Predicting Microstegium vimineum invasion in intact forests of the southern Blue Ridge
Mountains, U.S.A.
5
Dean P. Anderson, Monica G. Turner, Scott M. Pearson, Thomas P. Albright, Robert K. Peet
and Ann Wieben
D.P. Anderson (Corresponding author): Landcare Research, P.O. Box 40, Lincoln, New
Zealand. Email: andersond@landcareresearch.co.nz
10
M.G. Turner · A. Wieben: Department of Zoology, University of Wisconsin – Madison, 430
Lincoln Drive, Madison, WI 53760.
S.M. Pearson: Biology Department, Mars Hill College, Mars Hill, NC 28754
15
T.P. Albright: Department of Forest and Wildlife Ecology, University of Wisconsin,
Madison, WI 53706, USA.
R.K. Peet: Department of Biology, University of North Carolina, Chapel Hill, NC 2759920
3280.
Date: 10 September 2010
Word count: 6504
25
1
Abstract
The spread and establishment of invasive plant species is determined by interacting
broad-scale factors that influence the movement of propagules across the landscape and finescale factors that determine local suitability for recruitment. Shade tolerance may facilitate
30
deep incursions of non-native invasives into intact forest communities, but detection of such
species can be difficult because occurrences may be sparse and subsequent rates of spread are
typically slow. Further, the distribution of such species may exhibit spatial aggregation that is
not explained by environmental factors because propagules are not likely to have reached all
areas of a landscape. We examined broad- and fine-scale factors that may influence the
35
distribution of the shade-tolerant Microstegium vimineum (Trin.) A. Camus in forests of the
southern Blue Ridge Mountains, U.S.A. We modeled the spatial structure of M. vimineum to
predict its presence in intact forest and gain insight into the spatial scale of the present
invasion. Analysis using Markov-chain Monte Carlo revealed that, at broad scales, intact
forests surrounded by areas with high human activity and low forest cover were at highest risk
40
of M. vimineum invasion. At fine spatial scales, the probability of M. vimineum presence
increased with increasing native species richness, increasing soil pH and decreasing basal area
of acidophilic shrubs (Ericaceae). After accounting for environmental covariates, spatial
parameters revealed that intact forests within 3 km of established M. vimineum populations
were at an elevated risk of invasion.
45
Keywords
invasive species, Markov-chain Monte Carlo, propagule pressure, soil fertility, speciesdistribution model, species richness, variogram
2
Introduction
50
Non-native invasive plant species are recognised as a major threat to ecosystem
structure and function (Vitousek et al. 1987; Wilcove et al. 1998; Asner et al. 2008; Hejda et
al. 2009). Basic and applied environmental research in recent years has focused on
understanding factors that influence the spread and establishment of invasive species, with the
eventual aim of predicting and controlling invasions. A common finding in invasive research
55
is that invasive plant species abundance increases with human-related disturbance and
movement of propagules along roads, trails and water ways (Hodkinson and Thompson 1997;
Von der Lippe and Kowarik 2007). Rates of establishment are lower in intact natural areas
(Lonsdale 1999) where disturbance and invasive propagule pressure are low (Eschtruth and
Battles 2009), however shade-tolerant invasives can have detrimental and long-term impacts
60
on intact forests (Martin et al. 2009). Detection of such species can be especially difficult in
areas of dense, closed-canopy forest because occurrences of the invader may be few and its
subsequent rate of spread is often slow. Nonetheless, understanding the spatial patterns of
such invasions is critical for anticipating future changes in forest understory composition.
Furthermore, models that predict the landscape patterns of vulnerability for intact forest can
65
help target locations where control is likely to be warranted and effective.
