(1) Identifying processes that shape species geographical ranges is a prerequisite for understanding environmental change. Currently, species distribution modelling methods do not offer credible statistical tests of the relative influence of climate factors and typically ignore other processes (for example, biotic interactions and dispersal limitation).

(2) We use a hierarchical model fitted with MCMC to combine ecologically plausible niche structures using regression splines to describe unimodal but potentially skewed response terms. We apply spatially explicit error terms that account for (and may help identify) missing variables.

(3) Using three example distributions of European bird species, we map model results to show sensitivity to change in each covariate. We show that the overall strength of climatic association differs between species and that each species has considerable spatial variation in both the strength of the climatic association and the sensitivity to climate change.

(4) Our methods are widely applicable to many species distribution modelling problems and enable accurate assessment of the statistical importance of biotic and abiotic influences on distributions.