Varying nonlinear dependencies in habitat selection: estimating instead of imposing functional forms

Abstract

Spatial heterogeneity of habitats and different foraging strategies can result in dissimilar patterns of habitat selection among individuals in a population. Studies have demonstrated that incorporating individual variation can influence model inferences. Thus, individual variation is increasingly being incorporated in habitat selection studies. Our objective was to advance the concept of individual variation in habitat selection by incorporating varying shapes (i.e., function forms) of responses among individuals. We used simulation modeling to develop a new analytical framework and introduce a new habitat selection metric, the Normalized Selection Ratio (NSR). Our results demonstrated the ability of the NSR to correctly estimate the strength and shape of complex simulated patterns of habitat selection, while simultaneously protecting against over-fitting. Using a simulated population of individuals, we showed how our approach can scale-up individual responses to facilitate population-level inference. We demonstrated how hierarchical clustering of individual-level response curves can identify and quantitatively describe different types of habitat selection within a population. When applied in a temporally dynamic framework, we showed that the NSR can detect ecological dynamics in habitat selection with quantitatively different inferences from analyses that pool data over time. We illustrated application of our approach using global positioning system (GPS) telemetry data for grizzly bears (Ursus arctos) in the Greater Yellowstone Ecosystem (GYE). We investigated the direction (preference or avoidance) and shapes of grizzly bear selection for whitebark pine (Pinus albicaulis) habitat during fall from 2007 to 2014. Our general conclusions support previous findings that grizzly bears exhibit a high degree of individual variation in habitat selection. Our approach of hierarchically clustering response curves detected 4 groups of grizzly bears with distinctly different patterns of whitebark pine habitat selection. Based on the group-level mean responses, 77% of sampled bears selected for whitebark habitat and 23% selected for non-whitebark pine habitats. Among the hierarchical groups that selected for whitebark pine, we observed substantial variation in the strength and density of whitebark pine being used. These results demonstrated the ability of our approach to identify, quantify, and organize individual differences in habitat selection and improve our understanding of grizzly bear ecology in the GYE.