Dynamics of animal joint space use: a novel application of a time series approach

Animal use is a dynamic phenomenon, emerging from the movements of animals responding to a changing environment. Interactions between animals are reflected in patterns of joint space use, which are also dynamic. High frequency sampling associated with GPS telemetry provides detailed data that capture space use through time. However, common analyses treat joint space use as static over relatively long periods, masking potentially important changes. Furthermore, linking temporal variation in interactions to covariates remains cumbersome. We propose a novel method for analyzing the dynamics of joint space use that permits straightforward incorporation of covariates. This method builds upon tools commonly used by researchers, including kernel density estimators, utilization distribution intersection metrics, and extensions of linear models.

We treat the intersection of the utilization distributions of two individuals as a time series. The series is linked to covariates using copula-based marginal beta regression, an alternative to generalized linear models. This approach accommodates temporal autocorrelation and the bounded nature of the response variable. Parameters are easily estimated with maximum likelihood and trend and error structures can be modeled separately. We demonstrate the approach by analyzing simulated data from two hypothetical individuals with known utilization distributions, as well as field data from two coyotes (Canis latrans) responding to appearance of a carrion resource in southern Texas.

Our analysis of simulated data indicated reasonably precise estimates of joint space use can be achieved with commonly used GPS sampling rates (s.e.=0.029 at 150 locations per interval). Our analysis of field data identified an increase in spatial interactions between the coyotes that persisted for the duration of the study, beyond the expected duration of the carrion resource. Our analysis also identified a period of increased spatial interactions before appearance of the resource, which would not have been identified by previous methods.

We present a new approach to the analysis of joint space use through time, building upon tools commonly used by ecologists, that permits a new level of detail in the analysis of animal interactions. The results are easily interpretable and account for the nuances of bounded serial data in an elegant way.