Spatial confounding in Bayesian species distribution modeling

1) Species distribution models (SDMs) are currently the main tools to derive species niche estimates and spatially explicit predictions for species geographical distribution. However, unobserved environmental conditions and ecological processes may confound the model estimates if they have direct impact on the species and, at the same time, they are correlated with the observed environmental covariates. This, so-called spatial confounding, is a general property of spatial models and it has not been studied in the context of SDMs before. 2) We examine how the estimation accuracy of SDMs depends on the type of spatial confounding. We construct two simulation studies where we alter spatial structures of the observed and unobserved covariates and the level of dependence between them. We fit generalized linear models with and without spatial random effects applying Bayesian inference and recording the bias induced to model estimates by spatial confounding. After this we examine spatial confounding also with real vegetation data from northern Norway. 3) Our results show that model estimates for coarse scale covariates, such as climate covariates, are likely to be biased if a species distribution depends also on an unobserved covariate operating on a finer spatial scale. Pushing higher probability for a relatively weak and smoothly varying spatial random effect compared to the observed covariates improved the model's estimation accuracy. The improvement was independent of the actual spatial structure of the unobserved covariate. 4) Our study addresses the major factors of spatial confounding in SDMs and provides a list of recommendations for pre-inference assessment of spatial confounding and for inference-based methods to decrease the chance of biased model estimates.