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Abstract Grazing can alter the spatial heterogeneity of
vegetation, influencing ecosystem processes and biodi-
versity. Our objective was to identify why grazing causes
increases in the spatial heterogeneity of vegetation in
some cases, but decreases in others. The immediate ef-
fect of grazing on heterogeneity depends on the interac-
tion between the spatial pattern of grazing and the pre-
existing spatial pattern of vegetation. Depending on the
scale of observation and on the factors that determine an-
imal distribution, grazing patterns may be stronger or
weaker than vegetation patterns, or may mirror the spa-
tial structure of vegetation. For each possible interaction
between these patterns, we make a prediction about re-
sulting changes in the spatial heterogeneity of vegeta-
tion. Case studies from the literature support our predic-
tions, although ecosystems characterized by strong plant-
soil interactions present important exceptions. While the
processes by which grazing causes increases in heteroge-
neity are clear, how grazing leads to decreases in hetero-
geneity is less so. To explore how grazing can consis-
tently dampen the fine-scale spatial patterns of compet-
ing plant species, we built a cell-based simulation model
that features two competing plant species, different graz-
ing patterns, and different sources of vegetation pattern.
Only the simulations that included neighborhood interac-
tions as a source of vegetation pattern produced results
consistent with the predictions we derived from the liter-
ature review.
Keywords Spatial heterogeneity · Spatial dependence ·
Herbivory · Competition · Disturbance
Introduction
The potential for grazing to alter the spatial heterogene-
ity of vegetation has both theoretical and practical im-
portance. Its theoretical significance stems from our in-
creasing appreciation of the influence of pattern on pro-
cess. Although Watt (1947) recognized how vegetation
pattern can control microclimate and soil factors, as well
as biotic interactions in neighboring patches, only rela-
tively contemporary researchers have extended his work.
We now have evidence that pattern influences the spread
of disturbance, the movement and persistence of organ-
isms, and the redistribution of matter and nutrients (re-
viewed by Turner 1989; Pickett and Cadenasso 1995).
Especially in semi-arid terrestrial ecosystems, patchiness
may play a critical role in maintaining ecosystem pro-
ductivity by concentrating limiting resources (Ludwig
and Tongway 1995; Aguiar and Sala 1999). If grazing al-
ters the spatial structure of an ecosystem, it will have po-
tentially important consequences for a wide variety of
ecosystem functions.
From a practical or management perspective, an im-
portant issue is the relationship between spatial heteroge-
neity and biodiversity. Changes in spatial heterogeneity
caused by grazing imply changes in habitat diversity, and
influence the diversity of consumers ranging from in-
sects to birds and mammals (Smith 1940; England and
DeVos 1969; Grant et al. 1982; Bock et al. 1984; Dennis
et al.1998). Grazing also influences plant diversity in
many ecosystems (Milchunas and Lauenroth 1993), but
it is not clear whether changes in spatial pattern
drive this effect. When grazing increases plant diversity
primarily by reducing competition (Collins et al 1998),
the spatial distribution of grazing may not matter. But
grazing can also affect plant diversity by creating en-
vironmental heterogeneity at different spatial scales
(McNaughton 1983; Sommer 2000).
Grazing offers a potentially important tool for conser-
vation management because of its influence on habitat
structure and biodiversity (Collins et al. 1998). Weber et
al. (1998) concluded that grazing impacts on vegetation
P.B. Adler (
✉
) · W.K. Lauenroth
Graduate Degree Program in Ecology and
Department of Rangeland Ecosystem Science,
Colorado State University, Fort Collins, CO 80523, USA
e-mail: petera@lamar.colostate.edu
D.A. Raff
Department of Civil Engineering,
Colorado State University, Fort Collins, CO 80523, USA
Oecologia (2001) 128:465–479
DOI 10.1007/s004420100737
P.B. Adler · D.A. Raff · W.K. Lauenroth
The effect of grazing on the spatial heterogeneity of vegetation
Received: 18 November 2000 / Accepted: 19 April 2001 / Published online: 3 July 2001
© Springer-Verlag 2001
dynamics depended in large part on heterogeneity
in grazing pressure, and “consequently, manage-
ment...should account for spatial grazing aspects”
(p 687). To use grazing as a management tool, however,
we must be able to predict when grazing will increase
rather than decrease spatial heterogeneity. Previous re-
views have focused on how large herbivores respond to
environmental heterogeneity (Bailey et al. 1996; Pastor
et al. 1997; Hobbs 1999). While these reviews recog-
nized that grazing influences spatial heterogeneity, they
do not explain why grazing increases heterogeneity in
some cases, but decreases it in others.
In this review, we focus on two basic questions. The
first, with relevance to management issues, asks when
does grazing increase the spatial heterogeneity of vegeta-
tion? Initially, we attempted to answer this question by
focusing on the influence of ecosystem productivity, eco-
system type, and grazer selectivity. However, none of
these factors successfully revealed general trends among
case studies in the literature. Only after isolating the in-
teraction between the spatial pattern of grazing and the
pre-existing spatial pattern of vegetation at a specific
scale, ignoring the biological details of each case, were
we able to generate useful predictions. The observation
that grazing can consistently dampen the fine-scale pat-
terns of competing plant species in very different ecosys-
tems led us to ask a second, and more theoretical ques-
tion, how does grazing decrease spatial heterogeneity?
To address this question, we built a simulation model to
explore the consequences of alternative explanations.
We begin our analysis by defining spatial heterogene-
ity. Next we discuss influences on the spatial distribution
of grazing pressure, frequently overlooked in studies of
grazing and vegetation. In the following section we ex-
plain our predictions, then show that they are largely
consistent with the results of published case studies from
a wide variety of ecosystems. Finally, we use the simula-
tion model to test how grazing can have consistent ef-
fects on the spatial heterogeneity of competing plants
species despite contrasting effects on their relative abun-
dance.
What is spatial heterogeneity?
Because the term spatial heterogeneity has been used in
such diverse ways (Kolasa and Rollo 1991), it is espe-
cially important to define it clearly. When spatial hetero-
geneity is measured using non-spatial statistics, it corre-
sponds to spatial variability; when it is measured using
spatially explicit metrics, it corresponds to spatial pat-
tern. We followed the latter approach, operationally de-
fining spatial heterogeneity in terms of spatial depen-
dence: the relationship between the values of one vari-
able observed at different locations. When spatial depen-
dence is strong, given the value of a variable at one loca-
tion we can make reasonable predictions of the value of
that variable at another location. In the absence of spatial
dependence, we find no relationship between the values
of the variable, even if the observations are very close
together. Significant spatial dependence implies non-ran-
domness or pattern, while spatial independence implies a
random pattern. Likewise, we associate strong spatial de-
pendence with spatial heterogeneity, and weak spatial
dependence with spatial homogeneity. This definition
equates spatial homogeneity with spatially random data,
not with perfectly uniform, invariant data.
