Spatial confounding in joint species distribution models

Joint species distribution models (JSDMs) are a popular method for analysing multivariate abundance data, with important applications such as uncovering how species communities are driven by environmental processes, model-based ordination to visualise community composition patterns across sites and variance partitioning to quantify the relative contributions of different processes in shaping a species community. One issue that has received relatively little attention in the study of joint species distributions is that of spatial confounding: when one or more of the environmental predictors exhibit spatial correlation, and spatially structured random effects such as spatial factors are also included in the model, then these two components may be collinear with each other. Through a combination of simulations and case studies, we show that if not managed properly, spatial confounding can result in misleading inference on covariate effects in a spatially structured JSDM, along with difficulties in interpreting ordination results and incorrect attribution of variation to environmental processes in a species community. We present one approach to treat spatial confounding called restricted spatial factor analysis, which is designed to ensure that the covariate effects retain their full explanatory power, and ordinations constructed using the spatial factors explain species covariation beyond that accounted for by the measured predictors. We encourage ecologists to consider the inferences they seek to make from spatially structured JSDMs and to ensure that the covariate effects and ordinations they estimate and interpret are aligned with their scientific questions of interest.