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Volume 3, Issue 1 art6 p. 1-18
Article
Open Access

Spatial ecology of refuge selection by an herbivore under risk of predation

Tammy L. Wilson

Corresponding Author

Tammy L. Wilson

Department of Wildland Resources and Ecology Center, Utah State University, 5230 Old Main Hill, Logan, Utah 84322 USA

Present address: Southwest Alaska Inventory & Monitoring Network, National Park Service, 240 West 5th Avenue, Anchorage, Alaska 99501 USA.

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Andrew P. Rayburn

Andrew P. Rayburn

Department of Wildland Resources and Ecology Center, Utah State University, 5230 Old Main Hill, Logan, Utah 84322 USA

Present address: Department of Plant Sciences, University of California, Davis, One Shields Avenue, Davis, California 95616 USA.

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Thomas C. Edwards Jr.

Thomas C. Edwards Jr.

Department of Wildland Resources and Ecology Center, Utah State University, 5230 Old Main Hill, Logan, Utah 84322 USA

U.S. Geological Survey, Utah Cooperative Fish and Wildlife Research Unit, 5290 Old Main Hill, Logan, Utah 84322 USA

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First published: 24 January 2012
Citations: 10

Corresponding Editor: J. Drake.

Abstract

Prey species use structures such as burrows to minimize predation risk. The spatial arrangement of these resources can have important implications for individual and population fitness. For example, there is evidence that clustered resources can benefit individuals by reducing predation risk and increasing foraging opportunity concurrently, which leads to higher population density. However, the scale of clustering that is important in these processes has been ignored during theoretical and empirical development of resource models. Ecological understanding of refuge exploitation by prey can be improved by spatial analysis of refuge use and availability that incorporates the effect of scale. We measured the spatial distribution of pygmy rabbit (Brachylagus idahoensis) refugia (burrows) through censuses in four 6-ha sites. Point pattern analyses were used to evaluate burrow selection by comparing the spatial distribution of used and available burrows. The presence of food resources and additional overstory cover resources was further examined using logistic regression. Burrows were spatially clustered at scales up to approximately 25 m, and then regularly spaced at distances beyond ∼40 m. Pygmy rabbit exploitation of burrows did not match availability. Burrows used by pygmy rabbits were likely to be located in areas with high overall burrow density (resource clusters) and high overstory cover, which together minimized predation risk. However, in some cases we observed an interaction between either overstory cover (safety) or understory cover (forage) and burrow density. The interactions show that pygmy rabbits will use burrows in areas with low relative burrow density (high relative predation risk) if understory food resources are high. This points to a potential trade-off whereby rabbits must sacrifice some safety afforded by additional nearby burrows to obtain ample forage resources. Observed patterns of clustered burrows and non-random burrow use improve understanding of the importance of spatial distribution of refugia for burrowing herbivores. The analyses used allowed for the estimation of the spatial scale where subtle trade-offs between predation avoidance and foraging opportunity are likely to occur in a natural system.

Introduction

The perceived risk of predation can lead to behavioral changes of prey in the presence of predators (Laundré et al. 2001). In these cases, predators can cause suboptimal use of forage (sensu Charnov 1976, Ford 1983) by inducing behaviors that reduce the risk of predation by the prey (Brown et al. 1999, Cresswell et al. 2010). Perceived predation risk also influences habitat selection patterns of prey (Abramsky et al. 1996, Creel et al. 2005, Cresswell et al. 2010). For example, some herbivores relying on vigilance behavior to avoid predators will select sites with reduced vegetation height, allowing them visually to detect predators more easily (Karels and Boonstra 1999, Iason et al. 2002, Cresswell et al. 2010). Alternatively, some herbivores prefer forage patches with dense overstory vegetation that reduces their detection by predators (Jacob and Brown 2000). Herbivores may rely on a combination of these techniques, adjusting behavior as needed for different conditions within their use areas (Creel et al. 2005). Regardless of whether or not an animal uses vigilance or concealment for predator avoidance, many may also use structures, such as trees or burrows, to aid in their escape from predation. These structures represent resources that affect the distribution of herbivores as they balance the perceived risk of predation against foraging needs.

