Popul Ecol (2008) 50:145–157
DOI 10.1007/s10144-008-0078-4
ORIGINAL ARTICLE
Relationship between resource selection, distribution,
and abundance: a test with implications
to theory and conservation
Chris J. Johnson Æ Dale R. Seip
Received: 3 July 2007 / Accepted: 20 January 2008 / Published online: 27 February 2008
The Society of Population Ecology and Springer 2008
Abstract Much of applied and theoretical ecology is
concerned with the interactions of habitat quality, animal
distribution, and population abundance. We tested a technique that uses resource selection functions (RSF) to scale
animal density to the relative probability of selecting a
patch of habitat. Following an accurate survey of a reference block, the habitat-based density estimator can be used
to predict population abundance for other areas with no or
unreliable survey data. We parameterized and tested the
technique using multiple years of radiotelemetry locations
and survey data collected for woodland caribou across four
landscape-level survey blocks. The habitat-based density
estimator performed poorly. Predictions were no better
than those of a simple area estimator and in some cases
deviated from the observed by a factor of 10. We developed a simulation model to investigate factors that might
influence prediction success. We experimentally manipulated population density, caribou distribution, ability of
animals to track carrying capacity, and precision of the
estimation equation. Our simulations suggested that interactions between population density, the size of the
reference block, and the pattern of distribution can lead to
large discrepancies between observed and predicted population numbers. Over- or undermatching patch carrying
capacity and precision of the estimator can influence
C. J. Johnson (&)
Ecosystem Science and Management Program,
University of Northern British Columbia, 3333
University Way, Prince George, BC, Canada V2N 4Z9
e-mail: [email protected]
D. R. Seip
British Columbia Ministry of Forests and Range,
1011 4th Ave, Prince George, BC, Canada V2L 3H9
predictions, but the effect is much less extreme. Although
there is some empirical and theoretical evidence to support
a relationship between animal abundance and resource
selection, our study suggests that a number of factors can
seriously confound these relationships. Habitat-based density estimators might be effective where a stable, isolated
population at equilibrium is used to generate predictions
for areas with similar population parameters and ecological
conditions.
Keywords Caribou Estimation Habitat Population Resource selection function
Introduction
Habitats are a key element in understanding the population
dynamics and distribution of many plants and animals
(Morris 2003). Indeed, one of the primary causes of the
global decline in biodiversity is habitat alteration and loss
(Hoekstra et al. 2005). Despite the importance of habitats,
there are few general constructs and even fewer theoretical
motivations to guide scientific progress in this area.
Although we recognize a paucity of theory, three connected
and evolving foci have directed much of the past and
present research by habitat ecologists. First, habitat ecology—the study of a population’s response (e.g., change in
distribution or abundance) to variation in the suite of biotic
and abiotic resources that constitute habitats—is firmly
rooted in a description of an individual’s life-history
requirements with an emphasis on variation within or
among populations and across space and time. Niche theory has served as a dominant and useful construct for
describing habitat use in an evolutionary context (Pulliam
2000).
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Given an increased emphasis by ecologists on the study
of spatial and temporal processes, the second and more
recent focus of habitat ecologists has considered the relationship between habitat selection and species distribution
(Lohmus 2003). When attempting to understand and predict the distribution of animals in relation to habitats, we
often assume that the strength of selection correlates with
fitness (Railsback et al. 2003; McLoughlin et al. 2006).
This assumption underlies the application of some speciesdistribution models to conservation planning (Boyce and
Waller 2003; Seip et al. 2007) and provides a framework to
link selection to evolution.
The third and most recent focus of habitat ecologists is
developing quantitative links between habitat selection,
animal distribution, and population density (Boyce and
McDonald 1999; Pearce and Ferrier 2001; Nielsen et al.
2005). Intuitively, animals should distribute themselves
according to the quality of habitats, as indexed by a
selection metric. If selection is consistent with fitness, we
should find more animals in better-quality habitats (Loegering and Fraser 1995). This logic has been applied to
questions of applied ecology, wildlife management, and
conservation. As an example, Boyce and McDonald (1999)
presented a technique that produces quantitative relationships between resource selection and animal density.
Contemporary applications of this approach include Ciarniello et al. (2007) who used a resource selection function
(RSF) and a population estimate (sensu Boyce and
McDonald 1999) to explain variation in the density of
grizzly bears (Ursus arctos) between two landscapes, and
Seip et al. (2007) who used the same technique to predict
the number of woodland caribou (Rangifer tarandus caribou) displaced by snowmobile traffic. Despite numerous
applications of this and other similar approaches to questions of conservation and management (e.g., Boyce and
Waller 2003; Apps et al. 2004; Gaines et al. 2005), there
have been few empirical studies that directly test the
relationship between animal density and habitat selection.
This is despite dialogue, simulation exercises, and some
limited data suggesting that a correlation between habitat
selection and animal density might apply to a narrow range
of circumstances only (Van Horne 1983; Hobbs and Hanley 1990; Nielsen et al. 2005).
We used multiple years of animal locations and survey
data to test whether a relationship between the selection of
habitat patches, animal distribution, and abundance occurs
at the scale of landscapes. Our study animal was woodland
caribou, a species with relatively simple resource requirements and strong habitat selection affinities during the time
of year we conducted our population surveys (Terry et al.
2000; Jones 2007). Furthermore, the distribution and
quality of late-winter habitat is subject to few large-scale
natural disturbances, leading to a relatively static
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Popul Ecol (2008) 50:145–157
environment for assessing habitat–population relationships
across years. Here, we define a landscape as an ecological
area with a grain equal to a single foraging patch
([0.06 ha) and an extent defined by the range of a subpopulation isolated to high-elevation forested and alpine
habitats (223–143 km2).
Our test first involved developing a RSF for radio-collared caribou, which quantified the strength of selection for
a number of different habitat components (Manly et al.
2002). Then, we applied a simple but logical habitat-based
density estimation technique (Boyce and McDonald 1999)
to iteratively estimate and compare the predicted with the
observed number of caribou in four blocks during 3 years
of surveys. As a follow-up to our empirical test, we
developed a simulation model that allowed us to explore
factors that might influence the relationship between habitat selection, animal distribution, and abundance. We
modified the parameters of the simulation model to assess
how variation in animal density, failure to match patchcarrying capacity, bias in animal behavior, and error in the
habitat-based density estimator influenced predictions of
animal numbers.
Methods
Study area
The study area encompassed approximately 4,012 km2 of
mountainous and plateau landscape centered at 12120 W
53500 N, 100 km east of Prince George, BC, Canada
(Fig. 1). Climate, topography, and resulting vegetation
associations vary considerably across that area (Meidinger
and Pojar 1991). The dominant low-elevation ecosystem
occurs from valley bottoms to 1,100–1,300 m and consists
of coniferous forests of hybrid white spruce (Picea glauca 9 P. engelmannii), subalpine fir (Abies lasiocarpa), and
to a lesser degree lodgepole pine (Pinus contorta) on disturbed or dry sites. The uppermost forested regions are
characterized by climax forests with canopies of Engelmann spruce (P. engelmannii) and subalpine fir. Subalpine
parkland is found at the forest–alpine ecotone and supports
small, stunted, subalpine fir. Alpine tundra has the most
severe climatic conditions accommodating shrubs, herbs,
bryophytes, and lichens, with sporadic underdeveloped
trees occurring in krummholz form.
Animal locations and survey data
From 1988 to 1993, 29 female woodland caribou (mountain ecotype) were captured by net-gun fired from a
helicopter and fitted with very-high-frequency (VHF)
Popul Ecol (2008) 50:145–157
147
Fig. 1 Blocks surveyed for
woodland caribou found in
central British Columbia,
Canada, and locations of
caribou recorded during surveys
conducted in 1999, 2002, and
2005
radiotelemetry collars (Terry et al. 2000). Animals were
relocated using single-engine airplanes at a median interval
of 33 days during the winter, as defined by seasonal elevation changes in habitat occupancy. Given the relatively
long relocation interval, we assumed behavioral independence between animal locations. These locations were used
to quantify resource selection by the study population.
Between mid-February and late March of 1999, 2002,
and 2005, we performed a single stratified survey for
woodland caribou. The study area was divided into four
blocks, and a helicopter was used to survey high-elevation
subalpine and alpine areas typical of late-winter habitat
(Terry et al. 2000). One pilot and two observers inspected
terrain for caribou or tracks at or near tree line. Where
caribou tracks were noted, we conducted systematic searches until individuals or groups of caribou were sighted.
Using a sample of marked animals, previous researchers
reported that approximately 87% of woodland caribou are
located using this technique during late winter (Wittmer
et al. 2005a).
Statistical definition of habitat selection
We used RSFs to quantify the influence of vegetative and
topographic factors on the distribution of woodland caribou
(Manly et al. 2002). Typically, an RSF consists of a
number of coefficients (bi) that quantify selection for or
avoidance of some environmental feature. Coefficient sign
and strength is a product of variation in the distribution of
each environmental feature measured at a sample of animal
locations and a comparison set of random sites.
We used conditional fixed-effects logistic regression to
estimate coefficients for our RSF analysis. Fixed-effects
logistic regression allows one to pair samples that are
related according to some behavioral or other matching
criterion (Compton et al. 2002). Here, the likelihood is
premised on the difference between two or more paired
samples of cases and controls or, in this instance, used and
random comparison locations. Matching controlled for
variation in habitats and behavior of caribou over time and
space. We clustered the fixed-effects regression on each
animal location and five randomly selected comparison
sites. Comparison sites quantify the availability of resources and were sampled from within a circle that was
centered on the preceding telemetry location and had a
radius equal to the 95th percentile movement distance for
that particular relocation interval. For simplicity, we considered this resource-selection function to be representative
of the range of behaviors caribou demonstrated over their
median relocation interval.
We developed RSFs using vegetation and topographic
variables that are correlated with the distribution of
woodland caribou during winter (Terry et al. 2000). Vegetation was represented by a broad-scale biogeoclimatic
ecosystem classification (BEC) system (Meidinger and
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Pojar 1991). The BEC is a hierarchical framework that
groups ecosystem units according to similarities in climate,
soil, and vegetation. In cases where occupancy was low,
geographically adjacent BEC variants were generalized to
BEC zone. In total, we related caribou distribution to six
BEC zones or variants: high-elevation alpine tundra (AT
un and AT unp) and low-elevation sub-boreal spruce zones
(SBS dw1, SBS vk, SBS wk1), and the midelevation
Engelmann spruce–subalpine fir cariboo wet cold (ESSF
wc3), wet cool parkland (ESSF wcp), cariboo wet cool
(ESSF wk1), and Misinchinka wet cool (ESSF wk2) variants. A full description of the zones can be found in
Meidinger and Pojar (1991).
Recognizing the coarse-scale of the vegetation mapping
and the affinity of woodland caribou for subalpine parkland
(ESSF wcp and low-elevation AT), we included a variable
representing the distance of animal and random locations
from tree line. The exact definition of tree line varies across
the study area, but we assumed it occurred in a constant
band from 1,800 to 1,820 m. Also, caribou are known to
forage across habitats on sloped terrain (Terry et al. 2000).
We used a digital elevation model (25 9 25-m pixel resolution) to generate an image of terrain steepness and a
quadratic term to represent avoidance of flat and very-steep
habitats.
Popul Ecol (2008) 50:145–157
correlation indicating greater number of locations in bins
with larger RSF scores. As a second, more conservative,
measure of prediction success, we used the ROC to assess
the classification accuracy of the most parsimonious RSF
model (Pearce and Ferrier 2000). This is a conservative
estimate because we assume that all random locations are
absent of caribou (Boyce et al. 2002). We considered a
model with an ROC score of 0.7–0.9 to be a ‘‘useful
application’’ and a model with a score [0.9 as ‘‘highly
accurate’’ (Boyce et al. 2002).
We used bootstrapped 95% confidence intervals (CIs) to
assess the strength of effect of each predictor covariate on
the dependent variable. Poor power and inconclusive statistical inference is expected from covariates with
confidence intervals that approach or overlap 0. Coefficients generated for an RSF design are correct, but standard
errors (SE) might not truly represent sampling variation
(Johnson et al. 2006). Thus, we generated bootstrapped CIs
using the bias-corrected method and 1,000 replicates of
each model (Mooney and Duval 1993). We used the
Pregibon Db and leverage (i.e., hat) statistics as well as
the Hosmer and Lemeshow Dv2 statistic to identify cases
and clusters that had a large influence on the parameters
of the model. We used tolerance scores to assess variables within each model for excessive multicollinearity
(Menard 1995).
Model selection, fit, and prediction
Predicting the distribution of woodland caribou
The population survey was conducted during late winter;
thus, we developed RSFs for that season only (29 January–
31 March). We fit four RSF models to the caribou use and
availability data: BEC; BEC + slope2; BEC + distance to
tree line; BEC + distance to tree line + slope2. We used
Akaike weights (w) generated with the small sample
Akaike’s information criterion (AICc) to average coefficients across models (Anderson et al. 2000). The AIC
provides evidence for selection of the most parsimonious
model but does not permit evaluation of discriminatory
performance. We used k-fold cross-validation and the
receiver operating characteristic (ROC) to evaluate the
predictive success of the most parsimonious RSF model
(Boyce et al. 2002). We wanted to be extremely confident
that our final model predicted the distribution of monitored
caribou, as this is a requirement for developing and evaluating the habitat-based density estimator; thus, we applied
both the k-fold and ROC technique. The k-fold procedure
was performed five times withholding 20% of the data for
each iteration. A Spearman rank correlation was used to
assess the relationship between predicted probability of
occurrence for withheld caribou locations and their frequency within ten equally spaced bins defined by the range
of predicted scores. A predictive model will have a high
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A prediction generated with an RSF model is proportional
to the true probability of occurrence and is calculated as
wð xÞ ¼ exp ðb1 x1 þ b2 x2 þ þ bk xk Þ
ð1Þ
We populated Eq. 1 with coefficients (b1…bi) from the
regression models and applied that equation to the
respective Geographical Information System (GIS) data
(x1…xi). We grouped all predicted values into ten synthetic
habitat classes representing a low to a high relative
probability of occurrence and successively greater
strength of selection. We used percentiles calculated from
the predicted RSF scores (w) from the observed caribou
locations to define class break points (Johnson et al. 2005).
The RSF map was generated only for high-elevation areas
where the population survey was conducted ([1,500 m).
Predicting the number of woodland caribou
We used the RSF-based population estimation model of
Boyce and McDonald (1999) to test the relationship
between habitat selection, animal distribution, and population density. We used that model because of its logical
Popul Ecol (2008) 50:145–157
149
and mathematical simplicity and contemporary relevance
in the ecological literature (e.g., Boyce and Waller 2003;
Apps et al. 2004; Gaines et al. 2005; Ciarniello et al. 2007;
Seip et al. 2007). The model was parameterized using
survey data from four blocks and our final RSF model
describing the relative probability of caribou occurrence
across the study area.
We used the number of observed caribou in a reference
block and the relative probabilities of occurrence to calculate the density of animals within the ten synthetic RSF
habitat classes found within each prediction block. The
midpoint of RSF values was used to distribute animal
habitat use U(xi), among the i = 1, ..., 10 habitat classes,
U ðxi Þ ¼ wðxi ÞAðxi Þ=Ri wðxi ÞAðxi Þ
ð2Þ
where w(x) is the midpoint (i.e., median) RSF value from
Eq. 1 for the observed caribou locations, A(x) is the area of
the respective synthetic RSF derived habitat classes, and x
is a vector of habitat variables. The number and density of
caribou in the ith habitat class of the reference area was
then calculated as Ni = N 9 U(xi) and Di = Ni/A(xi),
where N is the total count for the survey block. Estimates
of animal density were then multiplied by the total area of
each RSF habitat class (j) in the remaining survey blocks,
and when summed across
classes provided a total
^
population estimate N for each block,
N^ ¼ Rj Dðxi ÞA0 xj
ð3Þ
We performed the population estimation procedure for
the four survey blocks, iteratively replacing the reference
population and redefining Eq. 3. Alternating block as the
reference population allowed us to make 12 comparisons
between predicted and observed population numbers for a
total of 36 comparisons across the 3 survey years. As a test
of the predictive ability of the habitat-based density
estimator, we compared predictions using the RSF model
to predictions calculated using the simple density of
animals in the reference block not adjusted by strength of
selection or area for each habitat class,
D ¼ N=A
ð4Þ
For each prediction from either the RSF or the simple
density estimator, we calculated the difference from the
observed number of caribou in that survey block. We used a
Mann–Whitney U test to determine if the accuracy of
estimates from the RSF and simple density estimator differed.