Species distribution modelling is a common ecological tool for examining species’
responses to environmental conditions (Austin and Meyers 1996; Midgley et al. 2002;
Matthiopoulos et al. 2004) and can contribute to our understanding of invasive movement and
establishment. In its most simple form, this approach assumes that a species is distributed
70
according to environmental conditions, and that individuals in a population have equal chance
of arriving at all locations in a specified study area. Important ecological processes (e.g.,
3
behaviour, dispersal, reproduction, competition and predation), however, are likely to affect
distribution patterns in addition to environmental factors (Wagner and Fortin 2005). In the
case of invasive plant species, invasion is an ongoing process. Even if a species has covered
75
the extent of a region at a broad scale, it is likely to be absent in certain areas because
propagules have not yet arrived in sufficient numbers to become established.
If an invasive species is not well established across a landscape one would expect to
find high spatial structure that is not accounted for by environmental variables in a species
distribution model (Henebry 1995; Wagner and Fortin 2005). This may result in absences in
80
favourable areas predicted by the model, because the species has not yet arrived in those
locations. Alternatively, high propagule pressure may lead to presences in areas predicted to
be relatively unsuitable. With regard to inference, spatial structure excluded from statistical
models can lead to inflated type I error rates (Cliff and Ord 1981; Lichstein et al. 2002) or
erroneous inference on model parameters (Kühn 2007). If modelled appropriately, however,
85
inference on model parameters should be correct (Bannerjee et al. 2004; Wagner and Fortin
2005), and spatial structure can provide insight into biological process (Legendre 1993; Palma
et al. 1999). For an invasive-plant-species model, residual spatial structure should indicate a
lack of equilibrium and the spatial scale of establishment around a focal source of propagules.
Existing vegetation survey data could be a valuable resource for detecting invasion
90
patterns, especially in habitats where species may be inconspicuous and spread slowly. The
feasibility of such analyses is also improved because new statistical approaches provide
methods for testing predicted relationships among variables and quantifying residual spatial
structure in data even when sampled occurrences are sparse within a large data set. In this
study, we developed Bayesian models to analyze vegetation data that were collected in intact
4
95
forests over seven years across a 16,000-km2 mountainous region for which presence of a
non-native invasive herb was recorded. We modeled the spatial structure of the species
occurrence in relatively undisturbed forests to identify plot- and landscape-level covariates of
present presence and to quantify the spatial scale of the invasion process.
Our focal species was Microstegium vimineum (Trin.) A. Camus, (Japanese stilt
100
grass), a C4 annual grass native to Asia (Barden 1987). It was first recorded in the eastern
United States in 1917 (Fairbrothers and Gray 1972) and is now widely distributed (Redman
2008). Microstegium vimineum is shade tolerant (Winter et al. 1982) and can become the
dominant herbaceous species in invaded areas (Barden 1987; Cole and Weltzin 2005; Redman
2008), altering community composition (Fairbrothers and Gray 1972; Barden 1987) and
105
ecosystem processes (Kourtev et al. 1998; Ehrenfeld et al. 2001). It is primarily gravity
dispersed and has limited dispersibility (Cheplick 2010). At fine spatial scales, it forms dense,
discrete patches, and evidence suggests that this pattern is influenced by mid-story canopy
cover and soil pH (Cole and Weltzin 2004, 2005). We used a region-wide analysis of
presence/absence data collected in natural undisturbed forests to address two questions: (1)
110
what local and landscape factors influence the probability of presence of M. vimineum?; and
(2) what is the scale of spatial structure in the data that is not accounted for by the
environmental variables?
The establishment of M. vimineum should be influenced by propagule pressure and
suitability of growing conditions for herbaceous species. Consequently, we anticipated that
115
the probability of presence would increase with increasing proximity to human vectors for
propagules (roads and development) and decrease with increasing intact forest cover. At the
scale of this study, we expected invasives to do well in environments where native herbs do
5
well (Lonsdale 1999; Stohlgren et al. 1999; Sandel and Corbin 2010); therefore, we expected
a positive relationship between native herbaceous species richness and the probability of
120
presence of M. vimineum. In particular, increasing soil pH and cation concentrations should
facilitate establishment of M. vimineum (Peet et al. 1998; Peet et al. 2003; Adams and
Engelhardt 2009). Shading by trees and shrubs is not expected to inhibit the shade-tolerant M.
