Model complexity affects species distribution projections under climate change

International audience; Aim: Statistical species distribution models (SDMs) are the most common tool to predict the impact of climate change on biodiversity. They can be tuned to fit relationships at various levels of complexity (defined here as parameterization complexity, number of predictors, and multicollinearity) that may co-determine whether projections to novel climatic conditions are useful or misleading. Here, we assessed how model complexity affects the performance of model extrapolations and influences projections of species ranges under future climate change. Location: Europe. Taxon: 34 European tree species. Methods: We sampled three replicates of predictor sets for all combinations of 10 levels (n = 3-12) of environmental variables (climate, terrain, soil) and 10 levels of multicollinearity. We used these sets for each species to fit four SDM algorithms at three levels of parameterization complexity. The >100,000 resulting SDM fits were then evaluated under environmental block cross-validation and projected to environmental conditions for 2061-2080 considering four climate models and two emission scenarios. Finally, we investigated the relationships of model design with model performance and projected distributional changes. Results: Model complexity affected both model performance and projections of species distributional change. Fits of intermediate parameterization complexity performed best, and more complex parameterizations were associated with higher projected loss of current ranges. Model performance peaked at 10-11 variables but increasing number of variables had no consistent effect on distributional change projections. Multicollinearity had a low impact on model performance but distinctly increased projected loss of current ranges. Main conclusions: SDM-based climate change impact assessments should be based on ensembles of projections, varying SDM algorithms as well as parameterization complexity, besides emission scenarios and climate models. The number of predictor variables should be kept reasonably small and the classical threshold of maximum absolute Pearson correlation of 0.7 restricts collinearity-driven effects in projections of species ranges.