Estimating encounter location distributions from animal tracking data

Ecologists have long been interested in linking individual behaviour with higher level processes. For motile species, this ‘upscaling’ is governed by how well any given movement strategy maximizes encounters with positive factors and minimizes encounters with negative factors. Despite the importance of encounter events for a broad range of ecological processes, encounter theory has not kept pace with developments in animal tracking or movement modelling. Furthermore, existing work has focused primarily on the relationship between animal movement and encounter rates while the relationship between individual movement and the spatial locations of encounter events in the environment has remained conspicuously understudied. Here, we bridge this gap by introducing a method for describing the long-term encounter location probabilities for movement within home ranges, termed the conditional distribution of encounters (CDE). We then derive this distribution, as well as confidence intervals, implement its statistical estimator into open-source software and demonstrate the broad ecological relevance of this distribution. We first use simulated data to show how our estimator provides asymptotically consistent estimates. We then demonstrate the general utility of this method for three simulation-based scenarios that occur routinely in biological systems: (a) a population of individuals with home ranges that overlap with neighbours; (b) a pair of individuals with a hard territorial border between their home ranges; and (c) a predator with a large home range that encompassed the home ranges of multiple prey individuals. Using GPS data from white-faced capuchins Cebus capucinus, tracked on Barro Colorado Island, Panama, and sleepy lizards Tiliqua rugosa, tracked in Bundey, South Australia, we then show how the CDE can be used to estimate the locations of territorial borders, identify key resources, quantify the potential for competitive or predatory interactions and/or identify any changes in behaviour that directly result from location-specific encounter probability. The CDE enables researchers to better understand the dynamics of populations of interacting individuals. Notably, the general estimation framework developed in this work builds straightforwardly off of home range estimation and requires no specialized data collection protocols. This method is now openly available via the ctmm R package.