A vector of point processes for modeling interactions between and within species using capture‐recapture data

Abstract

Capture-recapture 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 capture-recapture models are used to infer the spatial pattern of the individual locations and population density. Individual locations, referred to as activity centres, are defined as the locations around which the individuals move. These activity centres are typically assumed to be independent, and their spatial pattern is modelled 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 paper, we consider a vector of point processes from the general class of interaction point processes and develop a model for capturerecapture 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 normalising 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 of Liang and Jin (2013), which scales well when modelling more than one species. Finally, we adopt an inference method for jointly sampling the latent activity centres and the population size based on the algorithm of Geyer and Møller (1994). 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 capture-recapture 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 leopand population density at the park.

Multistage hierarchical capture–recapture models

“…In many cases, the distribution [s] serves as a prior and is specified as a bivariate uniform distribution over the study area, which implies a complete spatial random point process for s i before the data are observed. Various approaches have been proposed to generalize the model for s i such as allowing it to be a heterogeneous spatial point process (e.g., Diana et al, 2022;Sutherland et al, 2015). Following the procedure we described in the previous section, we express the posterior distribution associated with the SCR model as…”

“…In many cases, the distribution $$$ \left[\mathbf{s}\right] $$$ serves as a prior and is specified as a bivariate uniform distribution over the study area, which implies a complete spatial random point process for $$$ {\mathbf{s}}_i $$$ before the data are observed. Various approaches have been proposed to generalize the model for $$$ {\mathbf{s}}_i $$$ such as allowing it to be a heterogeneous spatial point process (e.g., Diana et al, 2022; Sutherland et al, 2015).…”

On the identifiability of the trinomial model for mark‐recapture‐recovery studies

“…Time‐varying individual covariates present challenges in the study of marked animals in wild populations. Whether researchers are interested in the effects of breeding status (Pradel, 2005), location (Borchers & Efford, 2008; Diana et al, 2022; McLaughlin & Bar, 2021), or measures of fitness like body mass (Bonner & Schwarz, 2006) or parasite load (Argáez et al, 2020), these variables can only be observed when an animal is detected by physical capture or other means. The resulting data will have many missing values that need to be handled in some way.…”