Spatial heterogeneity as we have defined it varies
with scale. In field studies, the scale of observation is de-
fined at the lower end by the frame size (the unit of sam-
pling, such as a quadrat or pixel) and at the upper end by
the overall extent of the study area (Atkinson 1997).
Measures of spatial heterogeneity are sensitive to both
quantities. Consider a landscape composed of two patch
types. The patch types are distinguished by a difference
in the mean of a randomly distributed variable. If we
sample the variable only within one patch type, we find
no spatial heterogeneity. However, if we move up in
scale by increasing the extent of our sampling to include
both patch types, we will find strong spatial heterogene-
ity (Fig. 1).
Previous authors have quantified spatial heterogeneity
using measures of spatial dependence such as vario-
grams (Sarnelle et al. 1993; Pastor et al. 1998) and
autocorrelation indices (Riera et al. 1998). Spatial de-
pendence can also be described by fractal dimension
(Palmer 1988; Milne 1991; Ritchie 1998). Throughout
this paper we will refer only to spatial heterogeneity, and
not to spatial dependence, hoping to make the discussion
more accessible to readers unfamiliar with the more
technical term.
Factors influencing the spatial distribution of grazing
Although research on sources of spatial pattern in vege-
tation is central to ecology, factors controlling the spatial
distribution of grazing pressure may be less familiar to
some ecologists. In the wildlife and rangeland manage-
ment literature, controls on grazing distribution have
been extensively reviewed (Coughenour 1991; Bailey et
al. 1996; Hobbs 1996, 1999). Here we summarize the in-
466
Fig. 1 Conceptual representation of “patchy” data: within each
patch, the cover data is distributed randomly, creating low spatial
dependence, equivalent to spatial homogeneity. At a larger scale
spanning the distinct patches, the cover data is spatially depen-
dent, and displays spatial heterogeneity
fluence of resources, predators and social behavior, plant
quality feedbacks, and human management on spatial
patterns of grazing.
The most obvious controls on grazing distribution are
resources, primarily food, but also water and minerals in
terrestrial systems. Senft et al. (1987) presented a hierar-
chical foraging model: grazers often select the landscape
unit richest in resources, then the most productive com-
munities within the landscape, and so on, down to the
most palatable species within a feeding station (defined
as the area an ungulate can graze without moving its
feet). In both wild and domestic terrestrial grazing sys-
tems, grazing pressure typically decreases, even expo-
nentially (Valentine 1947), with distance from water
(Andrew 1988; Pickup et al. 1998; Turner 1999; Nash et
al. 1999). Physical constraints such as steep slopes may
limit access to high resource areas (Coughenour 1991;
Bailey et al. 1996). The grazer’s habitat is structured by
the interaction of resources and such constraints.
Predators can exert considerable influence on the dis-
tribution of grazing. Studies from marine and aquatic
systems clearly show that the threat of predation ex-
cludes herbivores from otherwise suitable habitat (Hay
1981a, 1981b; Hay et al. 1983; Andrew 1993; McConk
1997). Social behavior such as herding, which may be
related to predation risk (reviewed in McNaughton
1984), can increase the probability of concentrated graz-
ing pressure.
Feedbacks between grazing and plant quality may be
important sources of spatial pattern in grazing, especially
in terrestrial systems. Secondary production depends on
both the quantity and quality of available forage (Hobbs
and Swift 1985). While grazing reduces the quantity of
available forage, in many systems it increases forage
quality, typically measured as nitrogen or crude protein
content (Coppock et al. 1983b; McNaughton 1984; du
Toit et al. 1990; Jefferies et al. 1994), although other es-
sential minerals such as sodium may respond similarly
(McNaughton et al. 1997). Possible mechanisms for the
increases in nutrient concentrations following grazing
may include a reduction in senescent material, mainte-
nance of leaves in an early phenological state (Richards
et al. 1962; Hobbs 1999), or increases in belowground
available nitrogen (Holland and Detling 1990). Such
positive feedbacks promote the continued use of previ-
ously grazed patches. However, for animals to continue
re-grazing a previously grazed patch, a minimum quanti-
ty of forage will also be necessary. Hobbs and Swift
(1988) showed that patch grazing is more likely to occur
in productive systems than dry systems: although forage
quality may increase in both cases, only in more produc-
tive ecosystems is regrowth rapid enough to provide the
minimum required quantity of forage.
While patch grazing may produce short-term positive
feedbacks, changes in composition may eventually cause
negative feedbacks (Coppock et al. 1983a; Pastor et al.
1998). When the short-term increases in forage quality
caused by grazing are outweighed by compositional
shifts towards unpalatable or low-nitrogen plant species,
patch grazing cannot persist (Jefferies et al. 1994; Pastor
et al. 1997). Such shifts in composition are more likely
to occur in ecosystems where very distinct plant func-
tional groups compete, such as grass-shrub steppe or tun-
dra or mixed hardwood-coniferous forests, and where the
abundance of the dominant species declines with graz-
ing.
Most management activities in domestic grazing sys-
tems promote uniform grazing distribution. At the land-
scape scale, herding, water development, and fencing are
used to manipulate animal distribution, and may play
a larger role in transforming native grazing systems
than the substitution of domestic grazers for wild ones
(Hartnett et al. 1997). Within fenced pastures, increases
in the intensity and/or duration of grazing causes an in-
crease in the proportion of habitat in grazed patches
(Berg et al. 1997; Cid and Brizuela 1998).
