Landscape Heterogeneity Shapes Predation in a Newly Restored Predator Prey system

Abstract

Because some native ungulates have lived without top predators for generations, it has been uncertain whether runaway predation would occur when predators are newly restored to these systems. We show that landscape features and vegetation, which influence predator detection and capture of prey, shape large-scale patterns of predation in a newly restored predator-prey system. We analysed the spatial distribution of wolf (Canis lupus) predation on elk (Cervus elaphus) on the Northern Range of Yellowstone National Park over 10 consecutive winters. The influence of wolf distribution on kill sites diminished over the course of this study, a result that was likely caused by territorial constraints on wolf distribution. In contrast, landscape factors strongly influenced kill sites, creating distinct hunting grounds and prey refugia. Elk in this newly restored predator-prey system should be able to mediate their risk of predation by movement and habitat selection across a heterogeneous risk landscape.

Full text

LETTER
Landscape heterogeneity shapes predation in a newly
restored predator–prey system
Matthew J. Kauffman,
1
*

Nathan
Varley,
2
Douglas W. Smith,
3
Daniel R. Stahler,
3à
Daniel R.
MacNulty
4
and Mark S. Boyce
2
Abstract
Because some native ungulates have lived without top predators for generations, it has
been uncertain whether runaway predation would occur when predators are newly
restored to these systems. We show that landscape features and vegetation, which
influence predator detection and capture of prey, shape large-scale patterns of predation
in a newly restored predator–prey system. We analysed the spatial distribution of wolf
(Canis lupus) predation on elk (Cervus elaphus) on the Northern Range of Yellowstone
National Park over 10 consecutive winters. The influence of wolf distribution on kill
sites diminished over the course of this study, a result that was likely caused by territorial
constraints on wolf distribution. In contrast, landscape factors strongly influenced kill
sites, creating distinct hunting grounds and prey refugia. Elk in this newly restored
predator–prey system should be able to mediate their risk of predation by movement and
habitat selection across a heterogeneous risk landscape.
Keywords
Antipredator response, catchability, kill occurrence, native predator, predation risk,
predator restoration, prey refugia, risk map, territoriality, trophic cascades, vulnerability.
Ecology Letters (2007) 10: 690–700
INTRODUCTION
Global efforts are underway to restore and conserve
remnant populations of apex predators including lions
(Panthera leo), grizzly bears (Ursus arctos) and wolves (Canis
lupus) (Treves & Karanth 2003). Restoring predators to the
large landscapes of their historic range has the potential to
maintain biodiversity by recovering the strong but indirect
species interactions inherent to these systems (Crooks &
Soule 1999; Terborgh et al. 2001; Soule et al. 2005).
However, such community-level benefits of carnivore
restoration may come at a cost to their native ungulate
prey, which form the basis of recreational and subsistence
hunting by humans (Orians et al. 1997; Eberhardt et al. 2003;
Nilsen et al. 2004). The perception that reintroduced
predators will devastate native prey is a primary concern
for some stakeholders, and successful carnivore restoration
efforts often hinge on resolving these and other human–
carnivore conflicts (Orians et al. 1997; Treves & Karanth
2003).
Native ungulates that have lived without predators are
expected to become naı¨ve and less vigilant, increasing their
vulnerability to predation (Berger 1999; Berger et al. 2001;
Sand et al. 2006). For example, in only 4 years at least 10
adult moose (Alces alces) fell prey to grizzly bears at the
frontier of bear recolonization in the greater Yellowstone
area as compared with no records of predation where both
had existed for 100+ years (Berger et al. 2001). The history
1
Division of Biological Sciences, University of Montana, Misso-
ula, MT 59812, USA
2
Department of Biological Sciences, University of Alberta,
Edmonton, AB T6G 2E9, Canada
3
Yellowstone Center for Resources, Wolf Project, PO Box 168,
Yellowstone National Park, WY 82190, USA
4
Department of Ecology Evolution and Behaviour, University of
Minnesota, St Paul, MN 55108, USA
*Correspondence: E-mail: mkauffm1@uwyo.edu
Present address: US Geological Survey, Cooperative Fish and
Wildlife Research Unit, University of Wyoming, Laramie, WY
82071, USA.
àPresent address: Department of Ecology and Evolution, Uni-
versity of California, Los Angeles, CA 90095, USA.
Ecology Letters, (2007) 10: 690–700 doi: 10.1111/j.1461-0248.2007.01059.x
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

of introductions of exotic predators to predator-free islands
illustrates that novel predators can markedly reduce popu-
lations of native prey and cause local extinctions (Fritts &
Rodda 1998; Knapp et al. 2001; Blackburn et al. 2004). If
native ungulate prey are naı¨ve and thus highly susceptible to
predation wherever they encounter recolonizing native
predators, similar reductions in prey numbers might be
expected (Berger et al. 2001; Sand et al. 2006). Unfortu-
nately, we know little about the ways in which native prey
interact with their new predators or the mechanisms that
govern these predator–prey interactions (but see Hebble-
white et al. 2005).
Theory suggests that native predator–prey systems
persist over the long term due to heterogeneity in
predation rates caused by prey refugia in space or time
(Fryxell et al. 1988; Kareiva & Wennegren 1995; Ellner
et al. 2001). Whether or not native prey can benefit from
such refugia when their historical predators are returned
will depend on the mechanisms by which prey refugia are
created and the retention of the prey’s ability to exploit
them. Do the rates and patterns of predation by newly
restored predators exhibit high levels of heterogeneity, and
if so what mechanisms govern the predation process?
Quantifying the spatial structure of predation by recolo-
nizing carnivores would enhance our understanding of
apex predator effects on native prey populations (Sinclair
& Arcese 1995).
In this study, we quantified the spatial structure of wolf
predation on elk (Cervus elaphus) during winter on the
Northern Range (NR) of Yellowstone National Park
(YNP), USA. Wolves were reintroduced to YNP in 1995
after being extirpated from this ecosystem in the 1930s
(Bangs & Fritts 1996). During the 10 years since reintro-
duction, the NR wolf population increased from 14 wolves
in three packs to 84 wolves in six packs (Fig. 1a). Over this
time period, 92% of the ungulate prey taken by wolves
during winter have been elk (Smith et al. 2004). We
evaluated landscape-level variability in wolf predation on
elk and found that spatial patterns of predation are more
strongly influenced by landscape features than by wolf
distribution.
