Spatial regression methods capture prediction uncertainty in species distribution model projections through time

Aim: The uncertainty associated with species distribution model (SDM) projections is poorly characterized, despite its potential value to decision makers. Error estimates from most modelling techniques have been shown to be biased due to their failure to account for spatial autocorrelation (SAC) of residual error. Generalized linear mixed models (GLMM) have the ability to account for SAC through the inclusion of a spatially structured random intercept, interpreted to account for the effect of missing predictors. This framework promises a more realistic characterization of parameter and prediction uncertainty. Our aim is to assess the ability of GLMMs and a conventional SDM approach, generalized linear models (GLM), to produce accurate projections and estimates of prediction uncertainty. Innovation: We employ a unique historical dataset to assess the accuracy of projections and uncertainty estimates from GLMMs and GLMs. Models were trained using historical (1928-1940) observations for 99 woody plant species in California, USA, and assessed using temporally independent validation data (2000-2005). Main conclusions: GLMMs provided a closer fit to historic data, had fewer significant covariates, were better able to eliminate spatial autocorrelation of residual error, and had larger credible intervals for projections than GLMs. The accuracy of projections was similar between methods but GLMMs better quantified projection uncertainty. Additionally, GLMMs produced more conservative estimates of species range size and range size change than GLMs. We conclude that the GLMM error structure allows for a more realistic characterization of SDM uncertainty. This is critical for conservation applications that rely on honest assessments of projection uncertainty.