We hypothesized that if a relationship existed between habitat
selection, animal density, and population numbers, the
predictions from the RSF-based estimator for each survey
block should have a smaller difference from the observed
number of caribou relative to population predictions
generated using a simple density estimator (Eq. 4).
Simulated distribution and population estimates
We developed a simulation model to test a number of factors
that might influence the accuracy of the habitat-based density
estimator (Fig. 2). Similar to the analysis of the empirical
data, the model consisted of four survey blocks each containing ten habitat patches. For each replicate of the
simulation, animals were introduced sequentially to the
landscape at the beginning of the winter and distributed randomly or semirandomly among the four blocks. Once an
animal was placed in a survey block, it was forced to occupy
the most highly selected habitat patch if that patch had not
reached the predetermined carrying capacity. Occupation of
each of the ten habitat patches was determined by RSF scores
that varied in increments of 0.1 and ranged from 0.1 to 1.0.
RSF scores were consistent among survey areas, but the area
of patches varied. The area of the ten habitat patches in the
simulated Bearpaw, Torpy, Severeid, and Otter blocks
decreased systematically in increments of 5, 4, 3, and 1 km2,
N
Torpy (220 km2)
Otter (55 km2)
Severeid (165 km2)
Bearpaw (275 km2)
Fig. 2 Schematic representation of the simulation model used to
explore factors influencing the accuracy of a habitat-based population
density estimator. The four virtual population blocks are to scale and
consisted of ten patches incrementally decreasing in area. Quality of
patches increased as color lightened and patch size decreased. For
most simulations (solid arrow), caribou dispersed incrementally from
the circular area, randomly selected a block, and then occupied the
patch with the greatest resource selection function (RSF) value (i.e.,
light block, RSF value = 0.9–1.0) that was below the predetermined
carrying capacity. Dispersals continued until the density of caribou, as
a percentage of maximum carrying capacity, was achieved across the
study area. For the scenario that incorporated geographic bias (dashed
arrow), caribou first occupied the most westerly blocks (Bearpaw)
and then proceeded in an easterly direction. Following the simulated
dispersal of caribou, each block served as a reference population to
predict numbers in the remaining three blocks (sensu Boyce and
McDonald 1999). The simulated number of caribou in the remaining
blocks then served as the test for the estimation protocol
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150
Popul Ecol (2008) 50:145–157
respectively, for total areas of 275, 220, 165, and 55 km2. We
arbitrarily decided that the Bearpaw block could support 120
animals. Following this decision, maximum abundance in
each patch within each survey block was calculated using Eqs.
2 and 3 and was a product of the area and the RSF score for that
patch (Boyce and McDonald 1999).
Initially, we parameterized the model to distribute the
maximum number of animals (N = 312) across the study
area under conditions where survey blocks were selected
randomly and animals were forced to fill the most highly
selected habitats first. Ultimately, selection of each patch
within a block was determined by the predetermined RSF
score (0.1–1.0). The outcome of this base-case scenario
was approximately deterministic (i.e., all patches were
occupied to their capacity) and resulted in population distribution that was predicted near perfectly by the RSF
density estimator. We then proceeded to test the relative
influence of a number of ecological factors that we
hypothesized might influence the predictive ability of the
RSF estimation procedure. Because we anticipate different
ecological conditions for each application of the habitatbased density estimator (Boyce and McDonald 1999) and
derivations of that model, we did not explicitly bind each
hypothesis to the observed data for mountain caribou.
Thus, simulation parameters represent a full range of
conditions potentially experienced by model practitioners
but include those observed for this study population.
from the size of the reference block and a biased occupancy
of that block.
Variation in population density and geographic bias
Model error
Where populations occur at densities less than the ecological carrying capacity of their range, opportunities exist
to underutilize habitats of high quality. Thus, undermatching could be a simple product of annual variation in
animal distribution for low-density populations, such as the
mountain caribou we observed. To test this hypothesis, we
simulated the distribution of populations with successively
fewer individuals relative to carrying capacity. For each
simulation, we introduced a population with 10% fewer
individuals up to a maximum reduction of 90% (N = 312–
31). We conducted this simulation under conditions in
which animals were randomly and semirandomly distributed among blocks. In the latter case, we modified the
simulation routine to bias occupancy of blocks geographically (i.e., geographic bias) from west to east by 10%
increments. Thus, the probability of an animal occupying
the Bearpaw block was 10% greater than the next most
westerly block, Torpy, and 30% more likely when compared with the most easterly, Otter, block (Fig. 1).
Geographic bias represented systematic patterns in caribou
distribution that might affect the accuracy of the density
estimator. We hypothesized an interaction effect resulting
All model coefficients and associated GIS data are associated with some error. When these data are applied to
estimation procedures, the resulting uncertainty could be
substantial. To test this assertion, we varied the parameters
of the habitat-based density estimator systematically for
each experimental population. We allowed the RSF value
and area of each patch to vary randomly according to a
score drawn from a uniform distribution. We repeated this
experiment four times, increasing the total magnitude of
variation in 10% increments from 10 to 40%.
We simulated the distribution of woodland caribou 200
times for each level of each treatment. As with the
empirical test, we used the distribution of simulated animals for a survey block to predict population numbers for
the remaining three blocks, resulting in a total of 12
comparisons (i.e., Eqs. 2, 3). Our metric for comparison
across experimental treatments was the percentage difference in observed from predicted population numbers. We
used a balanced analysis of variance (ANOVA) to test for
differences in prediction resulting from the four factors we
manipulated experimentally: variation in animal density
(with and without geographic bias), underfitting and
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Overmatching/undermatching: incongruence between
density and patch quality
An accurate habitat-based population estimator requires a
strong positive relationship between resource selection and
the potential for a patch to contain greater numbers of animals.
Furthermore, this relationship must scale directly to other
areas. However, RSFs may be a poor proxy of habitat quality
or animals may be incapable of relating population density to
resource availability when making selection decisions. We
modified the simulation model so that the distribution of
animals did not directly match the equilibrium value of the ten
patches. For each simulated distribution, animals selected the
best-quality patches first, but the maximum allowable density
of those patches was allowed to vary stochastically. These
levels of imprecision represented the inability of caribou to
accurately relate selection to abundance. We repeated the
experiment four times, letting the density of animals in each
patch vary positively or negatively by 10, 20, 30, and 40% of
the predetermined carrying capacity. The percentage overfit
or underfit for each replicate was selected from a uniform
distribution constrained by the maximum allowable variation
for that experiment (i.e., 10–40%).
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overfitting distribution relative to patch quality, and variation in estimates due to error in model parameters. We
generated 12 predictions of population density for each
simulation (i.e., each of the four blocks sequentially served
as a reference); however, for statistical analyses, we randomly selected and used one prediction only. This allowed
us to test two additional factors: reference block and predicted block. Density is a product of area; thus, we
hypothesized that a large difference in area of the reference
and predicted block would lead to inaccurate total population estimates.
The dependent variable for statistical comparisons was
percentage difference in predicted and observed population
numbers; thus, we applied a square root transformation to
the absolute values. For post hoc comparisons, we used
Tamhane’s T2 test for unequal variances. We assessed the
magnitude of effect for each factor using the partial etasquared (g2) statistic. Eta-squared does not partition the
total explained variation but does provide a factor-specific
measure of effect size (Pierce et al. 2004). We used Stata
(Intercooled, V7.0, College Station, TX, USA) to conduct
simulations and statistical analyses.
Results
RSF models of habitat selection and distribution
We used 208 animal and 1,040 random locations to parameterize four ecologically plausible RSF models describing
the distribution of woodland caribou. In total, 33% of the
telemetry locations fell within the boundaries of the four
survey blocks, and 94% occurred in similar high-elevation
habitats ([1,200 m; X ¼ 1; 539; ±1 SD = 365). This
suggested a strong relationship between the distribution of
animals with VHF collars and animals counted during annual
population estimates (Fig. 1).
The best RSF model was the most complex and consisted
of covariates for BEC, distance to tree line, and quadratic
terms for slope (Table 1). For that model, an AIC w of
0.64 revealed some model selection uncertainty, which was
Table 2 Averaged coefficients (b) and bootstrapped 95% confidence
intervals (CI) for resource selection function models for woodland
caribou of central British Columbia, Canada, monitored from 1988 to
1995
Covariate
BEC-AT
BEC-SBS
Xb
1.537
-4.676
95% CI
0.481 to 4.874
-21.055 to 3.810
BEC-ESSF wc3
1.440
BEC-ESSF wcp
2.177
BEC-ESSF wk1
-0.417
-1.486 to 3.059
BEC-ESSF wk2
-0.061
-0.928 to 3.272
Distance to tree line (km)
-0.018
-0.001 to 0.001
0.005
-0.053 to 0.073
-0.001
-0.002 to 0.001
Slope-linear
Slope-squared
0.774 to 4.590
1.570 to 2.466
BEC biogeoclimatic ecosystem classification, AT alpine tundra, SBS
sub-boreal spruce, ESSF Engelmann spruce–subalpine fir caribou
accommodated through the use of model averaging. Large
coefficients suggested selection for ESSF wcp parkland followed by AT areas and avoidance of forested habitats in the
SBS BEC zone (Table 2). Across those areas, caribou
selected for moderate slopes and avoided AT habitats as the
distance from tree line increased (Table 2). However, CIs for
a number of these variables overlapped 0, suggesting high
variance in model parameters resulting from model selection
uncertainty and sampling variation. The k-fold cross-validation procedure suggested that the most complex model was a
good predictor of the distribution of monitored woodland
caribou (
rs ¼ 0:878; P \ 0.001). The mean ROC score
(X ¼ 0:826; SE = 0.01) supports this finding.
Using the RSF scores we estimated the total area of the
ten habitat classes for each block. Total area of survey
block varied considerably with the Bearpaw block, having
the largest area at 222.7 km2, followed by the Otter, Torpy,
and Severeid blocks, with areas of 214.3, 143.1, and
110.1 km2, respectively (Fig. 3). The Torpy block had the
greatest amount of high-quality class 9, and 10 habitat
(19.2 km2), followed by the Bearpaw block (17.5 km2).