MATERIALS AND METHODS
We quantified spatial patterns of wolf predation on NR elk
by analysing the factors that influence the spatial distribu-
tion of elk killed by wolves in winter during the first
10 years of wolf recovery. We estimated the extent to
which variation in kill locations (Fig. 1b) was determined by
the annual distribution of wolf territories (Fig. 1a) or
physical features of the landscape where elk and wolves
interact. We also evaluated whether the strength of
landscape variables changed through time as wolves
expanded their distribution and wolf predation on elk
became less novel. The primary data for these analyses is a
GIS data set of the spatial locations of elk killed by wolves
during 1996–2005.
Surveys for wolf-killed elk
During each winter, ground and aerial surveys for wolf-
killed prey were conducted by crews tracking the wolf
packs with radiotelemetry. All of the kills used in our
analysis came from two 30-day periods in the early (mid-
November to mid-December) and late (March) winters of
1996–2005, when wolf packs were intensively monitored by
ground and air crews. These efforts resulted in 774
locations of wolf-killed elk across the NR (Fig. 1b). Smith
et al. (2004) used a double-count method to evaluate
observation error in these surveys and found that ground
crews are biased towards detecting wolf-killed elk in close
proximity to the road system, with no kills found further
than 7.23 km from the road. However, aerial surveys were
not biased with respect to vegetation type (conifer forest
vs. open sage/grasslands) or roads. While an estimated
27% of total kills went undiscovered, the two survey
efforts conducted simultaneously (45% of our kills were
detected from the air, 71% from the ground and 17% by
both survey methods) resulted in minimal detection bias
with respect to the landscape features used in our analysis
(Smith et al. 2004).
Wolf kills are distinguished readily from kills made by
other carnivores. Kills were classified as wolf-caused when
wolves were observed making the kill, or evidence
supported wolves as the cause (e.g. wolves were observed
feeding on a fresh carcass). Necropsies were performed
on the vast majority of kills (‡90%), and evidence from
the carcass site such as chase tracks and signs of struggle
also were used to evaluate cause. In rare cases, cougar
(Puma concolor) kills were usurped by wolves, but these
tended to be discernible by evidence that cougars had
cached a carcass. Grizzly bears occasionally kill elk, but
only rarely in the winter when, for the most part, bears
are denning.
Kill site model
We used logistic regression to estimate a model of the
relative probability of a kill by analysing the spatial attributes
of known kill locations vs. random available locations in the
NR study area (Manly et al. 2002). We employed a matched
case–control design with strata consisting of 774 kills
matched to 20 control points each randomly selected from
within the NR study area (Hosmer & Lemeshow 2000).
Case–control logistic regression fits the following likelihood
for each stratum (k¼774):
Letter Landscape shapes wolf predation 691
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

lkðbÞ¼ eb0xk;1
eb0xk;1þeb0xk;2þþeb0xk;21 ð1Þ
where bis a vector of fitted coefficients, x
k,n
are the
explanatory variables for observation n(1 ¼the kill loca-
tion, 2–21 ¼the random locations) in stratum k. This
equation is not interpretable as the probability that a
predation event will occur at a given location. Rather, it is
the probability that the location with data x
k,1
is in fact the
kill site relative to the 20 control locations. However, the set
of fitted coefficients are interpretable as the odds ratio as in
standard logistic regression (Hosmer & Lemeshow 2000).
Relative probability of kill occurrence was calculated with
respect to a reference vector (x
r
), defined as the set of mean
values for each variable within the domain of availability.
The resulting odds ratio expression for a given landscape
location (x) was calculated following Keating & Cherry
(2004) as:
WðxjxRÞ¼exp½b1ðx1x1;RÞþþbnðxnxn;RÞ:ð2Þ
Because the true probability of a predation event for any
individual location (30 ·30 m grid cell) on the NR is close
to zero, random locations are unlikely to include kill
2005
2004
20032002
20012000
1999
19981997
20052005
20042004
2003200320022002
2001200120002000
19991999
19981998199719971996
Legend
Park road
Agate Creek
Buffalo Fork
Chief Joseph
Crystal Creek
Druid Peak
Geode Creek
Leopold
Rose Creek
Slough Creek
Specimen Ridge
Swan Lake
Tow e r
(pack territories and kills)
010 km
(a)
(b)
10
km
05
Figure 1 The spatial distribution of wolf pack territories and wolf-killed elk on Yellowstone’s Northern Range, 1996–2005. Wolf pack
territory boundaries (panel a) are represented by an 80% kernel home range. Wolf-killed elk (panel b) are colour coded according to the pack
that made the kill. The legend in panel (a) gives the colour codes for both pack territories and kills (in panel b, grey circles ¼dispersers or
unformed pack).
692 M. J. Kauffman et al. Letter
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

locations and we assume the odds ratio to be interpretable
as relative probability of kill (Keating & Cherry 2004). Thus,
aW(x|x
R
)¼1 denotes no difference between location i
and the reference (mean probability on the landscape),
whereas a W(x|x
R
)¼10 would indicate a kill probability 10
times greater than the average.
Accounting for elk distribution
One obvious driver of the spatial distribution of wolf-killed
elk is the spatial distribution of elk themselves. During winter
elk select south-facing grassland habitats, where the snow
level is not deep or crusted enough to impede their ability to
forage (Houston 1982; Skovlin et al. 2002). On the NR, it is
well known that snow accumulation throughout winter
(if deep enough) pushes elk to lower-elevation winter range;
thus, elk distribution on the landscape changes within and
among annual winter seasons. We sought to account for this
by estimating the spatial distribution of elk with an existing
NR habitat model derived from radiocollared elk that includes
– among other habitat variables – the influence of recorded
annual variability in snow accumulation (Mao et al. 2005).
Although the NR elk population has declined since wolf
reintroduction (Smith et al. 2004; White & Garrott 2005),
our habitat model assumed (aside from the influence of
snow) that the relative distribution of elk within each year
was constant. As in the original elk habitat model of Mao
et al. (2005), we used the daily snow water equivalent (SWE)
estimated from an existing snow model that interpolates
SWE across Yellowstone National Park from 28 fixed snow
measurement sites (Wockner et al. 2006). We averaged the
daily SWE estimates within the four 2-week periods from
which the kills were collected each winter. We used a natural
log transformation of the Mao et al. (2005) Resource
Selection Function (RSF) as our estimate of elk use in our
kill-site analysis. Within the case–control design of our kill-
site model, the elk variable assigned to each of the 20
random control locations came from the same 2-week
period of the winter in which the kill occurred.
