A trophic cascade recently has been reported among wolves, elk, and aspen on the northern winter range of Yellowstone National Park, Wyoming, USA, but the mechanisms of indirect interactions within this food chain have yet to be established. We investigated whether the observed trophic cascade might have a behavioral basis by exploring environmental factors influencing the movements of 13 female elk equipped with GPS radio collars. We developed a simple statistical approach that can unveil the concurrent influence of several environmental features on animal movements. Paths of elk traveling on their winter range were broken down into steps, which correspond to the straight-line segment between successive locations at 5-hour intervals. Each observed step was paired with 200 random steps having the same starting point, but differing in length and/or direction. Comparisons between the characteristics of observed and random steps using conditional logistic regression were used to model environmental features influencing movement patterns. We found that elk movements were influenced by multiple factors, such as the distance from roads, the presence of a steep slope along the step, and the cover type in which they ended. The influence of cover type on elk movements depended on the spatial distribution of wolves across the northern winter range of the park. In low wolf-use areas, the relative preference for end point locations of steps followed: aspen stands Ͼ open areas Ͼ conifer forests. As the risks of wolf encounter increased, the preference of elk for aspen stands gradually decreased, and selection became strongest for steps ending in conifer forests in high wolf-use areas. Our study clarifies the behavioral mechanisms involved in the trophic cascade of Yellowstone's wolf-elk-aspen system: elk respond to wolves on their winter range by a shift in habitat selection, which leads to local reductions in the use of aspen by elk.

For gregarious animals the cost-benefit trade-offs that drive habitat selection may vary dynamically with group size, which plays an important role in foraging and predator avoidance strategies. We examined how habitat selection by bison (Bison bison) varied as a function of group size and interpreted these patterns by testing whether habitat selection was more strongly driven by the competing demands of forage intake vs. predator avoidance behavior. We developed an analytical framework that integrated group size into resource selection functions (RSFs). These group-size-dependent RSFs were based on a matched case-control design and were estimated using conditional logistic regression (mixed and population-averaged models). Fitting RSF models to bison revealed that bison groups responded to multiple aspects of landscape heterogeneity and that selection varied seasonally and as a function of group size. For example, roads were selected in summer, but not in winter. Bison groups avoided areas of high snow water equivalent in winter. They selected areas composed of a large proportion of meadow area within a 700-m radius, and within those areas, bison selected meadows. Importantly, the strength of selection for meadows varied as a function of group size, with stronger selection being observed in larger groups. Hence the bison-habitat relationship depended in part on the dynamics of group formation and division. Group formation was most likely in meadows. In contrast, risk of group fission increased when bison moved into the forest and was higher during the time of day when movements are generally longer and more variable among individuals. We also found that stronger selection for meadows by large rather than small bison groups was caused by longer residence time in individual meadows by larger groups and that departure from meadows appears unlikely to result from a depression in food intake rate. These group-size-dependent patterns were consistent with the hypothesis that avoidance of predation risk is the strongest driver of habitat selection.

Summary 1.Resource selection functions (RSFs) are becoming a dominant tool in habitat selection studies. RSF coefficients can be estimated with unconditional (standard) and conditional logistic regressions. While the advantage of mixed-effects models is recognized for standard logistic regression, mixed conditional logistic regression remains largely overlooked in ecological studies. 2. We demonstrate the significance of mixed conditional logistic regression for habitat selection studies. First, we use spatially explicit models to illustrate how mixed-effects RSFs can be useful in the presence of inter-individual heterogeneity in selection and when the assumption of independence from irrelevant alternatives (IIA) is violated. The IIA hypothesis states that the strength of preference for habitat type A over habitat type B does not depend on the other habitat types also available. Secondly, we demonstrate the significance of mixed-effects models to evaluate habitat selection of free-ranging bison Bison bison. 3. When movement rules were homogeneous among individuals and the IIA assumption was respected, fixed-effects RSFs adequately described habitat selection by simulated animals. In situations violating the inter-individual homogeneity and IIA assumptions, however, RSFs were best estimated with mixed-effects regressions, and fixed-effects models could even provide faulty conclusions. 4. Mixed-effects models indicate that bison did not select farmlands, but exhibited strong interindividual variations in their response to farmlands. Less than half of the bison preferred farmlands over forests. Conversely, the fixed-effect model simply suggested an overall selection for farmlands. 5. Conditional logistic regression is recognized as a powerful approach to evaluate habitat selection when resource availability changes. This regression is increasingly used in ecological studies, but almost exclusively in the context of fixed-effects models. Fitness maximization can imply differences in trade-offs among individuals, which can yield inter-individual differences in selection and lead to departure from IIA. These situations are best modelled with mixed-effects models. Mixed-effects conditional logistic regression should become a valuable tool for ecological research.

Summary 1.The selection for particular habitat patches can vary as a function of local and regional levels of anthropogenic disturbance. Although such functional responses can better reveal habitat loss for species of precarious status faced with dwindling resources, they remain rarely used in conservation planning. We show that functional responses can occur at multiple levels, even as nested hierarchies, and that they can explain the plasticity in habitat selection observed in threatened forest-dwelling caribou Rangifer tarandus caribou, within and among home-ranges. 2. Twenty-seven caribou were followed with global positioning system collars between 2005 and 2010. Generalized linear mixed models served as the basis from which we built multi-level functional responses characterizing how caribou alter their selection for closed-canopy conifer forests, depending upon the availability of these forests and the amount of cutovers and roads. 3. Caribou increased their selection for closed-canopy conifer forests in areas of their home-range that were comprised of a high proportion of recent cutovers during calving and summer and of high closed-canopy conifer forests during winter. Also, caribou that were established in highly disturbed areas displayed an overall stronger selection for conifer forests. These individuals further adjusted their selection for conifer forests in areas of their home-ranges that were largely comprised of recent cutovers. This concurrent response to local and global anthropogenic disturbances provides evidence of nested-hierarchical functional responses. 4. Synthesis and applications. Reliable characterization of disturbance effects on animals is necessary for conservation planning. Multi-level functional responses can accurately describe animal distribution, and we provided a framework for modelling these responses. Our multi-level functional responses indicate that fixing habitat requirements based on patterns of habitat selection for the average amount of disturbance can be misleading because it overlooks plasticity in the response of animals to habitat heterogeneity. For example, selection of closed-canopy conifer forests by caribou generally became stronger with increasing disturbance levels. Anthropogenic disturbance thus could not only lead to the functional loss of residual habitat, but it can also increase the 'relative value' of residual patches. Our study provides a tool for more thorough assessments of spatial variation in the attractiveness of resource patches and, presumably, in the fitness benefits.

Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis.