Joint species distribution modeling with competition for space

Joint species distribution models (JSDM) are among the most important statistical tools in community ecology. However, existing JSDMs cannot model mutual exclusion between species. We tackle this deficiency in the context of modeling plant percentage cover data, where mutual exclusion arises from limited growing space and competition for light. We propose a hierarchical JSDM where latent Gaussian variable models describe species' niche preferences and Dirichlet-Multinomial distribution models the observation process and competition between species. We also propose a decision theoretic model comparison and validation approach to assess the goodness of JSDMs in four different types of predictive tasks. We apply our models and methods to a case study on modeling vegetation cover in a boreal peatland. Our results show that ignoring the interspecific interactions and competition reduces models' predictive performance and leads to biased estimates for total percentage cover. Models' relative predictive performance also depends on the predictive task highlighting that model comparison and assessment should resemble the true predictive task. Our results also demonstrate that the proposed JSDM can be used to simultaneously infer interspecific correlations in niche preference as well as mutual competition for space and through that provide novel insight into ecological research.