Wolf distribution
We estimated the annual spatial distribution of wolves on
the basis of individual packs. To characterize pack territories
in a GIS, we constructed a utilization distribution (UD)
using a 95% kernel estimation (Seaman & Powell 1996) for
each pack from aerial locations of radiocollared wolves
(average number of locations ¼31) using a Home Range
extension for ArcView 3.2 (Hooge & Eichenlaub 1997). A
maximum of one location per pack per day was used for
kernel estimation. A smoothing factor of 1500 m was
chosen because it appeared to best approximate the extent
of territory boundaries known from field observations.
Aerial relocations of wolf packs known to be on a kill were
excluded from the UD estimation to reduce the spatial
dependence of kill sites on pack territories. Kernel percentile
values were divided by the number of cells within each
percentile category to approximate a probability distribution
such that all 30 ·30 m cells within a pack UD summed to
1. To account for variation in wolf pack size (range 2–37),
we multiplied each pack UD by the number of wolves
observed within each pack during winter. All individual pack
UDs for a given year were summed across the NR resulting
in an annual composite measure of wolf use.
Landscape variables
Explanatory landscape variables were derived from a GIS of
the study area and included: slope, openness, proximity-
to-roads, proximity-to-streams and SWE. Slope was derived
from a 30-m digital elevation model of YNP (range 0–70).
Openness was calculated as per Boyce et al. (2003) using the
sum of non-forested cells within a 500 ·500 m moving
window centred on each grid cell (range 0 [deep forest]–289
[open grassland]). The proximity-to-roads measure (range
0–13 435 m) was calculated as the shortest distance between
each grid cell and the nearest road. Trails and roads that
were not maintained were not included in our analysis.
Proximity-to-streams (range 0–2352 m) was calculated as
the shortest distance to the nearest major stream or river.
Snow was calculated as the average SWE for each of the
four 2-week periods during each winter (40 snow layers
total) and matched to kills as described for the elk variable
above. All landscape variables showed relatively low levels
of collinearity (r< 0.43), except for SWE and elk, which
were negatively correlated with r¼)0.80.
RESULTS
We began our analysis of the kill-site data by first building
a set of ÔencounterÕmodels in which elk and wolf
distributions alone describe the spatial distribution of kills.
A model including both elk and wolf distributions fit the
kill data much better than did single-term models that
included the distribution of only predator or prey
(likelihood ratio v
2
¼88.57, d.f. ¼1, P< 0.0001;
Table S1 in Supplementary Material). This indicates that
wolves were not simply making kills on the landscape in
strict proportion to the distribution of elk, or their own
spatial patterns of winter territory use.
To characterize the influence of landscape features on kill
occurrence, we constructed a set of Ôlandscape effectsÕ
models that retained the effects of wolves and elk in
addition to landscape features including: proximity-to-roads,
proximity-to-streams, openness, slope and snow. The best-
fit landscape model included all landscape variables and
Letter Landscape shapes wolf predation 693
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vastly outperformed the elk + wolf encounter model
(likelihood ratio v
2
¼270.11, d.f. ¼6, P< 0.0001;
Table 1; Table S1). Because these models take into account
the spatial distribution of elk and wolves, they indicate that
landscape factors strongly shape where wolves kill elk in this
newly restored predator–prey system.
To determine whether the factors controlling the
distribution of kills have changed over time, we built a
third set of Ôtime-varyingÕmodels that allowed the influence
of wolves and landscape factors to vary linearly through
time. Among other causes, such temporal changes could
result from learned hunting patterns by wolves in new
habitats, learned antipredator behaviour by elk, or intraspe-
cific predator interference as the number of wolf packs
increased. The best-supported time-varying models included
a negative wolf ·time interaction (likelihood ratio v
2
¼
23.66, d.f. ¼1, P< 0.0001; Table 1; Table S1), indicating
that the influence of wolf distribution on kills has
diminished over time. There was negligible support for
temporal interactions with landscape variables, indicating
that the types of habitats where wolves have killed elk have
changed little over the 10 years of wolf recolonization.
Likelihood ratio v
2
values and associated Pvalues (from
nested model comparisons) were non-significant for tem-
poral interactions with all landscape variable except for
distance-to-stream (slope ·time: v
2
¼0.43, P< 0.51;
open ·time: v
2
¼3.42, P< 0.06; road ·time: v
2
¼1.35,
P< 0.25; stream ·time: v
2
¼4.40, P< 0.04). We do not
believe that the significant stream ·time interaction is
indicative of a temporal change in wolf or elk behaviour
with respect to streams. Rather, we believe this results from
the addition of kills to our data set in the winter 2002–2003
from the newly formed Slough Creek Pack in 2002, which
has been making kills (n¼36) near the banks of lower
Slough Creek (Fig. 1).
We used k-fold cross-validation (Boyce et al. 2002) to
evaluate the predictions of kill sites by the kill occurrence
models. The kill data were partitioned into five equal sets,
and models were fit to each 80% partition of the data, while
the remaining 20% of the data were held out for model
evaluation. In each cross-validation, the estimated proba-
bilities were binned into 10 equal bins and correlated with
the observed proportion of kills within the evaluation set.
The average Spearman-rank correlations across the five
partitions of the data were 0.90, 0.96 and 0.95 for the best-fit
encounter, landscape effects and time-varying models,
respectively. Correlations of this magnitude indicate a very
good fit of models to data (Boyce et al. 2002).
To illustrate the patterns of predation revealed by our
analysis, we used our best-fitting (time-varying) model to
map relative annual probability of kill occurrence onto the
NR landscape for the 2005 winter (Fig. 2a). We modified
these model predictions at each landscape location to
approximate per capita predation risk by scaling each
probability of kill occurrence by the relative probability (log
transformed RSF) of elk occurrence from the Mao et al.
(2005) elk habitat model. In rescaling the probabilities in this
manner, we assume that elk density across the study area is
proportional to habitat use as estimated by Mao et al. (2005).