Although foraging theory assumes that consumers
constantly select at all scales, experimental evidence
suggests that at scales which are fine relative to the graz-
er, spatially random, or homogeneous grazing may oc-
cur, meaning that the spatial heterogeneity of grazing
will be low if we measure biomass removed per area at
many locations. A recent field trial using artificial vege-
tation mosaics showed that cattle were more selective
when choosing among large patches compared to small
ones (WallisDeVries et al. 1999). Wallace et al. (1995)
found that bison in Yellowstone National Park clearly
chose feeding areas non-randomly based on forage avail-
ability and topography, but feeding stations within feed-
ing areas were randomly located. Because of variability
in the behavior and selectivity of individual animals,
and foraging constraints imposed by herds, it seems rea-
sonable that gregarious behavior would increase the
likelihood of unselective grazing within grazed areas
(Augustine and McNaughton 1998). Relatively random
grazing should be most likely to occur at scales which
are small relative to the herbivore, among strong gener-
alist rather than selective grazers, in communities where
differences in plant quality among species or patches is
small (grasslands rather than grass-shrub steppes), and
perhaps with herding rather than solitary herbivores.
Interactions between spatial patterns of grazing
and vegetation
We hypothesize that the effect of grazing on the spatial
heterogeneity of vegetation depends on the interaction
between the spatial distribution of grazing and the pre-
existing spatial heterogeneity in vegetation. Factors such
as environmental heterogeneity, ecosystem productivity,
ecosystem type, and grazer selectivity may be the ulti-
mate determinants of patterns in grazing and vegetation,
but do not control the immediate effect of grazing on
spatial heterogeneity. When the spatial patterns of graz-
ing and vegetation are generated independently, then
changes in the spatial heterogeneity of vegetation depend
on the relative strength of spatial heterogeneity in graz-
467
ing and vegetation at a given scale of observation, de-
fined by the frame size and extent of sampling (Fig. 2).
If the spatial heterogeneity of grazing is stronger than the
spatial heterogeneity of vegetation, then the spatial het-
erogeneity of vegetation will increase following grazing.
We refer to this scenario as “patch grazing.” If the spatial
heterogeneity of grazing is weak relative to the spatial
heterogeneity of vegetation, then the spatial heterogene-
ity of vegetation will decrease. We call this scenario “ho-
mogeneous grazing.”
Examples of patch grazing (see next section) typically
involve the repeated grazing of small areas within other-
wise homogeneous grasslands promoted by the positive
feedback between grazing and forage quality, or, in ma-
rine and aquatic systems, the confinement of herbivores
to areas offering shelter from predators (Fig. 3A). Exam-
ples of homogeneous grazing often occur at smaller spa-
tial scales, where (relatively) randomly distributed graz-
ing overrides fine-scale spatial heterogeneity in vegeta-
tion created by environmental heterogeneity or neighbor-
hood interactions (Fig. 3B). Both patchy and homogene-
ous grazing can occur simultaneously, but at different
spatial scales (illustrated in Fig. 2). Under both patch
grazing and homogeneous grazing, the changes in spatial
heterogeneity will occur whether grazing has a positive
or negative effect on the vegetation variable of interest;
all that matters is that grazing alters the spatial pattern of
variability.
A different interaction occurs when grazing patterns
closely track vegetation patterns, or when both grazing
and vegetation respond to the same patterning agent,
such as topography. We refer to this scenario as “selec-
tive grazing,” following Senft et al.’s (1987) model that
extends to landscape scales the concept of selection, typ-
ically defined as the consumption of plant species out of
proportion with their abundance. At broader scales, ani-
mals may respond more directly to environmental factors
than to differences in forage quality, but the process is
sufficiently analogous to warrant use of the same term.
In the case of selective grazing, the effect of grazing on
spatial heterogeneity does depend on the qualitative ef-
fect of grazing on the vegetation (Fig. 2). Spatial hetero-
geneity will decrease if grazing reduces the contrast be-
tween vegetation patches by negatively affecting abun-
dance of the selected resource, but will increase if graz-
ing heightens the contrast in vegetation by positively af-
fecting resource abundance. We ignore the trivial case in
which both grazing and vegetation are homogeneous,
and the extremely unlikely case in which the spatial het-
erogeneity of grazing and vegetation are equal, but re-
468
Fig. 2 Flow chart showing predictions for the effects of grazing
on the spatial heterogeneity of vegetation. In the schematic draw-
ings, different shades of gray represent vegetation pattern, while
black dots show the distribution of grazing. The drawing on the
left, in which grazing distribution is generated independently of
vegetation pattern, demonstrates how the pattern of grazing de-
pends on the scale of observation: spatially extensive sampling
would reveal “patch grazing,” while sampling confined within a
grazed area (indicated by the dashed box) would observe “homo-
geneous grazing.” Spatial heterogeneity is measured by spatial de-
pendence
Fig. 3A, B Hypothetical autocorrelograms demonstrating interac-
tions between spatial patterns of grazing and vegetation. Arrows
indicate how the vegetation pattern will change as a result of graz-
ing. Lag distance refers to the geometric distance separating pairs
of sampling points. A Interaction 1: strong spatial heterogeneity in
grazing pressure introduces pattern into a randomly distributed
vegetation variable. B Interaction 2: randomly distributed grazing
pressure reduces the spatial heterogeneity of a patchy-distributed
vegetation variable. Both interactions can occur simultaneously at
nested spatial scales
spond to independent patterning agents (theoretically, no
change in spatial heterogeneity would occur).
An example of selective grazing negatively affecting
the selected resource occurs in the shortgrass steppe of
Colorado, where concentration of grazing pressure in
productive swales causes a shift towards the species
composition typical of uplands (Milchunas et al. 1989),
reducing spatial heterogeneity at the landscape level. Al-
though we found examples of selective grazing positive-
ly influencing resource levels, none of the case studies
measured vegetation spatial patterns. Jefferies et al.
(1994) reviewed studies from tundra ecosystems in
which herbivores selected for high nutrient content, early
successional vegetation, and maintained the vegetation
in that state, at least over ecological time scales. These
studies are distinct from examples of patch grazing, in
which grazing imposes heterogeneity in forage quality
on otherwise homogeneous vegetation. Unfortunately,
without direct measurements of pattern, we can only
speculate that selective grazing can increase spatial het-
erogeneity.
Results: evidence from the literature
If our predictions are correct, case studies reporting in-
creases in spatial heterogeneity following grazing should
represent patch grazing (since we found no examples of
selective grazing having a positive effect on resource lev-
els), while papers reporting decreases in spatial heteroge-
neity should represent homogeneous grazing or selective
grazing. In order to assign each case study to one of these
categories, ideally we would have quantitative informa-
tion on the spatial heterogeneity of grazing and on the
change in the spatial heterogeneity of vegetation. Howev-
er, few of the studies quantified spatial heterogeneity as
we have defined it, and those measuring pattern in both
grazing and vegetation were even more rare. Thus, our
classifications are subjective, but we indicate the strength
of the evidence for each classification (Tables 1, 2).