The spatial distribution of refuge resources can affect population abundance at a variety of conceptual scales (Doncaster 2001). And although a positive association between refuge clustering and animal density was observed for intertidal snails (Skov et al. 2011), it is still unclear how the spatial scale of resources specifically affects animal distribution and abundance. Multiscale evaluation of refuge resources can improve understanding about how refuges may be clustered, and how animals may use resource clusters to improve fitness. Multiscale analysis of point patterns is important because spatial patterns can change with the scale of observation, and therefore observations made at one scale can lead to opposite interpretation than those made at another (O'Neill 1979, Bissonette 1997).

We examined the spatial distribution of refuge resources and selection patterns of pygmy rabbits. Pygmy rabbits are vulnerable to predation by a suite of predators, including: long-tailed weasel (Mustela freneta), badger (Taxidea taxus), coyote (Canis latrans), and several species of birds of prey (Crawford et al. 2010). Pygmy rabbits are capable of digging their own burrows (Green and Flinders 1980a), and burrows are an important component of pygmy rabbit habitat (Green and Flinders 1980b). Additionally, pygmy rabbits are known to use more than one burrow or burrow system (Sanchez and Rachlow 2008). Further, correlation between above-ground vegetation resource depletion and time of burrow occupancy has been shown for pygmy rabbit burrow systems in Idaho, and this is hypothesized to result in burrow switching behavior (Price 2009). Except for the case of smaller and more isolated natal burrows (Rachlow et al. 2005), pygmy rabbits are not known to use residential burrows for food storage or nesting (Bradfield 1975). Therefore, burrows are likely to be primarily used for refuge from predators for this prey species.

Burrows may provide adequate refuge from avian predators and coyote, but may be ineffective protection from long-tailed weasel and badger, which are known to pursue prey in burrows. In these cases, additional cover provided by vegetation may be necessary for pygmy rabbits to avoid predation. Many researchers have studied use of burrows based on vegetation and site characteristics (e.g., Gabler et al. 2001, Simons and Laundré 2004, Larrucea 2007). These studies found a positive correlation between shrub cover and burrow use, but did not adequately account for factors that determined proportion of burrows used by rabbits, nor did they provide a mechanistic understanding of burrow use. We recently constructed spatial predictive models for pygmy rabbit burrows by modeling burrow abundance and rabbit use as separate processes (Wilson et al. 2010), but the potential mechanisms driving burrow selection remain elusive.

The overall objective of this study was to improve understanding of how prey select a refuge by examining the spatial distribution of available, self-created refuges. We used four spatially explicit burrow censuses to determine how burrows were distributed within sites scaled to pygmy rabbits. We determined if burrows were used in proportion to their availability, and then examined how vegetation cover affected burrow use by pygmy rabbits. We hypothesized that burrows would be spatially clustered, and that selection of refugia would be based on the availability of vegetation-based resources such as overhead cover and forage. Given these hypotheses, we expected that (1) burrow distribution would be significantly clustered, (2) that rabbits would not use burrows in proportion with their availability, (3) that rabbits would select burrows located near other burrows (high burrow density), and (4) that rabbits would use additional cover resources when selecting burrows.

Methods

Study area

The study was conducted on the Duck Creek allotment in Rich County, located in northern Utah, USA. The site was dominated by sagebrush (Artemisia tridentata ssp.) shrubsteppe vegetation, and known to be occupied by pygmy rabbits. Sagebrush cover in the study area was relatively continuous, with local variation caused by treatments meant to reduce sagebrush cover, and by broad scale topographic effects. The site harbored Uinta ground squirrels (Spermophilus armatus) and American badger, which are also primary burrowers. In addition, pocket gophers (Thomomys talpoides) created extensive burrow systems in the study area, but their burrows were not often open to the surface and were generally too small for pygmy rabbits. Commonly observed predators included golden eagle (Aquila chrysaetos), Northern Harrier (Circus cyaneus), coyote, long-tailed weasel, and badger. Predator densities were not measured, but were not expected to vary substantially within the study area. Sympatric lagomorphs included mountain cotton-tail rabbits (Sylvilagus nutallii) and white-tailed jack rabbits (Lepus townsendii), but these lagomorphs were not considered to be primary burrowers.