In 2005, the influence of landscape features created a
predation-risk landscape that was highly variable, with areas
of low and high risk varying by nearly two orders of
magnitude (Fig. 2a). In the early years after wolf reintro-
duction, wolf distribution also created considerable spatial
variation in risk. For example, comparing a risky area with a
refuge area, we found that an increase in wolf density that
caused a 10-fold increase in risk (relative to mean annual
risk) in 1996 caused only a 1.25-fold increase in risk in 2005
(Fig. 2b). Thus, during the first 10 years of wolf population
expansion in Yellowstone, wolf distribution became less
Table 1 Estimated coefficients for models used to estimate the probability of occurrence of wolf-killed elk on Yellowstone’s Northern
Range, 1996–2005
Effect
Landscape effects Time-varying Catchability
bSE bSE bSE
Elk 1.238 0.131 1.238 0.132 1.331 0.131
Wolf 1682.00 197.24 4988.00 706.44
Road )0.00013 2.14E-05 )0.00013 2.15E-05 )0.00012 2.06E-05
Stream )0.00078 0.00014 )0.00017 0.00032 )0.00080 0.00014
Openness 0.0026 0.0005 0.0046 0.0010 0.0028 0.0005
Slope )0.0749 0.0175 )0.0761 0.0176 )0.0795 0.0174
Slope
2
0.0028 0.0007 0.0028 0.0007 0.0030 0.0007
Snow 0.0112 0.0018 0.0115 0.0018 0.0120 0.0018
Wolf ·time )462.95 97.01
Openness ·time )0.00032 0.00015
Stream ·time )0.00011 4.94E-05
694 M. J. Kauffman et al. Letter
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important in determining variation in predation risk relative
to landscape features.
Logistic regression models such as the one we used are
sensitive to spatial variation in explanatory variables. If the
variability of a spatial attribute decreases through time, so
too will the strength of its influence (Garshelis 2000).
Therefore, we assessed whether the wolf distribution had
become less variable over the 10-year study period and
found that no temporal decline in the variance of the wolf
density index was evident (see Fig. S1). Rather, an increase
in overall variance was observed, in part because of the
emergence of areas of high wolf use where several packs
overlapped (Fig. 1a). These data, and our case–control
design that took account of the annual change in wolf
distribution, suggest that the decoupling of kills from wolf
distribution was not an artefact of an increasingly homo-
genized wolf distribution.
Attenuation of wolf territory influence on kill distribution
Because we did not find evidence for a temporal change in
the types of habitats where wolves killed elk, we believe that
profound shifts in elk behaviour or habitat use are not
responsible for the attenuating influence of wolves on kill
locations. Similarly, the per-capita kill rate for wolves on the
NR has not declined sharply over the study period (D.W.
Smith, unpublished data), suggesting that wolf packs
maintained a relatively constant annual kill rate. Given this,
it seems unlikely that a predator-dependent functional
response is responsible for the decoupling of predation
from predator distribution. To further examine the decou-
pling of kill sites from wolf distribution, we conducted
post-hoc analyses to explore a potential mechanism for this
phenomenon. We hypothesized that as the wolf population
increased, wolves shifted their territories away from the
areas where they were most successful at hunting elk (dark
blue patches in Fig. 2a) to reduce inter-pack conflict and
mortality. Thus, we investigated a mechanism whereby at
high densities wolf social structure and aggression avoidance
constrains the ability of packs to defend territories where
they make most of their kills.
Pack conflict
There is ample evidence that inter-pack conflict has
increased as the density of NR wolf packs has increased.
Long-term monitoring in this system has recorded 2.8 (±0.8
D
Predation Risk (relative)
< 0.1
> 6.0
0.3
0.7
1.1
1.5
1.9 4.4
4.0
3.5
3.1
2.7
2.3 4.8
0 5 10 km
5.2
5.7
C
(a)
(b)
0.1
1.0
10.0
100.0
0.0000 0.0002 0.0004 0.0006
Wolf density index
Relative predation risk
Risky, 1996 Risky, 2005
Refuge, 1996 Refuge, 2005
Figure 2 Relative risk of wolf predation for
elk on Yellowstone’s Northern Range, 2005
(panel a). Spatial variation in predation risk is
largely driven by landscape features, which
create a limited number of hunting grounds
where predation risk is often 10 times higher
than the landscape average (a map value of 1
denotes average risk). When first reintro-
duced, wolf pack distribution also strongly
influenced predation risk (panel b), but
this influence has largely diminished after
10 years of wolf population expansion. By
2005, variation in predation risk is largely
determined by landscape features that create
risky (location C in risk map) and refuge
(location D in risk map) habitats.
Letter Landscape shapes wolf predation 695
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SE) aggressive inter-pack interactions (i.e. intraspecific
chase/flee, attack or kill) per year during the first half of
the study period (1996–2000) and 11.8 (±2.6 SE) such
interactions per year during the latter half of the study
(2001–2005). Confirmed intraspecific killing by wolves
increased over the same period, from 0.8 (±0.3 SE) per
year to 2.5 (±1.0 SE) per year (D.W. Smith, unpublished
data). This increase in pack–pack aggression over the study
period represents an increasingly important spatial con-
straint on wolf territory selection and hunting patterns.
Estimating catchability across the Northern Range
To evaluate whether wolves have established their territories
in poorer hunting habitats through time, we estimated the
ÔcatchabilityÕof the landscape occupied by each wolf pack in
each year. We defined catchability as the relative probability
of kill occurrence that was due to elk density and habitat
features. We estimated catchability by fitting kill occurrence
models without wolf distribution as an explanatory variable.
We first fit a new model analogous to our best-fit landscape
effects model including elk distribution and all landscape
variables (but not wolf presence). Our catchability model is
thus a composite measure of prey availability and the
landscape attributes that influence wolf hunting success.
Annual catchability maps were derived from the odds ratio
of the catchability model coefficients (Table S2) using eqn 2.
Mean values across the NR were used as the reference for
each static variable, while the annual means were used for
the time-varying terms (elk and snow). We assumed that
annual catchability maps roughly approximate the relative
quality of wolf habitat as it relates to their likelihood of
successfully finding and killing elk.
We then sought to estimate the average catchability of
each pack’s winter territory as an index of territory quality.
We estimated mean catchability for each pack territory
(Fig. 3) as the sum of all catchability scores within the area
of the pack UD weighted by the UD values. The UDs of a
few wolf packs extended beyond the study area in some
years, so in these cases we rescaled the pack UD so that it
summed to one within the study area.