vimineum; however, an increasing local abundance of acidophilic Ericaceae shrubs, and hence
decreasing pH, should correspond with a decreasing probability of presence. Finally, because
125
of its limited dispersibility, we expected M. vimineum to not be at equilibrium in the
environment, (e.g. not present in all areas predicted to be suitable), and that this would be
reflected in the model variance. Explicit modelling of the spatial structure of model residuals
(errors) was expected to provide accurate inference on biological parameters and insights into
the scale of local invasions.
130
Methods
Study site and data acquisition
Data for this analysis were collected in the Southern Blue Ridge Province of the
southern Appalachian Mountains in western North Carolina, U.S.A. (Figure 1). The region is
135
largely forested and characterized by high topographic variation (250 m – 2,037 m asl). We
extracted data from the database of the Carolina Vegetation Survey (CVS), which collects
comprehensive data to characterize the natural vegetation of the region (Peet et al. 1998; Peet
et al. 2005). CVS sampling sites were located across a range of vegetation cover types that
were deemed to represent natural vegetation. A standardized sampling protocol recorded
140
vegetation composition and structure within a varying number of adjacent 10 x 10 m modules.
6
Most commonly 10 modules (1000 m2) were recorded as a 2 x 5 array. We extracted data
collected on M. vimineum from 1995 to 2001. The presence or absence of M. vimineum was
recorded at the site level and found 26 occurrences out of 434 sites. The number of modules
sampled varied between 1 and 10. Some of the modules were sampled in “aggregate”, which
145
means that only a single presence or absence record was available for multiple modules
within a site. Our response variable, consequently, is the presence/absence of M. vimineum
across all modules at a site, which we relate to a suite of landscape- and plot-level covariates
(Table 1).
150
Plot covariates
Plot covariates were those that were collected by the CVS. At each site the CVS
quantified the native herbaceous species richness, basal area of woody species, and soil
conditions. Species richness is scale dependent (Fridley et al. 2005), and because the number
of modules varied by site, we calculated the mean richness as the mean number of species per
155
100 m2 module. Shrub and tree basal area is the basal area of woody vegetation with a
diameter at breast height (dbh) of < 5 cm and ≥ 5 cm, respectively, divided by the area
sampled. The basal area of ericaceous shrubs was also extracted separately from the CVS data
base. Soil pH, and concentrations (parts per million) of calcium, magnesium and manganese
were measured in samples collected from the top 10 cm of mineral soil from each sampling
160
module (after removal of litter layer; Peet et al. 1998; Peet et al. 2003). Mean values for each
soil chemistry attribute across all modules at a site were used in the analysis. While soil
chemistry can vary at multiple spatial scales (Ettema and Wardle 2002) we were interested in
the relationship between broad-scale patterns in soils and the presence of M. vimineum.
7
165
Landscape covariates
Landscape covariates were those derived from GIS data and thought to influence the
distribution of M. vimineum. Elevation, slope and aspect were created from a digital elevation
map obtained from the National Elevation Database (Gesch et al. 2002). Aspect was
transformed to “southwestness” (sw):
170
sw = sin( + 22) + 1
where  is aspect. This index represents the directional deviation from the sun at the warmest
time of the day (Beers et al. 1996). We calculated an insolation index (s):
s = sin((/90) * 180) * sw
which incorporates slope () and the transformed southwestness variable (sw) (Gustafson et
175
al. 2003). We created a relative-slope-position index, which is a continuous measure of the
height of a pixel relative to its neighbors in a 7 x 7 cell neighborhood (Homer et al. 2004).
This index varies from 100 if a pixel is on a summit or ridge, (higher than all neighbouring
pixels), to 0 if it is the lowest in the neighbourhood, such as in a valley. The 7 x 7 cell
neighborhood (4.41 ha) was selected because it captures the relative slope position well in this
180
mountainous terrain.