“Strong” evidence was offered only by case studies that
used spatially explicit measures to quantify the spatial
heterogeneity of both grazing and vegetation. Quantita-
tive, but non-spatially explicit data, and qualitative de-
scription provided evidence of “moderate” strength.
Many of the studies focused on vegetation pattern, in-
cluding our own, offered no information on grazing pat-
tern. Our classification of these papers is based on “in-
complete” evidence. In the total absence of information
on grazing distribution, we assumed homogeneous graz-
ing. These levels of evidence apply to the use of the case
studies for our purpose, and do not reflect the strength of
the papers with respect to their original objectives.
Increases in spatial heterogeneity following grazing
To support our predictions, case studies reporting in-
creases in spatial heterogeneity following grazing should
contain evidence of patch grazing (Table 1). Increases in
spatial heterogeneity reported by papers studying homo-
geneous or selective grazing would provide evidence
against our predictions. Pastor et al. (1998) quantified
the spatial heterogeneity of both grazing and vegetation,
and demonstrated that spatial heterogeneity in consump-
tion by moose created similar spatial heterogeneity in
vegetation. Eight studies (Bakker et al. 1983; Coppock et
al. 1983b; McNaughton 1984; Ring et al. 1985; Kellner
and Bosch 1992; Lutge et al. 1996; Cid and Brizuela
1998; Posse et al. 2000), representing seven different
ecosystems, documented patch grazing by domestic or
wild ungulates. Presumably because of positive feed-
backs with forage quality (Hobbs and Swift 1988), the
grazers foraged in previously grazed areas, producing
dramatic changes in vegetation structure and sometimes
composition. The landscape-level contrasts between the
grazed patches and adjacent ungrazed or lightly grazed
vegetation caused an increase in spatial heterogeneity
relative to ungrazed landscapes. Both Ring et al. (1985)
and Cid and Brizuela (1998) documented changes in spa-
tial heterogeneity over time, as small grazed patches
formed, grew, and sometimes coalesced. Poff and
Nelson-Baker (1997) showed similar patterns in model
simulations of grazing in streams. Studies from three
aquatic systems (Hay et al. 1981a, 1981b; Hay et al.
1983; Andrew 1993; McConk 1997) found that the pres-
ence or absence of herbivores, often controlled by the
availability of shelter from predators, created areas of
low and high plant or algal biomass. The resulting mosa-
ic in biomass implies an increase in spatial heterogeneity
relative to entirely ungrazed habitat. In a laboratory ex-
periment, Sommer (2000) found that the spatial hetero-
geneity of benthic microalgal assemblages was increased
by the patchy grazing of one insect herbivore, but was
not affected by the relatively random grazing of a second
herbivore. Studies of piospheres, the zones surrounding
livestock watering points, generally show that strong
grazing intensity gradients produce corresponding gradi-
ents in vegetation (reviewed in Andrew 1988; recent
case studies include Pickup et al. 1998; Turner 1999;
Nash et al. 1999). The results from all of these case stud-
ies are consistent with our prediction.
Three studies in this group, however, contained evi-
dence of homogeneous grazing, and should have shown
decreases not increases in the spatial heterogeneity of
vegetation. Hartnett et al. (1996), working in the tall-
grass prairie of Kansas, found that grazing increased spe-
cies richness and fine-scale spatial heterogeneity. How-
ever, their descriptor of spatial heterogeneity, percent
dissimilarity in pairwise quadrat comparisons, is not spa-
tially explicit. Furthermore, Glenn et al. (1992) (Table 2)
used the same descriptor in nearby sites but reached the
opposite conclusion: grazing reduced heterogeneity at
fine scales.
Results in Belsky (1986) and Rietkerk et al. (2000)
present a stronger challenge to our hypothesis. Belsky
demonstrated that heavy, apparently unselective grazing
created a small-scale two-phase vegetation mosaic in a
469
470
Table 1 Case studies reporting increases in the spatial heterogeneity (SH) of vegetation
following grazing. In order to be consistent with our predictions, these papers should re-
present “patch” grazing, and not “homogeneous” (Homog.) or “selective” grazing (indi-
cated under Distribution). Under Evidence we indicate the strength of evidence for our
classification of the interaction. Strong evidence required quantitative, spatially explicit
description of both grazing and vegetation patterns. Moderate (Mod.) evidence required
non-spatial data or qualitative information on both grazing and vegetation pattern. In-
complete (Incmplt.) evidence occurred when no information on grazing distribution was
given, which in no way reflects the strength of the paper for its original purpose
Author System Grazer Distribution Evidence Description
Pastor et al. (1998) Boreal forest (Isle Royale, USA) Moose Patch Strong Patterns of moose-browsing introduced parallel pattern
in vegetation
Bakker et al. (1983) Grassland (N. Europe) Sheep Patch Mod. Patch-grazing led to areas with contrasting structure
and composition
Berg et al. (1997) Salt-marsh (N. Europe) Sheep Patch Mod. Patch grazing led to areas with contrasting structure
and composition
Cid and Brizuela (1998) Grassland (Pampas, Argentina) Cattle Patch Mod. SH first increased then decreased following introduction
of cattle to pasture
Coppock et al. (1983b) Grassland (mixed-grass prairie USA) Bison and Patch Mod. Bison preferentially grazed on prairie dog towns,
prairie dogs creating contrasts with less-grazed areas
Kellner and Bosch (1992) ) Grassland (S. Africa) Cattle Patch Mod. Patch grazing led to areas with contrasting structure
Lutge et al. 1996 and composition
McNaughton (1983, 1984) Grassland (Serengeti) Wild ungulates Patch Mod. Grazing lawns contrasted with adjacent, less-grazed areas
Posse et al. (2000) Grassland (Tierra del Fuego) Sheep Patch Mod. Grazing created and maintained “lawn” physiognomy
within tussock grassland
Ring et al. (1985) Grassland (mixed-grass prairie USA) Cattle Patch Mod. Patch grazing led to areas with contrasting structure
and composition
Piosphere studies (various) Mostly arid and semi-arid systems Livestock Patch Mod. Grazing intensity gradients extending from water sources