Field techniques

We censused all burrows large enough to be used by pygmy rabbits on four sites within the Duck Creek allotment. These sites were scaled to encompass an area that was expected to be used by an individual over the course of a year (∼6 ha). This does not imply exclusive use by one individual, but encompasses an area that would be available to at least one individual. Independent sampling locations were separated by >1 pygmy rabbit home range radii (∼140 m; Sanchez and Rachlow 2008). To ensure the presence of exploited burrows, the sites corresponded with the use-areas of four randomly-chosen pygmy rabbits that were monitored by radio telemetry for a separate study (Wilson et al. 2011). We centered 6-ha circles on the median Northing and Easting coordinates of all locations for a single individual to delineate each of the four sites.

Within each 6-ha area, two or three observers systematically searched for all burrows >8 cm in any dimension (height or width) within the circular site. The lower threshold of 8 cm was set in order to distinguish pygmy rabbit burrows from those of ground squirrels, which construct burrows that are typically <8 cm in both height and width (Laundré 1989). We recorded burrow locations using a ProMark3 survey grade GPS (Magellan Professional GPS, Carquefou, Cedex, France). We post-processed burrow locations with GNSS Solutions (v. 3.10.01; Magellan Navigation 2007) using one local and at least two regional base-stations. The resulting spatial precision of burrow locations was <3 cm for most burrows (see Rayburn et al. 2011 for details of GPS methodology). Maps of burrows are available in Appendix A.

We found and recorded over 3000 burrow entrances during the burrow censuses. While every attempt was made to find all burrows within the 6-ha areas, some burrows were inevitably missed due to observer error. However, we are confident that almost all of the burrows were found and recorded, thereby reasonably satisfying assumptions of spatial point pattern analysis. In addition to location, we marked pygmy rabbit use by recording the presence of scat near the burrow entrance. Burrows were considered to be used frequently if >5 pygmy rabbit pellets were found within 25 cm of the burrow entrance. Sites with <5 pygmy rabbits pellets were considered to be used rarely. Pygmy rabbit pellets overlapped in size with that from juvenile cottontail rabbits, which made false positive burrow identification possible (J. L. Rachlow, personal communication, Moscow, ID). To minimize this problem, the first author, who had five years of experience conducting burrow surveys, determined the presence of pygmy rabbit scat. Combined with the telemetry evidence of past occupancy, the observation of several pygmy rabbits during surveys, and the lack of observation of juvenile cottontail rabbits, this methodology minimized false presence errors.

We measured vegetation covariates at a randomly selected sample of the burrows. We determined the number of burrows to skip between vegetation measurements using a field-based randomization procedure based on the second hand of a watch. GPS locations were recorded at skipped burrows, but covariate information was not. Between 0 and 20 burrows were skipped between vegetation covariate sampling locations using this randomization procedure. We measured percent cover of overstory (>20 cm) and understory (<20 cm) vegetation at each sampled burrow using a 0.25-m2 square Daubenmire frame placed over the burrow. Plants <20 cm in height consisted of grasses, forbs and small shrubs that were considered forage resources for pygmy rabbits, but were inadequate to provide visual obstruction to protect rabbits from predation. Vegetation >20 cm in height provided sufficient visual obstruction to be considered as an additional source of cover for predator avoidance, as well as a source of forage.

We used kernel density estimation to calculate a continuous index of the amount of escape cover provided by burrows (no. burrows/m2). The value of the bandwidth parameter was set to be equal to the mean bandwidth (as estimated by least squares cross validation) for all burrows at each site (mean = 2.732, SD = 0.645), rounded to the nearest integer (3). This value was consistent with other studies on clustering in burrowing animals that considered burrow clusters to be defined by a collection of burrows <3 m apart (Hayes et al. 2007). We used measured cover variables and burrow density covariates in the logistic regression analysis described below.