We used the National Land Cover Database (NLCD) (Homer et al. 2004) to create
variables describing forest cover and human development. We calculated the percentage of
cells with forest cover in the 7 x 7 cell neighbourhood surrounding each site. Fragstats
(McGarigal and Marks 1995) was used to calculate forest-edge density in a 7 x 7 cell
185
neighborhood around each site. Impervious surface and human development were quantified
as the percentage (ranging from 0-100) in a 7 x 7 cell neighbourhood. Lastly, we used GIS
8
data on roads obtained from the Coweeta Long Term Ecological Research website
(http://coweeta.ecology.uga.edu) to quantify road density in km/km2 in a 7 x 7 cell
neighbourhood and to calculate distance to nearest road.
190
Modelling approach
Because of the high number of landscape and plot-level covariates and the inherent
multicollinearity, we used principal component analysis (PCA) to reduce the variables to
orthogonal axes. The PCA was conducted separately for landscape and plot variables so as to
195
facilitate the differentiation of local and landscape effects on M. vimineum. Markov chain
Monte Carlo was used to make Bayesian inference, which is an effective means for modelling
small sample sizes (Clark 2005) and residual spatial autocorrelation (Wagner and Fortin
2005). Due to the limited number of occurrences of M. vimineum and high computation time,
we explored 4 a priori models (Table 2), which were restricted to 2 or fewer covariates.
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Data analysis
We modelled the presence/absence data (yij) across sites (i) and years (j) as a
Bernouilli process:
yij ~ Bernouilli ij 
205
logit ij   X i    j   i   i
where θij is the probability of a presence, Xiβ is the product of the environmental covariates
and the associated coefficients, αj is a random year effect, and γi is an offset variable equal to
the natural logarithm of the number of modules sampled. The offset variable has a coefficient
fixed at 1 and serves to account for the differing sampling effort among sites. Environmental
9
210
covariates were scaled to have a mean 0 and standard deviation 1. A logit transform was used
to constrain the Bernouilli-distributed probability to the range 0 – 1.
We included a powered-exponential spatial covariance error structure (Cs) to account
for spatial autocorrelation not explained by the environmental covariates:
 i ~ N (0, Cs )
215

Cs   2 e  (d )
where σ2 is the variance, φ is a correlation-distance parameter, d is the distance between sites,
and κ is a smoothing parameter (Cressie 1993).
We employed a Bayesian approach and Markov chain Monte Carlo (MCMC) to obtain
posterior distributions for our model parameters. The posterior probability distribution is
220
proportional to the product of the yij and the θij likelihoods, and the priors.

p  param eters| data  Bin y ij | 1, ij  N Logit ij  | X i  ,  j ,  i ,  2 ,  , 
 N  | 0,1000
 N  j | 0,1000
  


 N ln  2 | ln3,1
 N ln  | ln1,1
 N ln  | ln1,1
The environmental parameters (β) and year effects (α) were sampled directly from the
225
conditional posteriors, and the spatial covariance parameters (σ, φ, κ) were sampled with a
Metropolis-Hastings rejection algorithm. Within-chain serial autocorrelation was assessed to
determine the appropriate thinning rate. Convergence on the posterior target distribution was
confirmed with a scale reduction factor (Rˆ ) < 1.2 calculated on 4 parallel chains (Gelman and
Rubin 1992; Gelman et al. 2004). Convergence for all models was achieved with 500,000
230
iterations, and posterior summaries were taken from 4 chains containing 200,000 samples
10
with a thinning rate of 10 (i.e., 80,000 samples). We used the Deviance Information Criterion
(DIC) to compare competing models (Spiegelhalter et al. 2002).
