Spatial decomposition of predation risk using resource selection functions: an example in a wolf-elk predator-prey system

Predation is a fundamental ecological and evolutionary process that varies in space, and the avoidance of predation risk is of central importance in foraging theory. While there has been a recent growth of approaches to spatially model predation risk, these approaches lack an adequate mechanistic framework that can be applied to real landscapes. In this paper we show how predation risk can be decomposed into encounter and attack stages, and modeled spatially using resource selection functions (RSF) and resource selection probability functions (RSPF). We use this approach to compare the effects of landscape attributes on the relative probability of encounter, the conditional probability of death given encounter, and overall wolf and elk resource selection to test whether predation risk is simply equivalent to location of the predator. We then combine the probability of encounter and conditional probability of death into a spatially explicit function of predation risk following Lima and Dill's reformulation of Holling's functional response. We illustrate this approach in a wolf-elk system in and adjacent to Banff National Park, Alberta, Canada. In this system we found that the odds of elk being encountered by wolves was 1.3 times higher in pine forest and 4.1 times less in grasslands than other habitats. The relative odds of being killed in pine forests, given an encounter, increased by 1.2. Other habitats, such as grasslands, afforded elk reduced odds (4.1 times less) of being encountered and subsequently killed (1.4 times less) by wolves. Our approach illustrates that predation risk is not necessarily equivalent to just where predators are found. We show that landscape attributes can render prey more or less susceptible to predation and effects of landscape features can differ between the encounter and attack stages of predation. We conclude by suggesting applications of our approach to model predator-prey dynamics using spatial predation risk functions in theoretical and applied settings.