Analyses

We used second-order spatial statistics that were appropriate for detecting non-random patterns in fine-scale point patterns to evaluate the spatial distribution of burrows (Wiegand and Moloney 2004). We conducted spatial analyses using the spatstat package (Baddeley and Turner 2005) in program R (R Development Core Team 2009). We used the common second-order spatial statistic Ripley's K (Ripley 1981) with Ripley edge correction to evaluate burrow patterns. We followed common practice in transforming the K-functions to L-functions (Besag 1977) to stabilize variance and facilitate interpretation (see Appendix B for additional information about K- and L- functions). Preliminary analyses of density surfaces created for rabbit burrow patterns suggested that burrows were affected by first order heterogeneity caused by topography and anthropogenic land-use (e.g., roads and treatments). As a result, inhomogeneous null models were fit for all L-functions in conjunction with Monte Carlo permutation procedures (Nsim = 499) to generate approximate 95% simulation envelopes. Values of L-functions that exceeded the 95% simulation envelopes indicated significant clustering of burrows, while values of L-functions that were lower than the 95% simulation envelopes indicated significant regularity between burrows. Simulation envelopes have been criticized for potentially leading to Type I errors when values of the evaluated function are close to values of the simulation envelopes (Loosmore and Ford 2006, Blanco et al. 2008). Thus, we interpreted the significance of small departures from the null model with caution (Blanco et al. 2008).

We used bivariate random labeling (e.g., Lancaster and Downes 2004) to test if pygmy rabbits used burrows according to their availability, given the underlying distribution of burrows. We conducted tests of the bivariate random labeling hypothesis using the rlabel function in spatstat with Monte Carlo permutations (Nsim = 499) again used to generate simulation envelopes. Under this hypothesis, the labels, or marks, associated with burrows (active or inactive) were conditionally independent and identically distributed, and the test of this statistical hypothesis involved generating simulated patterns from each burrow dataset by fixing burrow locations and randomly permuting burrow labels. For each burrow dataset, we then calculated L-functions for each permutation and compared to L-functions for the original pattern. Significant deviations relative to approximate 95% simulation envelopes were evaluated with the same interpretation as discussed above.

We evaluated the manner by which vegetation structure and burrow distribution affected burrow use by pygmy rabbits using individual logistic regression models for each study landscape (four sites), with pygmy rabbit pellets used as the indicator of pygmy rabbit exploitation. Burrow density (Density; defined above) was log-transformed for logistic analyses. Other covariates of interest included vegetation cover over 20 cm in height (Ocov) and vegetation cover under 20 cm in height (Ucov). Burrow density was included in all of the models in the candidate model set of 13 a priori models (Table 1) in order to account for expected spatial structure in burrow distributions. Tests for multicollinearity of covariates were preformed prior to fitting regression models. There was a weak negative correlation between overstory and understory cover on all landscapes, but the correlation was less than the minimum acceptable threshold for including variables in the same model (Pearson R < 0.5). Models were fit using PROC LOGISTIC in SAS. Mild over-dispersion was observed for one of the four sites (Table 2). We therefore used quasi-Akaike information criterion (QAIC) to evaluate relative support for the 13 models at each of the four sites (Burnham and Anderson 2002). We included main effects in all interaction models (Table 1).

Table 1. The a priori candidate models for logistic regression on burrow utilization by pygmy rabbits in the Duck Creek allotment in Rich County, Utah, USA. Density = modeled burrow density (n/m2), log transformed; Ocov = measured percent cover of all plants > 20 cm tall; Ucov = measured percent cover of all plants < 20 cm tall. Please note that all models that include an interaction term also include the main effects.
table image
Table 2. Quasi-Akaike information criteria (QAIC) model selection statistics of logistic regression models for four pygmy rabbit site in the Duck Creek allotment in Rich County, Utah, USA. Models showed some support (ΔQAICi < 2). The variance inflation factor ĉ is bold if statistically significant (p > 0.05) overdispersion was observed. If ĉ = 1 then there was no overdispersion, and the QAIC correction reduces to AIC. The sample size is shown next to the variance inflation factor (N = x).
table image

Results

There were between 612 and 1106 (mean = 778, 1 SD = 223) burrows in each 6-ha site. Of these, roughly 50% showed evidence of pygmy rabbit use (mean = 407, 1 SD = 118). Regardless of exploitation by pygmy rabbits, burrows were significantly clustered at distances up to approximately 25 m (Fig. 1, row 1). At broader scales, burrows were either randomly or regularly distributed. Similar patterns were observed for active burrows at all sites (Fig. 1, row 2).