Results
235
The first 3 axes of the principal components analysis of the landscape variables
accounted for 30.8%, 19.2% and 12.5% respectively of the variance (Table 3; Figure 2A). The
first axis largely describes the environmental gradient from areas with high human
development (buildings, roads, impervious surfaces, and forest edge) to areas with high forest
cover and high terrain indices. Axis 2 is dominated by the gradient from high to low
240
southwest aspects and solar indices. Axis 3 describes elevation and relative topographic
position with high values representing relatively flat slopes in valleys, and low axis values
represent high elevation areas on ridges (high terrain index). Road density was retained in
place of distance to nearest road in the PCA as it resulted in a higher proportion of variance
explained. We used only Axis 1 from the landscape variable PCA (LandscapePCA1) in our
245
subsequent modelling as preliminary analysis indicated that Axis 2 and 3 were not influential
predictors of M. vimineum.
The first 3 axes of the principal components analysis of plot variables accounted for
61%, 26% and 12% respectively of the variance (Table 4; Figure 2B). The PCA performed
on the plot-level variables captured the environmental variability resulting from the
250
interactions among soils, herbs and woody vegetation. We found that the PCA model that
resulted in the highest proportion of variance explained in the first axes included the variables
for mean species richness, Ericaceae shrub basal area and soil pH. The exclusion of the cation
variables was further justified by exploratory data analysis that showed that these variables
11
had no effect on the probability of presence of M. vimineum. We used only the first axis as a
255
predictor variable (PlotPCA1). This axis quantifies the gradient from low soil pH with
associated high basal area of Ericaceae shrubs to relatively high pH and high mean species
richness.
Model 1 for M. vimineum presence included LandscapePCA1, PlotPCA1, random year
effects and the spatial covariance structure. The 95% credible intervals for random year
260
effects all overlapped zero, indicating a lack of an important contribution. We subsequently
removed the year effects from this and all other models. The LandscapePCA1 and PlotPCA1
variables were not significantly correlated (r = 0.16). The 95% credible intervals for
regression parameters did not overlap zero (Table 5). The DIC value (1125) was substantially
lower than other model values (1163, 1171 and 1223). The intercept-only model (Model 4)
265
had the highest DIC value.
The positive regression parameter for landscape PCA1 in Model 1 suggests that as
forest cover increases (conditions associated with higher elevation, low edge density, low
development, low impervious surface etc), the probability of M. vimineum presence decreases.
The positive regression parameter for PlotPCA1 indicates that the probability of M. vimineum
270
presence increased with decreasing basal area of Ericaceae shrubs and increasing soil pH. The
probability of presence increased with increasing mean species richness of native species.
Model 1 may have the most explanatory power because it captures more completely the
influence of both landscape and plot-level environmental factors.
Models 2 and 3 examined separately the relationship between landscape and plot-level
275
factors and the occurrence of M. vimineum. The DIC value for the LandscapePCA1 model
was lower than that of the PlotPCA1 model, which provides some evidence that landscape
12
factors may be more important in determining the distribution and invasion patterns of M.
vimineum. In addition, the LandscapePCA1 and PlotPCA1 variables were scaled to have
mean 0 and standard deviation 1, which allows for comparison of resulting regression
280
parameters. Results of Model 1showed LandscapePCA1 parameter estimates were slightly
higher than PlotPCA1, however there was substantial overlap in the posterior parameter
distributions.
The posterior distributions of the correlation distance and smoothing parameters (φ
and κ) provide strong evidence for spatial structure in the data that is not attributable to the
285
environmental covariates (i.e. autocorrelation in model residuals). The inter-site distances in
this study are relatively well distributed across a range from approximately 0.1 to 250 km
(Figure 4A). Inspection of a powered-exponential variogram generated from the posterior
distributions of σ2, φ and κ indicate that the probability of M. vimineum occurrence is
correlated up to a distance of 3 to 4 km (Figure 4B).