After controlling for pack size, a decline through time in
the average catchability of elk within each pack’s winter
territory area was evident (multiple regression; pack size:
t¼)2.48, P¼0.0166; year: t¼)3.47, P¼0.0011), with
a significant pack size ·time interaction (t¼2.33, P¼
0.0238) whereby large packs had access to high-quality
hunting grounds and small packs were relegated to poor
hunting grounds over time (Fig. 3). A few large, compet-
itively dominant packs retained access to the best hunting
grounds over the 10 years, but the majority of pack
territories shifted away from the best hunting grounds as
wolf density increased. These results are consistent with our
hypothesis that individual wolf packs shifted their winter
territories away from but adjacent to the best hunting
grounds, thus decoupling kill locations from wolf distribu-
tion.
DISCUSSION
In this newly restored wolf-ungulate system, we found a
striking degree of spatial variability in predation at the
landscape level. Most of this variability appears to be caused
by physical features of the landscape where prey and
predator interact. Because we found a strong influence of
landscape variables on kill-site occurrence after accounting
for the distribution of predator and prey, we believe that
habitat mediates predation by influencing the occurrence or
outcome of wolf–elk encounters. Although the precise
mechanisms for a strong landscape influence on patterns of
predation in this system are unclear, we believe such
spatially heterogeneous rates of predation to be a general
feature of native (or restored) predator–prey systems. Our
study suggests that hunting grounds – habitat patches with
physical features favourable to hunting success of wolves –
exist on the NR, and that their distribution on the landscape
influences both territorial space used by wolves and spatial
variation in predation risk for elk. Further, the decoupling of
kill occurrence from predator distribution calls into question
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1995 1997 1999 2001 2003 2005
Mean catchability of pack territory
(2) (7)
(27)
(17)
(11)
(37)
Figure 3 The distribution of wolf packs on the Northern Range of
Yellowstone National Park in relation to elk catchability (»wolf
territory quality), 1996–2005. Wolf packs have responded to the
increase in the number of neighbouring packs by selecting habitat
that minimizes interpack conflict, resulting in pack territories with
significantly poorer catchability over time. Catchability scores were
standardized within years to account for the dependency of elk
distribution on observed snow levels (in all years, average
catchability ¼1). Bubble size scales with winter wolf pack size
(representative sizes shown in parentheses), and bubbles are colour
coded by pack according to the legend in Fig. 1.
696 M. J. Kauffman et al. Letter
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

the common assumption that predator distribution drives
predation risk. In this system, territorial constraints on
predator habitat selection and movement were the most
likely mechanisms for the spatial decoupling of predator and
kill sites.
Hunting grounds on the NR were flat, snow-covered
grasslands close to streams and roads. Such habitat features
can influence spatial patterns of predation by influencing
either pre- or post-encounter interactions between predators
and prey (Hebblewhite et al. 2005), and we believe both
mechanisms play a role in conferring riskiness to the NR
hunting grounds. The risky influence of these habitat
features for elk is consistent with the cursorial (as opposed
to stalking) hunting strategy of wolves. Streams and roads
provide convenient travel corridors that likely increase prey
encounter rates (Kunkel & Pletscher 2000), while open
habitats likely facilitate prey detection (Kunkel & Pletscher
2000; Creel et al. 2005). With few visual barriers, open
habitats could also enhance the wolvesÕability to sort
through an elk group and scan its members for vulnerable
individuals to attack (Mech et al. 1998; MacNulty et al. 2007)
(mean chase distance for a subset of kills was 978.20, SE
±141.73 m). Deep snow also favours wolves after encoun-
ters because it can hinder ungulate locomotion (Huggard
1993; Post et al. 1999). Similarly, streams and associated
channels and ravines provide physical obstacles that may
impede elk escape (Bergman et al. 2006). Overall, the
physical attributes of the hunting grounds identified in this
study are consistent with the natural history of wolf hunting
behaviour. This work suggests that in addition to the well-
documented pattern of wolf selection of prey made
vulnerable due to sex, age or body condition (Mech &
Peterson 2003), habitat may also influence predation rates
by mediating the successful identification, pursuit and
capture of vulnerable prey.
Hunting grounds of the NR are used by multiple wolf
packs, a situation that does not conform to the widely held
conceptual model of distinct territorial boundaries with
interstitial prey refuges that has been suggested on an
empirical (Mech 1977) and theoretical (Lewis & Murray
1993) basis. In Minnesota, boundaries between wolf pack
territories appear to function as buffers where most inter-
pack killings occur (Mech 1994) and where ungulate prey
densities are elevated (Hoskinson & Mech 1976). By
contrast, wolf territory overlap is high in the NR system,
and territory buffers do not appear to reduce the likelihood
of kill occurrence. Instead, the relative high density of wolf
and elk populations on the NR and the strong landscape
influence on predation success interact to create a pattern
of high territorial overlap where the best hunting
opportunities exist. In this system, it appears necessary
that multiple packs maintain access to some of the same
hunting grounds.
Predator distribution has been commonly used as a
surrogate for predation risk in ecological studies (e.g. Ripple
et al. 2001; Creel et al. 2005; Fortin et al. 2005); however, our
findings indicate that risk is a function of both predator
distribution and habitat features, with habitat playing the
larger role at high predator densities. Hopcraft et al. (2005)
found similar patterns for Serengeti lions (Panthera leo),
whereby lion kills were more closely associated with good
hunting habitats (in this case, stalking cover) than areas of
high prey abundance. In a study that was able to decompose
the stages of predation, Hebblewhite et al. (2005) found that
topographic features determined patterns of wolf–elk
encounters, while habitat (i.e. vegetation) mediated post-
encounter outcomes. Wolves are inefficient predators with
generally low hunting success (»20%; Smith et al. 2000) due,
in part, to the large size and defensive capabilities of their
prey. In wolf-ungulate systems, as in other large mammal
systems (Sinclair & Arcese 1995), prime-age adult prey are
largely invulnerable to predation, and predators are highly
selective, targeting the young, old or weak (Mech &
Peterson 2003). Our finding of strong landscape effects
on predation suggests that landscape features may often Ôtip
the balanceÕin predator–prey encounters, thus influencing
post-encounter outcomes. In addition to the constraint of
landscape and habitat on predation in the NR system, the
influence of the annual wolf distribution on kill occurrence
was weakened by the social interactions and territory
selection of the predators themselves. Lima (2002) has
encouraged ecologists to evaluate the influence of predator
behaviour on predator–prey interactions, especially those
occurring over large landscapes. Our findings suggest that
the manner in which predators organize themselves on the
landscape to reduce conflict with conspecifics may obscure
the relationship between predator distribution and predation
risk. We suspect that this phenomenon may be especially
important in predator–prey systems where patterns of
predation are strongly determined by landscape or habitat
features.
