Bayesian nonparametric inference for the overlap of daily animal activity patterns

The study of the interaction among species is an active area of research in Ecology. In particular, it is of interest to evaluate the overlap of their ecological niches. Temporal activity is one of the niche’s axes most commonly used to explore ecological segregation among animal species, and many contributions focus on the overlap of this variable. Once the information of the temporal activity is obtained in the wild, the data is treated as a random sample. There exist different methods to estimate the overlap. Specifically, in the case of two species, one possibility is to estimate the density of the temporal activity of each species and then evaluate the overlap between these density functions. This leads naturally to the analysis of circular data. Most of the procedures currently in use impose some rather restrictive assumptions on the probabilistic models used to describe the phenomena, and only provide approximate measures of the uncertainty involved in the process. In this article, we propose a Bayesian nonparametric approach which incorporates a well-defined noninformative prior. We take advantage of the data structure to define such a prior in terms of the predictive distribution. To the best of our knowledge, this is a novel approach. Our procedure is compared with a well-known method using simulated data, and applied to the analysis of real camera-trap data concerning two mammalian species from the El Triunfo biosphere reserve (Chiapas, Mexico).