290
Discussion
Our study shows that the probability of presence of the shade-tolerant M. vimineum in
native forest communities is related to fine-scale biotic and abiotic conditions, and broadscale land use in the surrounding area. In addition, the residual spatial structure in the data
295
suggests that establishment is influenced by the presence of M. vimineum in nearby areas. Our
empirical models are predictive for intact native forests, but not for the region as a whole
because we did not sample within highly disturbed areas. There is now overwhelming
evidence that human land-use practices increase rates of spread and establishment of invasive
plant species (Brown and Boutin 2009). Removal of native vegetation exposes the soil surface
13
300
for establishment (Hobbs and Huenneke 1992), roads and trails are efficient movement
corridors for propagules (Pauchard and Alaback 2004; Von der Lippe and Kowarik 2007;
Albright et al. 2009) and abandoned agricultural and forestry plots have altered soil chemistry
(Fraterrigo et al. 2005) and litter that favors invasives (Kuhman 2009). While the effect of
roads is substantial, it is often limited to adjacent areas, at least for shade-intolerate invasives
305
(Watkins et al. 2003; Flory and Clay 2006). It remains less clear how shade-tolerant species
are invading intact native plant communities, but recent studies suggest that the slower rate of
spread may make these invasions more difficult to detect (Martin et al. 2009).
The influence of broad-scale forest cover and human-related disturbance on the
probability of presence of M. vimineum was captured in LandscapePCA1. This axis quantifies
310
the range of conditions from high forest cover and low development to low forest cover and
high development in 7 x 7 pixel windows (4.41 ha). It represents the potential propagule
pressure in an area, because a location with little forest cover and high human activity is likely
to have greater exposure to dispersing propagules than large forest blocks with little human
presence. The positive relationship with LandscapePCA1 demonstrates, as expected, that
315
human disturbance and development facilitates invasive establishment. Roadsides act as
habitat and dispersal corridors (Christen and Matlack 2009). Although the vegetation
sampling was conducted in natural areas, results show that human activities in close proximity
influence invasive establishment. As a shade-tolerant species, M. vimineum is capable of
expanding from road sides and areas of human development into adjacent intact forests.
320
High herbaceous species diversity is predicted where growing conditions are
favourable and there exists high heterogeneity in essential resources (niche partitioning;
MacArthur 1970; Chesson 2000). At very fine scales (generally < 1 m), native herbaceous
14
species richness may offer some resistance to the spread of invasives into intact plant
communities via competitive interactions for limited resources (Brown and Peet 2003; Tilman
325
2004; Sandel and Corbin 2010). At broader scales, such as examined in this study (plots ≥ 100
m2), the high levels of resource heterogeneity due to topography, vegetation, light, and
edaphic conditions should be conducive for a shade-tolerant invasive (Stohlgren et al. 2006).
Indeed, our results indicate that where native richness is high the probability of M. vimineum
presence is high (see Adams and Engelhardt 2009). While M. vimineum easily invades areas
330
of high native richness, its presence and eventual dominance is expected to reduce native
richness (Adams and Engelhardt 2009; Hejda et al. 2009), and alter soil chemistry and
microarthropod communities (McGrath and Binkley 2009). A long-term times-series
sequence of native species richness from the time of invasion to the present (if available)
would be expected to show a steady decline in species richness as M. vimineum increases its
335
local dominance. Consequently, the high diversity plant communities in this region may be
especially susceptible to the detrimental impacts of M. vimineum invasions (Barden 1987;
Ehrenfeld et al. 2001; Cole and Weltzin 2004).
The positive posterior parameter distribution for PlotPCA1 in Models 1 and 3
highlights the complex and interacting factors operating at the plot level to influence the
340
probability of M. vimineum presence. Similar to many native species (Peet et al. 2003), M.
vimineum favours high fertility sites, which are associated with high pH and low basal area of
acidophilic Ericaceae shrubs. While evidence exists for an inhibitory shading effect (Cole and
Weltzin 2005; Cheplick 2010), our results suggest that woody vegetation, which is dominated
by Ericaceous shrubs, may influence the probability of presence by affecting the soil-fertility
345
gradient (see gradient in Figure 2B).