Population estimation of observed animals
Table 1 Differences in Akaike’s information criterion (AICc) scores
(D) and AICc weights (w) for candidate resource selection functions
(RSFs) for woodland caribou monitored from 1988 to 1995 across
central British Columbia, Canada
Model
k
AICc Di
AICc wi
BEC
5
6.4
0.026
BEC + slope2
7
1.5
0.296
BEC + distance to tree line
BEC + distance to tree line + slope2
6
8
5.7
0
0.037
0.640
BEC biogeoclimatic ecosystem classification
During 1999, 2002, and 2005, we counted 261, 281, and
376 caribou, respectively, across the four survey blocks.
Assuming a relatively stable population, distribution of
animals varied among blocks and years (Fig. 4). The
number of caribou counted on the Torpy block, for
example, differed between 2002 and 2005 by a factor of 6.
The accuracy of population predictions also varied among
block and year (Fig. 4). Of the 36 replicate predictions, the
best agreement between predicted and observed numbers
of caribou resulted in a difference of only two animals, and
123
152
Popul Ecol (2008) 50:145–157
100
180
90
160
Area of RSF Class (km2)
80
140
Otter
Severeid
Bearpaw
Torpy
70
60
Year - 1999
120
50
100
40
80
30
60
20
40
10
20
0
1
2
3
4
5
6
7
8
9
10
Otter
RSF Habitat Class
a total of 12 predictions were ± 20 animals from the true
count. However, we noted some extreme outliers, including
a tenfold deviation from the observed for the Torpy block
during 2002. Predictions from the habitat-based estimator
were similar in accuracy to those generated from the simple
density estimator (Z = 0.073, P = 0.942).
180
Torpy
Bearpaw
Severeid
Torpy
Bearpaw
Severeid
Torpy
Bearpaw
Year - 2002
160
Number of Predicted Caribou
Fig. 3 Total area (km2) of habitat classes for four landscape blocks as
defined by a resource selection function (RSF) for mountain caribou
monitored in central British Columbia, Canada. The RSF value and thus
the quality of habitat class increased from class 1 to class 10
Severeid
140
120
100
80
60
40
20
Population estimation of simulated animals
ANOVA resulted in statistically significant main and interaction effects for the six factors we tested using simulated
woodland caribou populations and explained a large portion
of the total observed variation (R2 = 0.771; Table 3). Effect
size measures suggested that the strongest relationship
between treatment and variation in observed from predicted
population estimates was population density (g2 = 0.433),
followed by reference block (g2 = 0.414), geographic bias
(g2 = 0.360), and interaction terms of reference block by
density (g2 = 0.325) and geographic bias by density and
reference class (g2 = 0.312). Post hoc analyses revealed
significant differences for all pairwise comparisons of population density up to a 70% reduction from carrying capacity.
Following this threshold, mean differences among predictions at 70 and 80%, 80 and 90%, and 70 and 90% of carrying
capacity were small and nonsignificant (P [ 0.998; Fig. 5).
We noted statistically significant differences in predictions
among all comparisons of reference class (P \ 0.001).
However, density interacted with reference class and geographic bias. For populations with B219 caribou, a 30%
reduction in density from carrying capacity, predictions
generated using the smallest reference block (Otter) were
123
Otter
180
Year - 2005
160
140
120
100
80
60
40
20
Otter
Census Block
Fig. 4 Observed (triangle) and predicted number of caribou for
survey blocks (x-axis) found in central British Columbia, Canada,
during 1999, 2002, and 2005. Filled and open symbols represent
population predictions generated using a resource selection function
(RSF) habitat-based estimator and a simple density estimator,
respectively. Population predictions were generated using observed
caribou numbers from corresponding reference blocks (circle
Otter, square Torpy, inverted triangle Severeid, diamond
Bearpaw)
Popul Ecol (2008) 50:145–157
Table 3 Results of analysis of
variance (ANOVA) testing the
simulated main and interaction
effects of animal density,
geographic bias in distribution,
over- and undermatching patchcarrying capacity, error in
model parameters, and choice of
reference or predicted block on
the predictive capacity of a
habitat-based population
estimation technique
153
Factor
df
F
P
Partial g2
Geographic bias
1
64605.0
\0.001
0.360
Density
9
9770.9
\0.001
0.433
Overmatching/undermatching
4
68.3
\0.001
0.002
Model error
5
308.2
\0.001
0.013
Reference block
3
27120.6
\0.001
0.414
Predicted block
3
4079.3
\0.001
0.096
Density 9 geographic bias
9
4351.8
\0.001
0.254
Density 9 reference block
27
2050.1
\0.001
0.325
Density 9 predicted block
27
257.8
\0.001
0.057
Density 9 geographic bias 9 reference block
30
1735.7
\0.001
0.312
extremely inaccurate; differences were not as extreme for the
other reference blocks (Fig. 5a). Predictions for the Bearpaw
block were highly variable and less accurate than the other
three blocks, but the interaction with density was less
extreme (Fig. 5b). The introduction of geographic bias
dampened the impact of density on prediction success but
only following a 20% reduction in population density
(Fig. 5c). The effect of overmatching and error in the prediction equation was statistically significant but less extreme
than the other factors (Figs. 6, 7). However, holding the other
factors at unperturbed levels, we did note differences from
observed as high as 33 and 96%, respectively.