There is little evidence that a temporal change in elk
antipredator behaviour provides an alternative explanation
for the decoupling of kills from predator distribution. A
potentially naı¨ve prey responding to a predator might
undergo such changes, but studies conducted so far on the
NR do not yield empirical support for profound elk
behavioural shifts relative to wolves. Several studies have
shown that elk respond to the risk of predation by wolves by
increasing vigilance levels (Laundre et al. 2001) or shifting
habitat use temporally (Creel et al. 2005; Gude et al. 2006).
However, these antipredator behaviours have not brought
about landscape-level changes in the distribution or beha-
viour of elk required to explain the results of our kill-site
analysis. This contention is supported by an NR study
evaluating elk habitat selection before and after wolf
Letter Landscape shapes wolf predation 697
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

reintroduction (Mao et al. 2005) that found that elk did not
shift their distribution away from wolf territories during
winter. In fact, wolf territory locations were a positive
predictor of elk habitat use (i.e. wolf and elk distributions
closely overlap). Also, elk increased their winter use of open
areas post-wolf reintroduction, despite our finding that such
habitats are more risky than forested areas. Further, an
analysis of GPS (Global Positioning System) collared elk on
the NR (Fortin et al. 2005) found that elk did not avoid the
core areas of wolf territories. Lastly, we found little support
for changes in the types of habitats where wolves have killed
elk over 10 years, a response we would expect if elk have
altered their habitat selection and movement patterns to
avoid encountering and being killed by wolves.
Visualizing our kill-site model as a map of relative
predation risk (Fig. 2a) provides some insights into how the
spatial scale of safe and risky patches influences the ability of
prey to manage the risk of predation while foraging, moving
and selecting habitats (Brown & Kotler 2004). The mosaic
of risky and safe habitat patches available to NR elk suggests
that elk can reduce their risk of wolf predation by making
movements on the order of 1–2 km, easily achieved within
daily movements (Fortin et al. 2005). This notion is
supported by recent findings showing that elk move out
of open areas when wolves are near (Creel et al. 2005) or
likely to occur (Fortin et al. 2005), and aggregate in
increasingly larger groups in open areas the longer wolves
are absent (Creel & Winnie 2005). The ability of elk to
mediate predation risk in such a dynamic way may explain
why elk do not avoid the riskiest habitat patches (Mao et al.
2005). Unlike the highly vulnerable native prey of intro-
duced predators, the heterogeneity of the landscape that elk
historically shared with wolves should allow them to
mediate their risk of predation from this newly restored
predator.
Our map of relative kill occurrence indicates that refugia
for elk of considerable size exist on the NR. The availability
of these refugia for elk, and their ease of accessing them,
should buffer the population from extreme levels of
predation. The existence of prey refugia also is likely to
influence long-term wolf and elk dynamics by reducing
predator-caused fluctuations in elk numbers, as found in
theoretical studies (Kareiva & Wennegren 1995). Since wolf
reintroduction, the NR elk population has declined by an
average of 8% annually (White & Garrott 2005), resulting in
much debate about the long-term equilibrium size of the elk
herd (Eberhardt et al. 2003; Vucetich et al. 2005; Varley &
Boyce 2006). The highly heterogeneous pattern of predation
found in this system offers a measure of assurance that
economically and socially valuable ungulate populations will
not suffer runaway predation as occurs with many exotic
predator invasions (Fritts & Rodda 1998; Knapp et al.
2001).
These results have implications for the potential of
restored predators to initiate trophic cascades by changing
the habitat-selection patterns or foraging behaviour of
their prey (i.e. behaviourally mediated trophic cascades;
Schmitz et al. 2004). Several studies on Yellowstone’s NR
have suggested that wolves are affecting willow (Salix
spp.), cottonwood (Populus spp.) and aspen (P. tremuloides)
communities by changing the behaviour of elk that heavily
browse these woody plants during winter (Ripple et al.
2001; Ripple & Beschta 2004; Beyer et al. 2007). However,
in our view, a rigorous test has been hindered thus far by
the lack of an empirical assessment of landscape-level
predation risk. We note that the strength of such
behaviourally mediated cascades will depend on the cost
and benefits of antipredator behaviour (i.e. avoiding or
foraging less efficiently in risky areas; Schmitz et al. 2004).
Our study makes clear that NR elk in winter face a clear
trade-off between forage quality and predation risk: most
of these browse communities are found in open, flat areas
near rivers and roads, which are risky places for elk.
However, we think it is unlikely to be optimal for elk to
simply avoid these resources, because many of them
provide forage during the critical winter months (Creel
et al. 2005; Mao et al. 2005) when NR elk (and other
northern ungulates) experience diminishing fat reserves
(Cook et al. 2001). This need for winter forage most likely
explains why elk have not made broad-scale changes in
winter habitat selection as a means of avoiding encounters
with wolves (Fortin et al. 2005; Mao et al. 2005). How elk
perceive and manage the trade-off between food and
safety will ultimately determine the existence and strength
of a behaviourally mediated trophic cascade in the NR
system.
ACKNOWLEDGEMENTS
We thank the Yellowstone Wolf Project winter study
volunteers for field assistance, D. Guernsey for logistical
support, R. Stradley for safe piloting, J. Mao for her elk
model, and H.L. Beyer for GIS support. J. Brodie, D.
Doak, J. Estes, M. Hebblewhite, J. Maron, E. Merrill, S.
Mills, O. Schmitz, L. Thurston, and two anonymous
referees provided valuable comments on the manuscript.
The authors were supported by Alberta Conservation
Association, The Camp Fire Conservation Fund, National
Geographic Society, National Park Foundation, National
Science Foundation, Natural Sciences Research Council of
Canada, Yellowstone National Park, and Yellowstone Park
Foundation. MJK was supported by a National Parks
Ecological Research Fellowship, generously funded by the
Andrew W. Mellon Foundation. DWS was partially sup-
ported by a grant from the National Science Foundation
(DEB-0613730).
698 M. J. Kauffman et al. Letter
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

REFERENCES
Bangs, E.E. & Fritts, S.H. (1996). Reintroducing the gray wolf to
central Idaho and Yellowstone National Park. Wildl. Soc. Bull., 24,
402–413.