15
There was substantial spatial structure in the M. vimineum data that was not explained
by the environmental covariates. The probability of presence at a given location was
influenced by the presence/absence of M. vimineum up to a distance of approximately 3 km
(Figure 4B). It is possible that the unexplained spatial structure could be due in part to
350
environmental variables that were not measured in this study. It is likely, however, that it is
indicative of a patchy spatial distribution due to dispersal limitation from established areas.
Although M. vimineum has been in the eastern United States since 1917, it is unlikely that its
propagules have had sufficient opportunity to get to all areas of the landscape, especially not
to intact native communities. The 3-km spatial structure may represent the average distance
355
around established areas in which invasion has occurred.
In conclusion, this study illustrates a valuable use for extensive vegetation datasets
that were gathered for other purposes and a methodology that can consider potential sources
of uncertainty (e.g., variation among years of data collection) and model sparse occurrences.
The goal of the CVS is to describe the natural vegetation of North Carolina, and sampling was
360
not conducted to document the patterns of non-native invasives. This and other similar
databases are available to address important ecological questions but are presently underutilised. Using the CVS data we found that intact forested areas in the southern Blue Ridge
Mountains that are surrounded by high levels of human activity and reduced forest cover are
at highest risk of M. vimineum invasion. Presently, areas within a 3-km distance of established
365
locations are also at elevated risks. The spatial scale of establishment should increase with
time as M. vimineum spreads across the landscape (Welk 2004), but invasion should be
slowest in low fertility sites with dense Ericaceae shrub cover. Given that M. vimineum is
known to form dense mats that substantially alter the native species composition and the
16
abiotic substrate (Barden 1987; Kourtev et al. 1998; Ehrenfeld et al. 2001; Cole and Weltzin
370
2005; Redman 2008; Hejda et al. 2009), the diversity in plant communities in the southern
Blue Ridge Mountains may generally decrease as M. vimineum spreads and increases its
dominance.
Acknowledgements
We appreciate helpful suggestions from Jim Clark on the methods used in this
375
analysis. Jeff Diez, Michelle Gooch and two anonymous reviewers provided helpful
comments on the manuscript. This study was funded by the Long-term Ecological Research
(LTER) Program of the National Science Foundation (DEB-0218001 and DEB-0823293,
Coweeta LTER).
380
17
Tables
Table 1. Data elements used in analysis
Data Elements
Description
yij
Presence or absence of M. vimineum at site i in year j
γi
Natural logarithm of number of modules sampled at site i
Plot-level variables
Herb_rich
Mean number of native species per 100-m2 module
Shrub_ba
Basal area of shrubs divided by number of modules
Tree_ba
Basal area of trees divided by number of modules sampled
EricaceaeShrub sampled
Basal area of Ericaceae shrubs
pH
Soil pH
Ca
Soil calcium concentration
Mg
Soil magnesium concentration
Mn
Soil manganese concentration
PlotPCA1
PCA axis 1 of plot-level variables
PlotPCA2
PCA axis 2 of plot-level variables
PlotPCA3
PCA axis 3 of plot-level variables
Landscape
Slope
Slope steepness in degrees
variables
Terrain
Terrain index indicating slope position in 7 x 7-cell
Impervious
Percentage of 30-m cell covered impervious surface
window of human development in 7 x 7-cell window
Developed
Percentage
ForestCover
Percentage of forest cover in 7 x 7- cell window
Elevation
Elevation in meters
Southwest
Aspect transformed into “southwestness”
Solar
Solar index accounting for terrain and southwestness
RoadDensity
Road density in 7 x 7-cell window
DistRoad
Distance to nearest road
EdgeDensity
Forest-edge density in 7 x 7-cell window
LandscapePCA PCA axis 1 of landscape variables
LandscapePCA PCA axis 2 of landscape variables
1 LandscapePCA PCA axis 3 of landscape variables
2
3
385
18
Table 2. A priori models.
