Addressing Missing Covariates in Species Distribution Models: Inferential Impacts and Mitigation via Joint Species Distribution Models

Arthur F. Rossignol , Frédéric Gosselin

Species distribution models (SDMs) are widely used in ecology to assess species distributions. Specifically, correlative SDMs are employed to infer relationships between species records and environmental variables. A classical approach to implementing such SDMs is to use parametric statistical models such as generalized linear mixed models (GLMMs). However, since species–environment relationships are complex, species distributions may depend on unobserved covariates. In this article, we first recall mathematical results showing that such “omitted covariates” typically introduce statistical issues that can bias inferences of observed-covariate effects or yield improper confidence intervals. So far, these results have received little attention in ecology. We then present a simulation study of the statistical impact of unobserved covariates on GL(M)M inference for continuous, count, and binary data. We assessed various regression methods, including both frequentist and Bayesian SDMs, as well as joint species distribution models (JSDMs) accounting for interspecific covariations in presence–absence data. In case of shared missing covariates, JSDMs provide an effective approach that mitigates inferential issues arising in presence–absence SDMs: they rightly increase covariate-slope magnitudes relative to single-species SDMs. We complemented these simulations by applying JSDMs and SDMs to real ecological datasets, revealing discrepancies in environmental-effect estimates and better predictive capacity for JSDMs. We recommend that ecologists fit JSDMs when dealing with community data to evaluate whether information can be extracted from between-species residuals. Ultimately, our results apply to any GL(M)M with suspected omitted variables, where generalized linear latent variable models (GLLVMs) could correct inference when jointly monitored entities share an important omitted covariate.