create parallel vegetation gradients
Andrew (1993) Temperate reef Sea urchins Patch Mod. Sea urchins maintained barren habitat, but only near shelter
Hay (1981a, 1981b), Coral reef Fish and Patch Mod. Heavy grazing near shelter altered vegetation relative
Hay et al. (1983) (Caribbean) sea urchins to nearby ungrazed areas
McConk (1997) Coral reef (Australia) Fish Patch Mod. Distribution of algal spp. determined by presence/absence
of herbivores
Sommer (2000) Artificial marine littoral Gastropod Patch Mod. Spatially heterogeneous grazing increased the heterogeneity
of microalgal assemblages
Belsky (1986) Grassland (Serengeti) Wild ungulates Homog. Mod. Grazing maintained a two-phase vegetation mosaic
Hartnett et al. (1996) Grassland (tallgrass prairie USA) Bison Homog. Incmplt. Bison grazing increased species richness
and “spatial diversity (heterogeneity)"
Rietkerk et al. (2000) Savanna (West Africa) Cattle Homog. Incmplt. Patch size in areas grazed moderately was larger than
in areas grazed at low intensity
471
Author System Grazer Distribution Evidence Description
Sarnelle et al. (1993) Artificial streams Snails Homog. Strong Grazing reduced SH of algal spp. cover
Sala et al. (1986) Grassland (Argentine pampas) Cattle Homog. Mod. Grazing reduced compositional differences between flooded
and dry sites
Fuhlendorf and Smeins (1998) Grassland (semiarid savanna USA) Cattle Homog. Incmplt. Grazing reduced patterning of vegetation caused by soil variability
Glenn et al. (1992) Grassland (tallgrass prairie USA) Cattle Homog. Incmplt. At small scales, grazing reduced plot dissimilarity
Mabbutt and Fanning (1985) Semi-arid woodland (Australia) Sheep Homog. Incmplt. Grazing initially heightened grove-intergrove contrasts,
and cattle then fragmented groves
Matus and Tóthmérész (1990) Grassland (central Europe) Cattle Homog. Incmplt. Grazing reduced the number of significant plant spp. associations
Milchunas and Lauenroth (1989); Grassland (shortgrass steppe USA) Cattle Homog. Incmplt. Grazing “smoothed” above and belowground biomass at very
Adler and Lauenroth (2000) small scales; grazing reduced SH of dominant plant spp. cover
Tracy et al. (1998) Grassland (Chihuahan desert) Cattle Homog. Incmplt. Grazing reduced SH of termite activity and litter cover
Bergelson (1990) Artificial grassland Slugs Selective Mod. Heavy grazing on Senecio patches reduced their aggregation
Dale and Zbigniewicz (1997) Boreal forest (Canada) Hares Selective Mod. Artificially heavy, selective browsing reduced
intensity of shrub spatial patterns
Gibson (1988) Grassland (Wales) Sheep Selective Mod. Selective grazing caused break-up of hummock-hollow pattern
Milchunas et al. (1989) Grassland (shortgrass steppe USA) Cattle Selective Mod. Heavy grazing in swales reduced ridge-swale differences
in vegetation
Bisigato and Bertiller (1997) Shrub-steppe (Argentina) Sheep Selective? Incmplt. Grazing caused fragmentation of vegetation patches
Table 2 Cases studies reporting decreases in the SH of vegetation following grazing. We
predicted that papers in this class would contain evidence of “Homog.” or “selective”
grazing (indicated under Distribution). Under Evidence we indicate the strength of evi-
dence for our classification of the grazing distribution. Strong evidence required quanti-
tative, spatially explicit description of both grazing and vegetation patterns. Mod. evi-
dence required non-spatial or qualitative information on both grazing and vegetation pat-
tern. Incmplt. evidence occurred when no information on grazing distribution was given,
which in no way reflects the strength of the paper for its original purpose. For abbrevia-
tions, see Table 1
Serengeti grassland. The removal of grazing changed
patterns in water infiltration (see Aguiar and Sala 1999;
Klausmeier 1999) and led to the disintegration of the
two-phase mosaic. The paper makes no mention of the
patch grazing phenomenon typical of other grassland
studies in this group, so we felt that this case represented
homogeneous grazing, for which we predicted the oppo-
site response: decreases in spatial heterogeneity follow-
ing grazing. Rietkerk et al. (2000) measured the scale de-
pendence of vegetation along a gradient of livestock
grazing intensity. Patchiness was fine scale in the lightly
grazed site, more coarse scale in a moderately grazed ar-
ea, and intermediate in scale in a very heavily grazed
site. Like the Belsky paper, apparently homogeneous
grazing increased heterogeneity through a strong positive
feedback between vegetation and infiltration.
The response observed by Rietkerk et al. appears
characteristic of systems in which spatial patterns of
vegetation are generated by plant-soil feedbacks and the
redistribution of nutrients. In desert grasslands of south-
western North America, grazing plays a role in the con-
version of fine-grained grassland vegetation to more
coarse-grained shrub-dominated vegetation (Schlesinger
et al. 1990). Tongway and Ludwig (1994) suggested
that the fine-scale resource regulation exercised by pe-
rennial grasses is very sensitive to degradation by graz-
ing. Mabbut and Fanning (1985), working in semiarid
Australian woodland, described a broader scale two-
phase vegetation mosaic created by similar plant-soil in-
teractions. However, they found that after a transient in-
crease in grove-intergrove contrasts, grazing eventually
fragmented the groves. In all these examples, grazing
caused a change in the distribution of soil water and nu-
trients, which in turn altered vegetation distribution.
Why do our predictions fail for this group of case
studies? One possibility is that we have misclassified
these papers as examples of homogeneous grazing. Graz-
ing in the two-phase mosaics of Australia is typically
very selective (J. A. Ludwig, personal communication).
But even if we classified these cases as selective grazing
our predictions would still fail, since we predict no
change in the scale of pattern in selective-grazing situa-
tions. More likely, these systems are unique in the
strength of their plant-soil interactions, and the fact that
resource redistribution is a primary source of vegetation
spatial pattern. In these ecosystems, plant mortality
caused by grazing leads to the redistribution and concen-
tration of resources in fewer, larger patches, unless se-
vere degradation results in the export of resources and
the disintegration of patches.