Berger, J. (1999). Anthropogenic extinction of top carnivores and
interspecific animal behaviour: implications of the rapid
decoupling of a web involving wolves, bears, moose and ravens.
Proc. R. Soc. Lond. B Biol. Sci., 266, 2261–2267.
Berger, J., Swenson, J.E. & Persson, I.-L. (2001). Recolonizing
carnivores and naı¨ve prey: conservation lessons from Pleistocene
extinctions. Science, 291, 1036–1039.
Bergman, E.J., Garrott, R.A., Creel, S., Borkowski, J.J., Jaffe, R. &
Watson, F.G.R. (2006). Assessment of prey vulnerability
through analysis of wolf movements and kill sites. Ecol. Appl.,
16, 273–284.
Beyer, H.L., Merrill, E.H., Varley, N. & Boyce, M.S. (2007). Willow
on Yellowstone’s northern range: evidence for a trophic cascade
in a large mammalian predator–prey system? Ecol. Appl., in press.
Blackburn, T.M., Cassey, P., Duncan, R.P., Evans, K.L. & Gaston,
K.J. (2004). Avian extinction and mammalian introductions on
oceanic islands. Science, 305, 1955–1958.
Boyce, M.S., Vernier, P.R., Nielsen, S.E. & Schmiegelow, F.K.A.
(2002). Evaluating resource selection functions. Ecol. Modell.,
157, 281–300.
Boyce, M.S., Mao, J.S., Merrill, E.H., Fortin, D., Turner, M.G.,
Fryxell, J. et al. (2003). Scale and heterogeneity in habitat
selection by elk in Yellowstone National Park. Ecoscience, 10,
421–431.
Brown, J.S. & Kotler, B.P. (2004). Hazardous duty pay and the
foraging cost of predation. Ecol. Lett., 7, 999–1014.
Cook, R.C., Cook, J.G., Murray, D.L., Zager, P., Johnson, B.K. &
Gratson, M.W. (2001). Development of predictive models of
nutritional condition for Rocky Mountain elk. J. Wildl. Manage.,
65, 973–987.
Creel, S. & Winnie, J.A., Jr (2005). Responses of elk herd size to
fine-scale spatial and temporal variation in the risk of predation
by wolves. Anim. Behav., 69, 1181–1189.
Creel, S., Winnie, J.A., Jr, Maxwell, B., Hamlin, K. & Creel, M.
(2005). Elk alter habitat selection as an antipredator response to
wolves. Ecology, 86, 3387–3397.
Crooks, K.R. & Soule, M.E. (1999). Mesopredator release and
avifaunal extinctions in a fragmented system. Nature, 400, 563–
566.
Eberhardt, L.L., Garrott, R.A., Smith, D.W. & White, P.J. (2003).
Assessing the impact of wolves on ungulate prey. Ecol. Appl., 13,
776–783.
Ellner, S.P. McCauley, E., Kendall, B.E., Briggs, C.J., Hosseini,
P.R., Wood, S.N. et al. (2001). Habitat structure and population
persistence in an experimental community. Nature, 412, 538–
542.
Fortin, D., Beyer, H.L., Boyce, M.S., Smith, D.W., Duchesne´, T. &
Mao, J.S. (2005). Wolves influence elk movements: behavior
shapes a trophic cascade in Yellowstone National Park. Ecology,
86, 1320–1331.
Fritts, T.H. & Rodda, G.H. (1998). The role of introduced species
in the degradation of island ecosystems: a case history of Guam.
Annu. Rev. Ecol. Syst., 29, 113–140.
Fryxell, J.F., Greever, J. & Sinclair, A.R.E. (1988). Why are
migratory ungulates so abundant? Am. Nat., 131, 781–798.
Garshelis, D. (2000). Delusions in habitat evaluation: measuring
use, selection, and importance. In: Research Techniques in Animal
Ecology (eds Boitani, L. & Fuller, T.K.). Columbian University
Press, New York, pp. 111–164.
Gude, J.A., Garrott, R.A., Borkowski, J.J. & King, F. (2006). Prey
risk allocation in a grazing system. Ecol. Appl., 16, 285–298.
Hebblewhite, M., Merrill, E.H. & McDonald, T.L. (2005). Spatial
decomposition of predation risk using resource selection func-
tions: an example in a wolf-elk predator–prey system. Oikos, 111,
101–111.
Hooge, P.N. & Eichenlaub, B. (1997). Animal Movement Extension to
Arcview 3.2, Version 2.0. Alaska Biological Science Center, US
Geological Survey, Anchorage, Alaska. http://www.absc.usgs.-
gov/glba/gistools/animalmovementdoca.pdf.
Hopcraft, J.G.C., Sinclair, A.R.E. & Packer, C. (2005). Planning for
success: Serengeti lions seek prey accessibility rather than
abundance. J. Anim. Ecol., 74, 559–566.
Hoskinson, R.L. & Mech, L.D. (1976). White-tailed deer migration
and its role in wolf predation. J. Wildl. Manage., 40, 429–441.
Hosmer, D.W. & Lemeshow, S. (2000). Applied Logistic Regression.
Wiley, New York.
Houston, D.B. (1982). The Northern Yellowstone Elk: Ecology and
Management. Macmillan, New York.
Huggard, D.J. (1993). Effect of snow depth on predation and
scavenging by gray wolves. J. Wildl. Manage., 57, 382–388.
Kareiva, P. & Wennegren, U. (1995). Connecting landscape patterns
to ecosystem and population processes. Nature, 373, 299–302.
Keating, K.A. & Cherry, S. (2004). Use and interpretation of lo-
gistic regression in habitat-selection studies. J. Wildl. Manage., 68,
774–789.
Knapp, R.A., Matthews, K.R. & Sarnelle, O. (2001). Resistance and
resilience of alpine lake fauna to fish introductions. Ecol. Monogr.,
71, 401–421.
Kunkel, K.E. & Pletscher, D.H. (2000). Habitat factors affecting
vulnerability of moose to predation by wolves in southeastern
British Columbia. Can. J. Zool., 78, 150–157.
Laundre, J.W., Hernandez, L. & Altendorf, K.B. (2001). Wolves,
elk, and bison: reestablishing the ‘‘landscape of fear’’ in
Yellowstone National Park, U.S.A. Can. J. Zoo., 79, 1401–1409.
Lewis, M.A. & Murray, J.D. (1993). Modeling territoriality and
wolf-deer interactions. Nature, 366, 738–740.