figure image

L-functions (solid lines) and approximate 95% simulation envelopes (Nsim = 499; dashed lines) for pygmy rabbit burrow patterns at sites in the Duck Creek allotment in Rich County, Utah, USA. Rows represent the three different sets of spatial analyses (from top to bottom): L-functions for all burrows, L-functions for active burrows only, and bivariate L-functions for tests of random labelling hypothesis regarding pattern of active burrows given locations of all burrows. Columns represent the four sites (from left to right): site 1, site 2, site 3, and site 4. The y-axis represents values of the L-functions and the x-axis represents the distance in meters at which the spatial structure is evaluated. In all plots, significant clustering of burrows is indicated if the L-function (solid lines) extends above the upper simulation envelope (dashed lines). The pattern of burrows is random if the L-function falls within the simulation envelope, and regular if the L-function falls below the simulation envelope.

The random labeling hypothesis was rejected at all sites except Site 3 (Fig. 1, row 3). This finding indicates clustered use of existing burrows by pygmy rabbits at three of the four sites, which means that pygmy rabbits did not use burrows in proportion to their spatial availability. Use of burrow clusters matched availability at the remaining site (Site 3), except at two scale ranges (∼5–20 m and 40–45 m; Fig. 1k). The observed pattern at Site 3 was likely affected by an intermittent drainage that bisected the sample area (Appendix A: Fig. A1).

Each site had different models included in the candidate model set (ΔQAIC < 2; Table 2, Appendix C). All four models with ΔQAIC < 2 on site 1 contained an interaction between burrow density and understory cover (Table 2). The interaction effect shows that the probability of rabbit use was positively correlated with burrow density at low values of understory cover, but negatively correlated with burrow density at high values of understory cover (Fig. 2). For site 2, there were two models with ΔQAIC < 2, both of which included an interaction between burrow density and overstory cover (Table 2). At this site, the probability of rabbit exploitation was negatively correlated with burrow density where overstory cover values were low, but positively correlated where overstory cover values were high (Fig. 2). Site 3 had three models within two ΔQAIC of the best model. The density-only model accounted for 32% of the QAIC weights at this site. The remaining candidate models had a positive correlation between overstory cover or a negative correlation with understory cover, respectively (Appendix D). There was considerable model selection uncertainty for site 4. The first two models indicated a positive correlation between the probability of pygmy rabbit burrow use and both burrow density and overstory cover (Appendix D). The third model included the interaction with understory, which was similar to the interaction at site 1, but not as strong.

figure image

Logistic interactions between ln(burrow density) and understory cover (site 1) and overstory cover (site 2) for two sites in the Duck Creek allotment in Rich County, Utah, USA. Each logistic function represents the relationship between the probability of pygmy rabbit burrow use and burrow density at each of seven levels of understory cover (Site 1) and overstory cover (site 2). Cover is represented by line symbol, shade and weight, with lightly shaded fine dashed lines indicating low cover values, proceeding incrementally to darkly shaded, heavy, solid lines indicating high cover. The values for % cover are 0.5, 3.0, 15.0, 37.5, 62.5, 85.0, 95.5. All of these cover values were observed for both used and unused burrows in both landscapes with significant interactions. The equation used to generate curves for were based on the parameter estimates from best model as chosen by QAIC model selection. These equations include main effects and interaction terms. Details about the mathematics used to generate the curves (including how main effects were handled) are available in Appendix E. The two vertical lines mark the range of observed burrow density. Inputs for burrow were displayed on this plot that fall outside the observed range of our data to show the characteristic shape of the logistic curve. No inference should be made about values of burrow density outside of the black bars.

Discussion

We used spatial analysis of refuge resource locations to evaluate within home range space use of a prey species. We found that there were many self-created burrows available for use by individuals, and that burrows were clustered up to ∼25 m and then regularly spaced at distances beyond ∼40 m. The shape and scale of this pattern was similar among sites, indicating generality in how burrows were distributed within the use areas of pygmy rabbits. We also observed that pygmy rabbits often did not use burrows in proportion to their availability, further suggesting resource selection based on forage or refuge quality of individual burrows or burrow clusters. Pygmy rabbits selected sites with a high level of escape resources, but burrow density and overstory cover were only part of the story. At some sites in this study, rabbits may have made a trade-off between maximum cover resources and maximum forage resources.