Decreases in spatial heterogeneity following grazing
Based on our predictions, studies reporting decreases in
spatial heterogeneity following grazing should corre-
spond to homogeneous grazing or selective grazing
(Table 2). We identified eight case studies representing
homogeneous grazing. Sarnelle et al. (1993) provided
the strongest evidence, using a geostatistical approach to
show that grazing by randomly distributed snails in arti-
ficial streams reduced the small-scale spatial heterogene-
ity of overstory algae. Sala et al. (1986) found that a
fine-scale vegetation pattern was erased by a “coarse-
grained” grazing distribution. Fuhlendorf and Smeins
(1998, 1999) showed that soil variability created
clear vegetation patterns in ungrazed but not in grazed
grasslands. Two studies from the shortgrass steppe of
eastern Colorado, described “smoothing” of vegetation
(Milchunas and Lauenroth 1989) and decreases in fine-
scale spatial heterogeneity under livestock grazing
(Adler and Lauenroth 2000). Tracy et al. (1998) reported
decreases in fine-scale spatial heterogeneity of termite
mounds and litter in grazed compared to ungrazed desert
grassland. In a central European pasture, grazing reduced
the number of significant plant species’ associations, in-
direct evidence for a decrease in spatial heterogeneity
(Matus and Tóthmérész 1990). Although these case stud-
ies provide support for our prediction, we recognize that
none of these studies, except for Sarnelle et al. (1993),
measured grazing distribution quantitatively, and many
offered no information on the spatial pattern of grazing.
However, the majority of these studies were conducted at
fine spatial scales, where typically broad-scale influenc-
es on animal distribution should be minor. Patch grazing
of the kind described in the previous section theoretical-
ly could occur at fine scales, but none of the papers men-
tioned the phenomenon.
Five studies reporting decreases in spatial heterogene-
ity following grazing contained evidence of selective
grazing. Bergelson (1990) showed that slugs grazed pref-
erentially on high-density patches of Senecio in an artifi-
cial vegetation mosaic, and had a randomizing effect on
the spatial pattern of Senecio seedlings. Grazing reduced
spatial heterogeneity of shrubs in a boreal forest commu-
nity under artificially high levels of herbivory (Dale and
Zbigniewicz 1997). Gibson (1988) found that selective
grazing of a dominant tussock grass caused homogeniza-
tion of a hummock-hollow vegetation mosaic. Grazing
reduced differences in plant composition between swales
and uplands in shortgrass steppe (Milchunas et al. 1989).
Prior work demonstrated much heavier grazing in swales
than uplands (Senft et al. 1985), suggesting that grazing
distribution responded primarily to vegetation pattern.
Finally, selective grazing caused the fragmentation of
shrub patches in Patagonian steppe, which we interpreted
as a loss of spatial heterogeneity at the landscape scale
(Bisigato and Bertiller 1997). The results of these studies
are consistent with our predictions.
Changes in spatial heterogeneity at nested spatial scales
Multi-scale studies provide clear evidence that the ef-
fects of grazing on spatial heterogeneity can be scale-de-
pendent. Pringle (1996) described the effect of grazing
by Atyid shrimp on algal communities in Puerto Rican
streams. In pools grazed by shrimp, two distinct commu-
472
nities were present: a “low-growing understory turf dom-
inated by sessile diatoms” in the deeper, grazed portion
of the pool, and a band of algae in the shallow margins
of the pool where predation risk prevented grazing. At
the scale of the whole pool, grazing increased spatial
heterogeneity by creating depth zonation of the commu-
nities. Within the grazed portion of the pool, however,
spatial heterogeneity decreased relative to the structural
complexity of the ungrazed community. Gelwick and
Matthews (1997) found very similar patterns in artificial
streams. In Yellowstone National Park grasslands grazed
by wild ungulates, Augustine and Frank (in press)
showed that grazing reduced spatial heterogeneity in soil
nitrogen and nitrogen mineralization at fine scales (m
2
)
but increased patchiness in soil nitrogen at a broader,
slope scale (5–30 m). In all three cases grazing appears
to have been distributed homogeneously at the finer
scale, but in patches at the broader scale. These studies
indicate the importance of specifying a particular spatial
scale before asking how grazing will alter spatial hetero-
geneity.
Theoretical implications
We found no cases in which grazing clearly increased the
spatial heterogeneity of some vegetation components,
while decreasing the heterogeneity of others. The consis-
tency of the heterogeneity response is particularly inter-
esting in cases of selective and homogeneous grazing:
how can grazing have positive effects on the abundance
of some individual plant species, negative effects on oth-
ers, but decrease the heterogeneity of all species (Adler
and Lauenroth 2000)? The implication is that the effect
of grazing on the size of each population in a community
is independent of its effect on each population’s spatial
structure. We built a simulation model to explore how
this could occur.
Modeling decreases in spatial heterogeneity
The objective of our modeling exercise was not to simu-
late a natural ecosystem, but simply to construct an ana-
lytical tool to help us formulate hypotheses. This tool
contains a vegetation component, in the form of two
plant species, a competitive dominant and an opportun-
ist; a grazing component, in the form of selective grazing
with a negative effect on the grazed species or unselec-
tive (homogeneous) grazing on both species; and an in-
dependent source of vegetation pattern. We modeled
three common sources of pattern in vegetation that are
likely to interact with grazing:
1. Disturbance: grazing can influence succession in dis-
turbed patches (Coffin et al. 1998), altering patch mo-
saics at a broader scale.
2. Environmental heterogeneity: the selection pressures
exerted by grazing can mask the effects of factors
such as soil texture that create pattern in the absence
of grazing (Fuhlendorf and Smeins 1998).
3. Neighborhood interactions: grazing may override the
fine-scale patterns formed by plant-level processes
such as local seed rain (Coffin and Lauenroth 1989;
Pastor et al. 1999), clonal growth (Klimes 1999), or
local resource depletion (Whittaker 1975; Tilman
1982).
The model is an adaptation of Tilman’s (1994) two spe-
cies competition model that demonstrates coexistence
between a competitive dominant (species 1) and a supe-
rior disperser (species 2). Species 1 can invade areas oc-
cupied by species 2 as well as unoccupied sites, but spe-
cies 2 can only invade unoccupied sites. Population dy-
namics in the model are determined by four parameters,
a mortality rate and colonization rate for each species.
Tilman’s model is neither spatially explicit, nor does it
contain pattern-generating mechanisms. We made the
model spatially explicit by running it on a grid of 40×40
square cells. Each cell corresponds to the area of an indi-
vidual mature plant and can be in only one of three
states: species 1, species 2, or empty. At each time step,
mortality precedes colonization. The number of cells of
each species to be killed or colonized is determined by
the mortality or colonization rate multiplied by the popu-
lation size, but the location of the affected cells is chosen
at random. Once a cell is colonized, establishment de-
pends on the state of the target cell (species 2 cannot es-
tablish in a cell occupied by species 1).
