Community confounding in joint species distribution models.

Joint species distribution models have become ubiquitous for studying species-environment relationships and dependence among species. Accounting for community structure often improves predictive power, but can also affect inference on species-environment relationships. Specifically, some parameterizations of joint species distribution models allow interspecies dependence and environmental effects to explain the same sources of variability in species distributions, a phenomenon we call community confounding. We present a method for measuring community confounding and show how to orthogonalize the environmental and random species effects in suite of joint species distribution models. In a simulation study, we show that community confounding can lead to computational difficulties and that orthogonalizing the environmental and random species effects can alleviate these difficulties. We also discuss the inferential implications of community confounding and orthogonalizing the environmental and random species effects in a case study of mammalian responses to the Colorado bark beetle epidemic in the subalpine forest by comparing the outputs from occupancy models that treat species independently or account for interspecies dependence. We illustrate how joint species distribution models that restrict the random species effects to be orthogonal to the fixed effects can have computational benefits and still recover the inference provided by an unrestricted joint species distribution model.