That burrows would be clustered at very short distances is not surprising because there are physiological limits to how far a small animal can travel through soil (Vleck 1979). Similarly, burrowing herbivores are central place or multiple central place foragers. Central place foragers are most likely to be found closer to the central place, thus a clustered use of refuge resources is expected (Rosenberg and McKelvey 1999, Wilson et al. 2011). Additionally, many burrowing animals, including Columbia ground squirrels (Spermophilus columbianus; Weddell 1989), degus (Octodon degus; Hayes et al. 2007), and European rabbits (Oryctolagus cuniculus; Cowan 1987), construct burrow systems with >1 entrance, which may result in a clustered pattern. For these herbivores, the increased number of burrow openings is considered to decrease their risk of predation (Hayes et al. 2007). Additionally, there is evidence that clustered resource patterns may be advantageous, allowing higher individual densities and perhaps aiding population persistence (Doncaster 2001).

While burrow patterns were clustered at finer-scales, patterns were random at intermediate scales and regular at broader-scales. The role of spatial scale in influencing the expected patterns of animal movement, foraging, and space use has not been adequately addressed (Börger et al. 2008). While the finer-scale clustered pattern is easily described by the physiology and foraging behavior of the study organism, the observed regularity at larger spatial scales is not as easily explained. This pattern could reflect the optimal spacing of refuge burrow clusters for animals that wish to maximize safety during foraging bouts in a heterogeneous landscape (e.g., Behrends et al. 1986). Our observation of both clustered and regular spacing of resources depending on the spatial scale at which burrow arrangement is observed illustrates the danger of transmutation errors (sensu O'Neill 1979) when interpreting results. In all cases, the interpretation of behavioral responses to predation risk change depending on the spatial scale observed. The ability to view pattern at multiple spatial scales is a strong advantage of the point pattern analysis methods employed here.

Prey species must balance feeding behaviors with those that allow them to avoid predation (Sih 1980). The spatially clustered pattern of burrows and burrow exploitation could therefore result from a prey species that is minimizing distance travelled from the relative safety of a burrow while foraging. Our observation that pygmy rabbits do not use burrows in proportion to their availability suggests that the perceived risk of predation may be driving this behavior. Short foraging bouts near cover have been observed for a variety of prey species, including vizcachas (Lagostomus maximus), which are reluctant to venture far from burrows when foraging in order to minimize their vulnerability to predation by reducing the distance to safety provided by burrows (Galende and Raffaele 2008). Similarly, white-throated sparrows (Zonotrichia albicollis) tended to forage preferentially near protective cover (Schneider 1984). These published observations of foraging behavior and our spatial analysis of self-created refuge exploitation lend support to the idea that central place foraging behavior is an evolutionary adaptation to predation risk (Lima and Dill 1990).

How optimal foragers under risk of predation select resources can be further understood through an examination of which factors affected burrow exploitation by pygmy rabbits. We observed that in addition to burrow density, overstory cover was a positive predictor of burrow use on some of the sites (Appendix D). Overstory cover was included in the supported models (ΔQAIC < 2) for all sites. This observation agrees with other studies of pygmy rabbits that found increasing sagebrush cover leads to an increased probability of pygmy rabbit occurrence (e.g., Green and Flinders 1980b, Simons and Laundré 2004, Larrucea and Brussard 2008). Overhead vegetative cover was also positively correlated with placement of burrows by degus, and is thought to reduce their risk of predation (Hayes et al. 2007). However, pygmy rabbits feed on big sagebrush, especially in winter (Green and Flinders 1980b), and sagebrush is the dominant overstory plant in our system (T. L. Wilson, unpublished data). Therefore, distinguishing forage abundance and protection provided by overhead cover is difficult. Despite this, the presence of significant interactions between burrow density and vegetation cover suggests that the spatial pattern of burrows and the presence of overhead cover may both be important for minimizing predation risk by pygmy rabbits.