At this point, the model is spatially explicit and pro-
duces results consistent with Tilman’s (1994) analytical
solutions (stochastic colonization causes minor depar-
tures), but still creates no spatial heterogeneity. We intro-
duced heterogeneity in three ways:
1. Disturbance was simulated at each time step by kill-
ing all cells in a randomly chosen patch of variable
size.
2. We simulated environmental heterogeneity, such as
differences in soils, by splitting the grid, and increas-
ing the mortality rate of species 1 on one half of the
grid (the colonization routines are unchanged).
3. To simulate neighborhood interactions, once a cell is
colonized we made the probability of establishment
conditional on the states of the eight neighboring
cells. The probability of establishment decreases lin-
early with the number of neighboring cells occupied
by the competing species. Thus, if species 1 colonizes
a cell completely surrounded by species 2, it has zero
probability of establishment; if species 2 occupies
none of the neighboring cells, the probability of es-
tablishment is one. This is the only form of the model
in which species 1 can be prevented from invading a
cell. Also, it is the only model that replaces uniform
dispersal with more realistic patterns of dispersal
mimicking local seed rain or clonal growth, a differ-
ence that can heavily influence model results (re-
viewed in Pacala and Levin 1997).
473
Grazing is modeled by increasing the mortality rates of
the grazed plant species, as observed in some field stud-
ies (Williams 1970; Moloney 1988). Therefore, in the
neighborhood interactions model, grazing should in-
crease the proportion of cells occupied by bare ground
during the colonization phase, reducing the likelihood of
negative neighborhood interactions and weakening spa-
tial heterogeneity, whether the competitive dominant
(species 1) or the disperser (species 2) is grazed.
Parameter selection and statistical analysis
The parameters in our model are aggregates of biological
processes. Colonization rate represents individual pro-
cesses such as seed production, dispersal, germination,
and, in the neighborhood interactions model, clonal
growth. Providing empirical support for the chosen pa-
rameters would be misleading. Therefore, we chose sets
of parameters that would best reproduce patterns ob-
served in the literature, and later discuss under what con-
ditions the chosen values would be reasonable. Based on
the average time to population equilibrium in our sto-
chastic version of the Tilman model, we arbitrarily chose
to end all runs at 20 time steps. Because spatial heteroge-
neity, and not abundance, was the variable of interest, we
controlled for large differences in abundances among the
disturbance, environmental heterogeneity, and neighbor-
hood models by adjusting colonization rates (parameter
values shown in Table 3).
We used Moran’s I, a coefficient of autocorrelation, to
measure the strength of spatial heterogeneity in the dis-
tribution of each species after each 20 time step run. Val-
ues of Moran’s I near zero indicate randomness, or spa-
tial homogeneity, while values significantly greater than
zero (positive spatial autocorrelation) or less than zero
(negative spatial autocorrelation), indicate spatial hetero-
geneity. To construct autocorrelograms, we plotted Mo-
ran’s I across increasing discrete lag distance classes. For
comparison of grazing treatments, we analyzed values of
Moran’s I from a short lag distance class (spanning
2–4 cells), the scale demonstrating the strongest spatial
heterogeneity in most of the model runs. We used S-
Plus 4.5 with a library of spatial functions written by
Reich and Davis (1998) to calculate Moran’s I.
Model results and discussion
Each model generated characteristic spatial patterns
(Fig. 4). The disturbance model generated significant
spatial heterogeneity, as measured by autocorrelation, at
small and moderate scales for species 1, but no signifi-
cant spatial heterogeneity for species 2. The environmen-
tal heterogeneity model produced significant spatial het-
erogeneity in both species, even at broad spatial scales.
In the neighborhood interactions model, spatial heteroge-
neity was significant for both species, but only at very
fine scales. The scales of pattern simply reflected our ar-
bitrary choices for the patch size of disturbance, the
structure of environmental heterogeneity, and the range
of neighborhood interactions.
To produce results consistent with our predictions
based on the literature review, the spatial heterogeneity
of both species, as measured by Moran’s I, must be low-
er in each of the three grazed scenarios compared to the
ungrazed scenario. Neither the disturbance model nor the
environmental heterogeneity model produced such re-
474
Table 3 Parameter values for
species 1 and 2 and abundance
(% cover) of both species after
20 time steps for the four graz-
ing treatments in each model
(n=10). G1 Species 1 grazed;
G2 species 2 grazed; G1,2 both
species grazed
Source of pattern Treatment Mortality Colonization Cover (%)
12 1 2 1 2
Disturbance Ungrazed 3.0 3.0 0.11 2.5 42.1 36.9
G1 5.0 3.0 0.11 2.5 33.5 49.7
G2 3.0 6.0 0.13 2.5 51.0 23.5
G1,2 4.5 4.5 0.11 2.5 35.4 41.4
Environmental heterogeneity Ungrazed 3.0 3.0 0.12 2.5 41.1 40.2
G1 5.0 3.0 0.12 2.5 27.4 60.6
G2 3.0 6.0 0.14 2.5 47.5 26.6
G1,2 4.5 4.5 0.12 2.5 47.5 26.6
Neighborhood Ungrazed 3.0 3.0 0.13 2.0 44.4 39.5
G1 5.0 3.0 0.13 2.0 29.1 57.4
G2 3.0 6.0 0.15 2.0 51.0 25.2
G1,2 4.5 4.5 0.13 2.0 34.4 46.5
Disturbance×neighborhood Ungrazed 3.0 3.0 0.20 2.5 43.6 34.0
G1 5.0 3.0 0.20 2.5 30.0 53.4
G2 3.0 6.0 0.22 2.5 53.4 17.5
G1,2 4.5 4.5 0.20 2.5 35.4 41.4
Environmental Ungrazed 3.0 3.0 0.20 2.5 41.0 39.7
heterogeneity×neighborhood G1 5.0 3.0 0.20 2.5 18.8 73.1
G2 3.0 6.0 0.22 2.5 48.7 26.9
G1,2 4.5 4.5 0.20 2.5 24.6 62.6
sults (Fig. 5A, B). In the disturbance model, while ho-
mogeneous grazing reduced the heterogeneity of both
plant species, the effect of selective grazing on popula-
tion size and spatial structure was correlated: Spatial het-
erogeneity decreased for the selected species, but in-
creased for the ungrazed species. Apparently, the species
not selected for by grazing was most successful in colo-
nizing disturbed patches. In the environmental heteroge-
neity model, the spatial heterogeneity of species 1 ap-
peared unaffected by selective grazing on either species,
but increased in response to homogeneous grazing. The
spatial heterogeneity of species 2 increased following
grazing on species 1, decreased following grazing on
species 2, and showed a slight increasing following ho-
mogeneous grazing.