Discussion
We present a novel set of data, in both temporal and spatial
scope, for testing a habitat-based population estimator. The
results of our empirical and simulation analyses suggest
that the relationship between habitat selection, animal
distribution, and population numbers is constrained and,
under some conditions, weak. The estimator developed
from an RSF equation was no better at predicting the
number of caribou than the more simple density estimator,
which did not consider habitat value. We do not believe,
however, that the negative results were a product of the
study species or resulting RSF. A number of factors suggest that mountain caribou are an excellent model species
for such tests. First, mountain caribou use a narrow range
of habitats and forage almost exclusively on a few genera
of arboreal lichen (Terry et al. 2000; Jones 2007). Specific
use of habitats will result in strong observable patterns of
habitat selection, a result supported by two forms of model
validation. Furthermore, large-scale natural disturbances
are infrequent across the late-winter range of the animals
we monitored (Stevenson and Coxson 2003). This argues
for little interannual variation in forage availability within
and among blocks and partially controls for the discrepancy between the timing of the monitoring and surveys.
Second, mountain caribou are a low-density ecotype, but the
study population is relatively stable (Wittmer et al. 2005a).
Given small numbers of animals, it is unlikely that density
dependence constrained selection of optimal habitats by
individual animals (Hobbs and Hanley 1990; Rosenzweig
1991). Third, despotic behavior, predation risk, and human
disturbance are important factors that can strongly influence
the behavior of animals (Reimers et al. 2003; Fortin et al.
2005) and confound predictions from theoretical models
such as the ideal-free distribution (Grand and Dill 1999).
Caribou are gregarious during winter; thus, at the scale of
our survey blocks, we did not expect the ‘‘despotic’’
behavior of a few dominant individuals to influence the
distribution of the population (Calsbeek and Sinervo 2002).
We did not include predation risk as a covariate in our RSF
model (Johnson et al. 2002), but wolves, the primary predator of caribou, typically do not use high-elevation habitats
during the late winter (Seip 1992). During each survey, we
noted few or no human activities across the reference blocks.
Although our empirical data suggest that the habitatbased population estimator poorly represents the relationship between habitat selection, distribution, and population
density, it is important to note that this test is specific to one
set of ecological circumstances. If the distribution of a
species correlates with habitat quality and the reference and
predicted population are at some form of relative equilibrium, then the technique should accurately predict the
number of animals across a fixed area. This was demonstrated by our base-case simulation. Other authors have had
some success with the technique we applied. Boyce and
Waller (2003), for example, used two independent reference populations to predict the number of grizzly bears that
an unoccupied ecosystem might support. They were careful
to note that their estimates might be biased by the density of
animals in their reference populations, which were assumed
to have reached equilibrium. Other researchers have
found positive relationships between population density
and amount of habitat or prey (Crête 1999; Carbone and
Gittleman 2002). However, there are numerous examples
123
154
Popul Ecol (2008) 50:145–157
(a)
X % Difference Observed vs. Predicted
350
Bearpaw
Otter
Torpy
Severeid
300
250
200
150
100
50
0
64
10
8
6
4
2
0
33
0
(b)
200
Bearpaw
Otter
Torpy
Sevreid
150
50
0
312 281 250 219 188 157 126 95
(c)
20
30
40
Fig. 6 Mean treatment effects and 95% confidence intervals of overand undermatching patch-carrying capacity in 10% increments on the
prediction success of a habitat-based population estimator for
simulated caribou populations
100
150
10
Maximum % Deviation From Patch Carrying Capacity
64
33
No geographic bias
Geographic bias
100
X % Difference Observed vs. Predicted
X % Difference Observed vs. Predicted
312 281 250 219 188 157 126 95
12
22
20
18
16
14
12
10
8
6
4
2
0
0
10
20
30
40
50
Maximum % Error Introduced to Patch Area and RSF Score
Fig. 7 Mean treatment effects and 95% confidence intervals of
introducing error to the parameters of the habitat-based population
estimator (Boyce and McDonald 1999) used to predict the number of
animals in simulated caribou populations
50
0
312 281 250 219 188 157 126 95
64
33
Population Size
Fig. 5 Mean interaction effects and 95% confidence intervals of
population density and a reference block, b prediction block, and
c geographic bias on prediction success of a habitat-based population
estimator for simulated caribou populations
in which a relationship between resource abundance and
population density was not observed (Haughland and Larsen 2004; Mitchell et al. 2005).
In comparison with our empirical analysis, the simulation routines were simplistic representations of animal
distribution and density (Fig. 2). However, this exercise
allowed us to explore a number of factors that might result
123
in discrepancies between true and predicted population
numbers for this technique and others premised on similar
logic (e.g., Laidre et al. 2002; Gaines et al. 2005). When we
compared individual factors, the accuracy of predictions
was most strongly affected by the density of the reference
population relative to ecological carrying capacity. The
population of mountain caribou we surveyed occurred at
numbers that were well below carrying capacity (Wittmer
et al. 2005b); thus, we manipulated the simulation to represent this reality. Given relatively few caribou per area of
habitat, the population of simulated or actual caribou could
disperse and distribute themselves freely among a number
of landscape blocks that differed in size. This annual variation in distribution has obvious negative implications for
the habitat-based density estimator. As an extreme example,
Popul Ecol (2008) 50:145–157
the entire population might choose to occupy only one
block in a single year, resulting in a relatively highobserved caribou density. Using the technique demonstrated here, we would then predict large numbers of
animals in the remaining areas, but survey efforts would
reveal no use. As we demonstrated via simulation, such
outcomes would be exacerbated by biased distribution to
relatively small or large blocks (i.e., geographic bias). This
result was partially echoed by the empirical data, but we did
not consistently find overestimation of caribou numbers for
the largest blocks based on reference populations in the two
smallest blocks (i.e., Torpy and Severeid; Fig. 1). Such
complexity is supported by the simulation model that produced a strong negative effect for prediction accuracy
following an interaction of caribou density, geographic
bias, and size of reference block.
