A vector of point processes for modeling interactions between and within species using capture-recapture data
Alex Diana, Eleni Matechou, Jim E. Griffin, Yadvendradev Jhala, Qamar Qureshi
Capture-recapture (CR) data and corresponding models have been used extensively to estimate the size of wildlife populations when detection probability is less than 1. When the locations of traps or cameras used to capture or detect individuals are known, spatially-explicit CR models are used to infer the spatial pattern of the individual locations and population density. Individual locations, referred to as activity centers (ACs), are defined as the locations around which the individuals move. These ACs are typically assumed to be independent, and their spatial pattern is modeled using homogeneous Poisson processes. However, this assumption is often unrealistic, since individuals can interact with each other, either within a species or between different species. In this article, we consider a vector of point processes from the general class of interaction point processes and develop a model for CR data that can account for interactions, in particular repulsions, between and within multiple species. Interaction point processes present a challenge from an inferential perspective because of the intractability of the normalizing constant of the likelihood function, and hence standard Markov chain Monte Carlo procedures to perform Bayesian inference cannot be applied. Therefore, we adopt an inference procedure based on the Monte Carlo Metropolis Hastings algorithm, which scales well when modeling more than one species. Finally, we adopt an inference method for jointly sampling the latent ACs and the population size based on birth and death processes. This approach also allows us to adaptively tune the proposal distribution of new points, which leads to better mixing especially in the case of non-uniformly distributed traps. We apply the model to a CR data-set on leopards and tigers collected at the Corbett Tiger Reserve in India. Our findings suggest that between species repulsion is stronger than within species, while tiger population density is higher than leopard population density at the park.