Lima, S.L. (2002). Putting predators back into behavioral predator–
prey interactions. Trends Ecol. Evol., 17, 70–75.
MacNulty, D.R., Mech, L.D. & Smith, D.W. (2007). A proposed
ethogram of large carnivore predatory behaviour, exemplified by
the wolf. J. Mammal., 88, 595–605.
Manly, B.F.J., McDonald, L.L., Thomas, D.L., McDonald, T.L. &
Erickson, W.P. (2002). Resource Selection by Animals: Statistical
Analysis and Design for Field Studies. Kluwer, Dordrecht, The
Netherlands.
Mao, J.S., Boyce, M.S., Smith, D.W., Singer, F.J., Vales, D.J., Vore,
J.M. et al. (2005). Habitat selection by elk before and after wolf
reintroduction into Yellowstone National Park. J. Wildl. Manage.,
69, 1691–1707.
Mech, L.D. (1977). Wolf-pack buffer zones as prey reservoirs.
Science, 198, 320–321.
Mech, L.D. (1994). Buffer zones of territories of gray wolves as
regions of intraspecific strife. J. Mammal., 75, 199–202.
Mech, L.D. & Peterson, R.O. (2003). Wolf–prey relations. In:
Wolves: Behavior, Ecology, and Conservation (eds Mech, L.D. &
Letter Landscape shapes wolf predation 699
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works

Boitani, L.). University of Chicago Press, Chicago, pp. 131–
157.
Mech, L.D., Adams, L.G., Meier, T.J., Burch, J.W. & Dale, B.W.
(1998). The Wolves of Denali. University of Minnesota Press,
Minneapolis.
Nilsen, E.B., Pettersen, T., Gundersen, H., Milner, J.M., Mysterud,
A., Solberg, E.J. et al. (2004). Moose harvesting strategies in the
presence of wolves. J. Appl. Ecol., 41, 1021–1031.
Orians, G.H., Cochran, P.A., Duffield, J.W., Fuller, T.K., Gutier-
rez, R.J., Hanemann, W.M., et al. (1997). Wolves, Bears, and their
Prey in Alaska: Biological and Social Challenges in Wildlife Management.
National Academy Press, Washington D.C.
Post, E., Peterson, R.O., Stenseth, N.C. & McLaren, B.E. (1999).
Ecosystem consequences of wolf behavioural response to
climate. Nature, 401, 905–907.
Ripple, W.J. & Beschta, R.L. (2004). Wolves and the ecology of fear:
can predation risk structure ecosystems? BioScience, 54, 755–766.
Ripple, W.J., Larsen, E.J., Renkin, R.A. & Smith, D.W. (2001).
Trophic cascades among wolves, elk and aspen on Yellowstone
National Park’s northern range. Biol. Conserv., 102, 227–234.
Sand, H., Wikenros, C., Wabakken, P. & Liberg, O. (2006). Cross-
continental differences in patterns of predation: will naı¨ve
moose in Scandinavia ever learn? Proc. R. Soc. Lond. B Biol. Sci.,
273, 1421–1427.
Schmitz, O.J., Krivan, V. & Ovadia, O. (2004). Trophic cascades:
the primacy of trait-mediated indirect interactions. Ecol. Lett.,7,
153–163.
Seaman, D.E. & Powell, R.A. (1996). An evaluation of the accuracy
of kernel density estimators for home range analysis. Ecology, 77,
2075–2085.
Sinclair, A.R.E. & Arcese, P. (1995). Population consequences of
predation-sensitive foraging: the Serengeti wildebeest. Ecology,
76, 882–891.
Skovlin, J.M., Zager, P. & Johnson, B.K. (2002). Elk habitat
selection and evaluation. In: North American Elk: Ecology and
Management (eds Toweill, D.E. & Thomas, J.W.). Smithsonian
Institution Press, Washington, D.C., pp. 531–555.
Smith, D.W., Mech, L.D., Meagher, M., Clark, W.E., Jaffe, R.,
Phillips, M.K. et al. (2000). Wolf-bison interactions in Yellow-
stone National Park. J. Mammal., 81, 1128–1135.
Smith, D.W., Drummer, T.D., Murphy, K.M., Guernsey, D.S. &
Evans, S.B. (2004). Winter prey selection and estimation of wolf
kill rates in Yellowstone National Park, 1995–2000. J. Wildl.
Manage., 68, 153–166.
Soule, M.E., Estes, J.A., Miller, B. & Honnold, D.L. (2005).
Strongly interacting species: conservation policy, management,
and ethics. BioScience, 55, 168–176.
Terborgh, J., Lopez, L., Nunez, P., Rao, M., Shahabuddin, G.,
Orihuela, G. et al. (2001). Ecological meltdown in predator-free
forest fragments. Science, 294, 1924–1926.
Treves, A. & Karanth, K.U. (2003). Human-carnivore conflict and
perspectives on a carnivore management worldwide. Conserv.
Biol., 17, 1491–1499.
Varley, N. & Boyce, M.S. (2006). Adaptive management for
reintroductions: updating a wolf recovery model for Yellow-
stone National Park. Ecol. Modell., 193, 315–339.
Vucetich, J.A., Smith, D.W. & Stahler, D.R. (2005). Influence of
harvest, climate, and wolf predation on Yellowstone elk, 1961–
2004. Oikos, 111, 259–270.
White, P.J. & Garrott, R.A. (2005). Yellowstone’s ungulates after
wolves – expectations, realizations, and predictions. Biol. Con-
serv., 125, 141–152.
Wockner, G., Singer, F.J., Coughenour, M. & Farnes, P. (2006).
Yellowstone Snow Model. Natural Resources Ecology Lab, Colorado
State University, Fort Collins, CO, http://www.nrel.colo-
state.edu/projects/yellowstone/.
SUPPLEMENTARY MATERIAL
The following supplementary material is available for this
article:
Table S1 Spatial variance in wolf density index through
time.
Figure S1 Model selection results for models of kill
occurrence.
This material is available as part of the online article
from: http://www.blackwell-synergy.com/doi/full/10.1111/
j.1461-0248.2007.01059.x
Please note: Blackwell Publishing is not responsible for the
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Editor, John Fryxell
Manuscript received 14 February 2007
First decision made 23 March 2007
Manuscript accepted 24 April 2007
700 M. J. Kauffman et al. Letter
2007 Blackwell Publishing Ltd/CNRS. No claim to original US government works