Models
Model 1
Model 2
Model 3
Model 4
Model elements
Intercept + LandscapePCA + PlotPCA
Intercept + LandscapePCA
Intercept + PlotPCA
Intercept
19
390
Table 3. Results of principal components analysis of landscape variables, including relative
importance of the first 3 axes and the loading values for each variable within the 3 axes.
Importance of components
Standard deviation
Proportion variance
Cumulative proportion
Loadings:
Slope
Terrain
Impervious
Developed
Forest cover
Elevation
Southwest
Solar
Road density
Edge density
Axis 1
1.82
0.31
0.31
-0.14
-0.22
0.25
0.46
-0.49
-0.12
Axis 2
1.38
0.19
0.50
0.11
-0.69
-0.69
Axis 3
1.12
0.12
0.62
0.27
-0.56
-0.16
-0.12
0.14
-0.72
-0.12
0.40
0.49
20
395
Table 4. Results of principal components analysis of plot variables, including relative
importance of the first 3 axes and the loading values for each variable within the 3 axes.
Importance of components
Standard deviation
Proportion variance
Cumulative proportion
Loadings:
pH
Ericaceae shrubs
Mean species richness
Axis 1
1.35
0.61
0.61
Axis 2
0.89
0.26
0.87
Axis 3
0.61
0.12
1.00
0.60
-0.46
0.65
0.48
0.86
0.17
0.64
-0.21
-0.74
21
Table 5. Posterior distribution summaries for parameters included in Models 1, 2, 3 and 4.
The DIC values for Model 1, 2, 3 and 4 were 1125, 1163, 1171 and 1223 respectively,
400
indicating that Model 1 best explains the data.
Models
Model 1
Intercept
LandscapePCA1
PlotPCA1
σ2
φ
Κ
Posterior Median
Lower 95% CI
Upper 95% CI
-11.60
1.84
1.50
24.30
1.13
0.70
-12.90
1.05
0.83
15.50
0.93
0.61
-10.20
2.62
2.18
34.80
1.35
0.81
Model 2
Intercept
LandscapePCA1
σ2
φ
κ
-6.53
1.79
25.20
0.95
0.91
-8.55
1.17
16.60
0.75
0.72
-4.69
2.25
33.50
1.11
1.09
Model 3
Intercept
PlotPCA1
σ2
φ
κ
-7.01
1.66
26.45
0.98
0.95
-8.93
1.23
15.45
0.72
0.83
-4.99
3.02
34.62
1.20
1.05
Model 4
Intercept
σ2
φ
κ
-2.75
32.54
1.06
0.98
-4.25
15.62
0.78
0.86
-1.18
44.81
1.20
1.10
22
Figure Captions
405
Figure 1. Location of study in western North Carolina in the eastern part of the U.S.A.
Vegetation plots are indicated with black dots.
Figure 2. First and second axes of the principal components analysis for landscape (A) and
plot-level (B) variables.
410
Figure 3. A) Histogram of inter-plot distances, and B) a variogram of residuals of model 3.
Median is shown with solid line and 95% credible intervals are dashed lines.
23
Tennessee
Asheville
North Carolina
415
Figure 1.
24
0.2
A)
Elevation Impervious Development
EdgeDensity
Slope
Road
Density
Forest cover
0.0
-0.2
-0.4
-0.6
Solar
Southwest
-0.8
Principal Component 2
Terrain
-0.4
-0.2
0.0
0.2
0.4
Principal Component 1
0.6
0.8
Ericaceae
basal area
0.4
pH
0.2
Species
richness
0.0
Principal Component 2
1.0
B)
-0.4 -0.2
0.0
0.2
0.4
0.6
Principal Component 1
Figure 2.
25
420
5000
2000
0
Frequency
A)
0
50
150
250
20
40
60
B)
0
Semivariance
80
Distance (km)
0
2
4
6
8
10
Distance (km)
Figure 3.
26
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