Resource Selection Functions Based on Use–Availability Data: Theoretical Motivation and Evaluation Methods

Abstract

Applications of logistic regression in a used–unused design in wildlife habitat studies often suffer from asymmetry of errors: used resource units (landscape locations) are known with certainty, whereas unused resource units might be observed to be used with greater sampling intensity. More appropriate might be to use logistic regression to estimate a resource selection function (RSF) tied to a use–availability design based on independent samples drawn from used and available resource units. We review the theoretical motivation for RSFs and show that sample “contamination” and the exponential form commonly assumed for the RSF are not concerns, contrary to recent statements by Keating and Cherry (2004; Use and interpretation of logistic regression in habitat-selection studies. Journal of Wildlife Management 68:774–789). To do this, we re-derive the use–availability likelihood and show that it can be maximized by logistic regression software. We then consider 2 case studies that illustrate our findings. For our first case study, we fit both RSFs and resource selection probability functions (RSPF) to point count data for 4 bird species with varying levels of occurrence among sample blocks. Drawing on our new derivation of the likelihood, we sample available resource units with replacement and assume overlapping distributions of used and available resource units. Irrespective of overlap, we observed approximate proportionality between predictions of a RSF and RSPF. For our second case study, we evaluate the classic use-availability design suggested by Manly et al. (2002), where availability is sampled without replacement, and we systematically introduce contamination to a sample of available units applied to RSFs for woodland caribou (Rangifer tarandus caribou). Although contamination appeared to reduce the magnitude of one RSF beta coefficient, change in magnitude exceeded sampling variation only when >20% of the available units were confirmed caribou use locations (i.e., contaminated). These empirically based simulations suggest that previously recommended sampling designs are robust to contamination. We conclude with a new validation method for evaluating predictive performance of a RSF and for assessing if the model deviates from being proportional to the probability of use of a resource unit.