We found interactions between burrow density and vegetation cover for the top-ranking model at two sites, and within a supported model set for another. Although the interactions occurred for overstory cover on one site, and for understory cover on the others, the negative relationship between overstory cover and understory cover suggest that the mechanism generating the interactions is the same for all three sites. In all cases, the expected positive relationship between the probability of pygmy rabbit use and burrow density is reversed, demonstrating that rabbits use areas of low overall refuge abundance (as measured by both burrow density and overstory cover) in order to access areas with high understory forage availability (Fig. 2). This observation suggests that pygmy rabbits are making a tradeoff between high forage availability (understory cover) and high safety (overstory cover and burrow density) in some cases.

That animals must choose between optimizing protection from predation with foraging opportunities is not a new insight (Sih 1980, Verdolin 2006). Our results quantify the spatial scale at which the subtle trade-off between foraging opportunity and predation risk is expected in a natural system. Further research in natural systems where observations are made at scales that capture normal prey movements is necessary to formalize this link between refuge distribution and foraging behavior. For example, both the amount of forage exploitation required to induce animals to make the risky decision to change burrow clusters, and the optimal distance moved, should be explored. Detailed observation of animal behavior in landscapes where predation pressure is experimentally manipulated would be required to test hypotheses regarding resource distribution and use in relation to predation risk.

Acknowledgments

We extend thanks to R. Groll and the landowners of the Duck Creek allotment for access to private lands. Research was funded by the Utah State University Ecology Center and supported by the U.S. Geological Survey Cooperative Fish and Wildlife Research Unit. Technicians G. Diamond, E. Goss, S. Hunt, R. Pyles, C. Simeon, and S. Weston assisted with field work. The RS/GIS lab, especially T.B. Murphy and C. Gerrard, assisted with the GPS unit and burrow analyses. A. J. Leffler helped with field work and provided valuable input on early drafts. We thank R. T. Larsen and M. B. Hooten for providing valuable comments during FSP review, and two anonymous reviewers for their helpful insights. Mention of specific products and services does not constitute endorsement by the United States Government or U.S. Geological Survey. Procedures were approved by the Utah State University Animal Care and Use Committee (Protocol #1258).

    Supplemental Material

    Appendix A

    figure image

    Pygmy rabbit burrow maps for the four sites censused in the Duck Creek Allotment in Rich County, Utah, USA. The color ramp shows burrow density ranging from low values in cool colors to high values in warm colors. Burrows are indicated by a circle. Burrows with five or more pygmy rabbit pellets are blue, and those with less than five are white.

    Appendix B

    The K-function is used to evaluate second order point processes for significant nonrandom spatial patterns assuming stationarity and isotropy. This function works by determining the intensity of events (number/per unit area) within a specified area of each point. K is estimated for a defined radius (h) from each point by Eq. 1.
    i2150-8925-3-1-art6-e01
    where h is the radius of a search window, λ is the intensity of event in the region, |D| is the area of the region, dij is the distance between the ith and jth events. K-hat is expected to be high if there is much clustering and low if the spacing is regular. The distribution of K-hat is non-linear so we applied a transformation to K-hat called L-hat (Eq. 2).
    i2150-8925-3-1-art6-e02
    Plotted against h, L-hat gives a visual representation of a point pattern across the range of h. The significant of a point pattern may be evaluated using Monte Carlo simulation envelopes; a point pattern is clustered if the value of the function above the upper limits of the simulation envelopes, and regular if the function is below the lower limits of the simulation envelope.

    Appendix C

    Table C1. QAIC model selection statistics of logistic regression models for four pygmy rabbit sites in the Duck Creek allotment in Rich County, Utah, USA. Models are grouped by support (models showing support: ΔQAICi < 2; models lacking support: ΔQAICi > 2). The variance inflation factor ĉ is bold if statistically significant (p > 0.05) overdispersion was observed. If ĉ = 1 then there was no overdispersion, and the QAIC correction reduces to AIC. The sample size is shown next to the variance inflation factor (N = x).
    table image
    Table C2. AIC model selection statistics of logistic regression models for four pygmy rabbit sites in the Duck Creek allotment in Rich County, Utah, USA. Models are grouped by support (models showing support: ΔAICi < 2; models lacking support: ΔAICi > 2).The sample size is shown next to the site name (N = x).
    table image

    Appendix D

    Table D1. Regression coefficient parameter estimates for all logistic regression models for four pygmy rabbit site in the Duck Creek allotment in Rich County, Utah, USA. Models are described in shorthand that is defined by Table 1 in the main manuscript. All interaction models include the main effects. Bold indicates models and coefficients that are statistically significant at p = 0.05.
    table image

    Appendix E

    The equations used to generate curves for Fig. 2 were based on the parameter estimates from best model as chosen by AIC model selection. In both cases I is a vector of burrow densities going from 1 to 8 in 0.01 increments. The interaction represented by the curves was generated by holding Oi (overstory cover) or Ui (understory cover) constant for each of the seven Daubenmier cover classes. The choice between Oi and Ui was based on which term showed a significant interaction with burrow density. The equations follow the general logistic form: e(intercept+main effect1+main effect 2+interaction effect)/(1 − e(intercept+main effect1+main effect 2+interaction effect)). If a third main effect was present in the selected model, then it was added to the basic equation described above. The equation used to generate the figure for Site 1 was: e(−54.3664+0.0144 × Oc + 12.2843 × I+0.6031 × Ui + −0.1365 × I × Ui)/(1 − e(−54.3664+0.0144 × Oc + 12.2843 × I+0.6031 × Ui + −0.1365 × I × Ui)). Where I and Ui are described above. Oc is a constant level of overstory cover (37.5). The equation used to generate the figure for Site 2 was: e(8.8149+−1.8040 × I+−0.2165 × Oi + 0.0573 × I × Oi)/(1 − e(8.8149+−1.8040 × I+−0.2165 × Oi + 0.0573 × I × Oi)). Regression coefficients for both equations come from the logistic regression analyses.

    ##Fig. 2 plots

    I1 = seq (1,8,by = .01)

    O1 = 0.5

    O2 = 3

    O3 = 15

    O4 = 37.5

    O5 = 62.5

    O6 = 85

    O7 = 95.5

    #Lil (Site 2) interaction term IXO

    IXO1 = I1 * O1

    exp1 = exp (8.8149 + −1.8040*I1 + −0.2165*O1 + .0573*IXO1)

    prob1 = exp1/(1+exp1)

    plot (I1,prob1, pch = 10, col = “white”, xlab = “Burrow Intensity”, ylab = “Probability of Use”)

    lines (I1,prob1, lty = 3, lwd = 1,col = “darkgray”, add = TRUE)

    IXO2 = I1 * O2

    exp2 = exp (8.8149 + −1.8040*I1 + −0.2165*O2 + .0573*IXO2)

    prob2 = exp2/(1+exp2)

    lines (I1,prob2, lty = 2, lwd = 1.5,col = “darkgray”, add = TRUE)

    IXO3 = I1 * O3

    exp3 = exp (8.8149 + −1.8040*I1 + −0.2165*O3 + .0573*IXO3)

    prob3 = exp3/(1+exp3)

    lines (I1,prob3, lty = 2, lwd = 2.5,col = “darkgray”, add = TRUE)

    IXO4 = I1 * O4

    exp4 = exp (8.8149 + −1.8040*I1 + −0.2165*O4 + .0573*IXO4)

    prob4 = exp4/(1+exp4)

    lines (I1,prob4, lty = 1, lwd = 1,col = “darkgray”, add = TRUE)

    IXO5 = I1 * O5

    exp5 = exp (8.8149 + −1.8040*I1 + −0.2165*O5 + .0573*IXO5)

    prob5 = exp5/(1+exp5)

    lines (I1,prob5, lty = 1, lwd = 1.5,col = “black”, add = TRUE)

    IXO6 = I1 * O6

    exp6 = exp (8.8149 + −1.8040*I1 + −0.2165*O6 + .0573*IXO6)

    prob6 = exp6/(1+exp6)

    lines (I1,prob6, lty = 1, lwd = 2.5,col = “black”, add = TRUE)

    IXO7 = I1 * O7

    exp7 = exp (8.8149 + −1.8040*I1 + −0.2165*O7 + .0573*IXO7)

    prob7 = exp7/(1+exp7)

    lines (I1,prob7, lty = 1, lwd = 5,col = “black”, add = TRUE)

    abline (v = 3.26)

    abline (v = 5.23)