One, two and three-dimensional geometric constraints and climatic correlates of North American tree species richness

The 'mid-domain effect' (MDE) has received much attention recently as a candidate explanation for patterns in species richness over large geographic areas. Mid-domain models generate a central peak in richness when species ranges are randomly placed within a bounded geographic area (i.e. the domain). The most common terrestrial mid-domain models published to date have been 1-D latitude or elevation models and 2-D latitude-longitude models. Here, we test 1-D, 2-D and 3-D mid-domain models incorporating latitude, longitude and elevation, and assess independent and concurrent effects of geometric constraints and climatic variables on species richness of North American trees. We use both the traditional 'global' regression models as well as geographically weighted regressions ('local' models) to examine local variation in the contribution of MDE and climatic variables to species richness across the domain. Our results show that in some dimensions the contribution of MDE to patterns of species richness can be quite substantial, and we show that in most cases a combination of MDE and climate predicted empirical species richness best in both local and global models. For the North American domain, MDE in the elevation dimension is clearly important in describing patterns of empirical species richness. We also show that the assumption of stationarity in global models is not met in the North American domain and that results of these models mask complex patterns in both the effect of MDE on richness and the response of species richness to climate. In particular we show the increased explanatory role of MDE in predicting species richness as domain edges are approached. Our results support the hypothesis that geometric constraints contribute to species richness patterns and we suggest the mid-domain effect should be considered alongside more traditional environmental correlates in understanding patterns of species diversity.