Another significant, but less important, source of error
revealed by our simulations was the inability of animals to
distribute themselves optimally in accordance with the
quality and density of habitat patches. Experimental evidence suggests that over- and undermatching of animal
density relative to food resources should be the norm, not
the exception (Kennedy and Gray 1993). Constraints on
competitive ability, movement, and knowledge can lead to
discrepancies in an ideal-free distribution. Our model of
distribution did not explicitly measure food intake, a
common surrogate for testing fitness, the direct outcome of
variation in an ideal-free distribution (Tregenza 1995). For
both empirical and simulation analyses, we assume that the
RSF predictions were proportional to the true probability of
use and that the relative probability was a close proxy of
habitat quality in a population context (Manly et al. 2002).
Researchers are now beginning to recognize the inherent
uncertainty in predictions resulting from spatially explicit
models (Regan et al. 2002). Although we noted a statistically
significant effect, simulations suggest that RSF coefficients
must be fairly imprecise and GIS data inaccurate before the
validity of population predictions is threatened. For empirically based applications of the habitat-based estimator, SE
associated with RSF coefficients will provide an approximate measure of uncertainty associated with sampling and
process variation (Elith et al. 2002).
Our simulations can provide some guidance to practitioners or theoreticians attempting to relate habitat selection to
population density using either the Boyce and McDonald
(1999) technique or derivations of the same logic (e.g.,
Gaines et al. 2005). Results strongly suggest that researchers
wishing to evaluate the usefulness of the technique and
relationships should first have a good understanding of variation in animal density across space and time. In cases where
one wants to estimate the maximum number of animals that
an area might contain, then the reference population should
be at some long-term equilibrium. Variation or uncertainty in
155
the number of animals occurring in the reference block will
produce variable and inaccurate estimates. Furthermore,
such inaccuracies will be magnified by differences in the
total area of the reference relative to the prediction block.
Metapopulation-like structures, such as we demonstrated,
are likely the most difficult application for this technique.
Populations that are small relative to carrying capacity and
that exhibit weak fidelity to annual ranges will lead to highly
variable annual estimates across multiple blocks. This is the
normal ecological circumstance for woodland caribou found
across our study area. Given reasonable precision in model
parameters, the habitat-based estimator might be effective
for simpler applications consisting of a stable, isolated
population easily observed in one well-defined survey block
and a prediction area of similar size and ecology.
If the habitat-based estimator technique (Boyce and
McDonald 1999) is prone to poor predictive success under
a range of uncertainties, then what options exist for conservation and management? Count models based on the
negative binomial or Poisson distribution are a recent
advancement in statistical ecology and have demonstrated
their value in relating survey data to environmental conditions (Pearce and Ferrier 2001; Barry and Welsh 2002).
Other approaches exclude the influence of environmental
factors and relate abundance to the spatial distribution and
relationship of observed individuals (He and Gaston 2000).
More simply, one can develop univariate linear relationships between some resources, prey density for example,
and animal abundance (Carbone and Gittleman 2002). As
with the habitat-based estimator, all of these approaches
suffer from limitations. The ecological interpretation and
meaningfulness of habitat use versus habitat availability
relationships has been questioned (Hobbs and Hanley
1990; Mysterud and Ims 1999), but appropriately constructed models can quantify competing choices on
heterogeneous landscapes (Johnson et al. 2002; Mauritzen
et al. 2003). Count, distribution, and simple density models
are premised on correlations between animal density and
environmental covariates only.
Our inability to effectively predict population numbers
has direct implications for applied ecology, management,
and conservation (Roloff and Haufler 1997). The implications to ecological theory are less obvious but we believe
equally important. The ideal-free distribution, for example,
predicts that habitat quality and density-dependent resource
use interact, leading to an equilibrium point where all
animals, regardless of patch quality, have access to a
similar level of resources (Fretwell and Lucas 1970).
Similarly, the mathematical description of metapopulation
dynamics has been expanded to include the distribution of
organisms across space and time relative to patch quality
(Hanski and Gilpin 1991; DeWoody et al. 2005; Freckleton
et al. 2005). Many of the fundamental principles of the
123
156
ideal-free distribution and metapopulation dynamics have
been applied repeatedly and critiqued on numerous fronts,
but they have rarely been tested using field data at largespatial scales (Tyler and Hargrove 1997).
Implicit to our understanding and observation of the
ideal-free distribution and metapopulation dynamics is a
functional relationship between animal abundance and
habitat quality. At an evolutionary scale, this relationship
must stand, but at ecological scales (i.e., interyear variation), we argue that other, more dynamic and less rigid,
factors may be at work. If these four survey blocks were to
be isolated into discrete subpopulations with long-term
extinction recolonization events, habitat quality might have
very little to do with population density or the probability
of occupancy and persistence. Likewise, our failure to
observe equivalent numbers of caribou in patches of habitat
of equal value across blocks suggests that this population
does not conform to an ideal-free distribution. This
assumes that our measure of habitat selection represents
resource quality and intake and animals have equal access
to all patches across the broader area. Although our ultimate conclusion might appear obvious, we must emphasize
that an abundance of highly selected habitats do not necessarily result in large populations and that variation in
population density can be independent of habitat quality.
Acknowledgments We thank M. Boyce, M. Gillingham, D. Heard,
and S. Nielsen for guidance on an earlier version of this manuscript.
We thank G. Watts for providing survey data. Two anonymous
reviewers provided constructive comments that greatly improved the
final paper.
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