overall space and elevation and has the greatest influence on spatial distribution of rockcress
12
individuals.
13
Elevation, soil moisture and vapor pressure deficit did not display any significant
14
influence on rockcress performance. Intra-specific interactions and insect herbivory are the main
15
drivers of rockcress performance. Additionally, indirect influence of inter-specific interactions
16
on rockcress performance were evident (Fig. 3, 4).
17
Discussion
18
Microhabitat preference
19
Spatial autocorrelation for plant performance and genetic variation indicate spatial aggregation
20
among related plants for general fitness, which is most likely a consequence of limited dispersal
21
and habitat heterogeneity. Facilitation among con-specific plants is a less likely explanation,
22
given inter-plant spacing among rockcress individuals was typically much greater than the reach 12
1
of canopies or root systems; the nearest neighbors of the rockcress plants were often other
2
species of plants. Genetic similarities decreased at shorter distances (