The neighborhood interactions model, in contrast, did
produce results consistent with our predictions (Fig. 5C).
The spatial heterogeneity of both species decreased un-
der grazing of either species 1 or 2, and also under ho-
mogeneous grazing. By combining the neighborhood in-
teraction model with the disturbance model, we pro-
duced results almost identical to those from the neigh-
borhood interactions model alone, except that spatial
heterogeneity was much stronger in all three scenarios
(Fig. 5D). Adding neighborhood interactions to the envi-
ronmental heterogeneity model, however, failed to “cor-
475
Fig. 4 Spatial patterns created
by models simulating A distur-
bance, B environmental hetero-
geneity, and C neighborhood
interactions. Each example
comes from one simulation of
the ungrazed scenario, produc-
ing abundances for both spe-
cies of 40–45%. On the left are
maps of cells occupied by spe-
cies 1 (in black) and species 2
(in gray) after 20 time steps
(empty cells are left white). On
the right are autocorrelograms
for both species. Large symbols
indicate significant values of
Moran’s I (Bonferroni correct-
ed α=0.0042)
rect” the results (Fig. 5E), probably because of the large
difference in the scale of environmental heterogeneity
and the scale of neighborhood interactions. If the envi-
ronmental heterogeneity were smaller scale, or the
neighborhoods more extensive, the model might produce
results consistent with our predictions.
In all the models, the effects on spatial heterogeneity
were subtle simply because grazing (increased mortality)
has a much stronger effect on abundance than on pattern.
Large increases in mortality quickly drive the grazed
species to extinction, making tests of spatial heterogene-
ity trivial. Therefore, we could only simulate “light graz-
ing” (small increases in mortality). Increasing the low
baseline mortality rate (3%), which is more consistent
with the mortality rates observed among cohorts of ma-
ture perennial plants than with the high rates of mortality
common among seedlings (Harper and White 1974; West
1979), had little effect on the model results. Although
the absolute strength of spatial heterogeneity changed,
the relative strength of spatial heterogeneity among the
grazing scenarios appeared robust.
Only models incorporating neighborhood interactions
produced results consistent with the predictions we de-
rived from the literature review. Based on these model
results, neighborhood interactions offer the best explana-
tion for the consistency in the spatial effects of grazing
despite variable effects on relative abundance. Replacing
uniform, long-distance dispersal with spatially explicit,
local dispersal was an important advance in modeling
competition and coexistence in plant communities
(Pacala and Levin 1997; Bolker and Pacala 1999). Our
analysis supports previous work showing that neighbor-
hood interactions may be equally important in modeling
the spatial response of communities to disturbance
(Coffin and Lauenroth 1989; Pastor et al 1999).
Conclusions
We began this review with two questions. The first, more
relevant to management applications, asked when does
grazing increase the spatial heterogeneity of vegetation?
We found that for different interactions between the spa-
tial patterns of grazing and vegetation we can make use-
ful predictions for changes in heterogeneity. This ap-
proach extends work by previous authors on grazing
(Sala 1988), predation (Schneider 1992), and disturbance
in general (Kolasa and Rollo 1991). These predictions
should enable conservation planners to use grazing as a
conservation tool. By managing the distribution of graz-
ing in relation to existing patterns of vegetation, we can
maintain or increase spatial heterogeneity at appropriate
scales. Just as grazing can be patchy, homogeneous, or
selective relative to vegetation, so can fire or wind-
storms. Therefore, our predictions should be useful not
only to grazing management but to the management of
disturbance in general. The second question, more theo-
retical in nature, asked how does homogeneous grazing
dampen fine-scale spatial heterogeneity? Implicit in this
question is an assumption that for homogeneous grazing
to have similar effects in quite different ecosystems, a
common mechanism must be operating. Our model re-
sults suggest that neighborhood interactions at the indi-
vidual plant scale, rather than disturbance events or un-
476
Fig. 5 Mean Moran’s I for
species 1 (competitive domi-
nant) and species 2 (dispersal
specialist) under four simulated
grazing scenarios using five
sources of vegetation pattern:
A disturbance, B environmen-
tal heterogeneity, C neighbor-
hood interactions, D distur-
bance and neighborhood
interactions, and E environ-
mental heterogeneity and
neighborhood interactions.
Error bars show SE (n=10).
UG Ungrazed; G1 species 1
grazed; G2 species 2 grazed;
G1,2 both species grazed
derlying environmental heterogeneity, may form the ba-
sis of this common mechanism.
By addressing pattern and scale, research on the inter-
action between spatial patterns of vegetation and grazing
tackles “the central problem in ecology” (Levin 1992).
So where to next? Our review identified many studies
that examined spatial patterns of vegetation in different
grazing treatments, some that discussed the spatial distri-
bution of grazing, but very few that measured both. In
order to properly test our predictions, both types of pat-
terns must be described. A more ambitious research
agenda is to expand our predictions, which forecast im-
mediate effects at one specified spatial scale, to broader
temporal and spatial dimensions using a combination of
modeling and field experiments. How will feedbacks be-
tween vegetation and grazing influence heterogeneity
over time? Can we predict the outcome of the interaction
between patterns of grazing and vegetation for the con-
tinuum of spatial scales, rather than for an isolated scale?
Solutions to these problems will provide a conceptual
framework on which to hang the initial pieces of under-
standing we have developed.
Acknowledgements Special thanks to Dan Milchunas for in-
valuable discussions and comments on previous versions of the
manuscript. Comments by J. Ellis, K. Metzger, J. Bradford, A.
Ellingson, R. Monson, one anonymous reviewer, and members of
the Burke-Lauenroth laboratory greatly improved the clarity of
this material. Support was provided by an NSF Graduate Fellow-
ship to P. B. A., the Shortgrass Steppe LTER Project (DEB-
9632852), and the Colorado Experiment Station (1-57661).
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