A two-species spatial occupancy model accommodating simultaneous spatial and interspecific dependence
Estimating the probability a sample unit is occupied by a species of interest is of fundamental interest in ecology. It is well known that non-detections during field sampling may result from absence or failure to detect a species that is present and occupancy models are popular for modeling occurrence probabilities when detection is imperfect. Occupancy models have been extended to account for interacting species and spatial dependence. However, both factors are likely to simultaneously influence occurrence probabilities. We propose a two-species spatial occupancy model that accommodates both inter-specific and spatial dependence. We use a point-referenced multivariate hierarchical spatial model to account for both spatial dependence and species interactions. We model spatial random effects with predictive process models and use data-augmentation and probit regression to improve efficiency of Markov chain Monte Carlo sampling. As an example, we model co-occurrence probabilities of Bobcat (Lynx rufus) and eastern gray squirrel (Sciurus carolinensis) with eMammal (emammal.wordpress.com) camera trap data collected from 6 mid-Atlantic states. We fit models from approximately 2/3 of camera trap data and validated models by calculating the Brier score from the remaining data, which we compare with occupancy models assuming interspecific and spatial independence.
The Brier score indicated predictions from the 2-species spatial occupancy model matched validation data better than occupancy models assuming interspecific and spatial independence, providing evidence that occurrence probabilities of both bobcats and eastern gray squirrels were influenced by spatial and interspecific factors. Eastern gray squirrels exhibited modest spatial dependence in occurrence probabilities, while bobcats exhibited little evidence of spatial dependence. Additionally, there was evidence that co-occurrence probabilities varied along a longitudinal gradient. The modest spatial dependence we found in squirrel occurrence probability is consistent with other studies that report residual spatial dependence in occurrence probabilities. Additionally, bobcats are an important predator of squirrels, but their preferred prey species can vary geographically, as reflected in the longitudinal variation in the strength of species dependence. The improved predictive performance of the 2-species spatial occupancy model highlights the importance of simultaneously accounting for spatial and interspecific dependence and suggests the potential broad utility of this approach for multi-species occupancy modeling.