Three-dimensional mid-domain predictions: geometric constraints in North American amphibian, bird, mammal and tree species richness patterns

The "mid-domain effect" (MDE) has received much attention 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 placed randomly within a bounded geographic area (i.e. the domain). Until now, domain limits have been described mostly in one-dimension, usually latitude or elevation, and only occasionally in two-dimensions. Here we test 1-D, 2-D and, for the first time, 3-D mid-domain models and assess the effects of geometric constraints on species richness in North American amphibian, bird, mammal and tree species. Using spatially lagged simultaneous autoregressive models, empirical richness was predicted quite well by the mid-domain predictions and the spatial autoregressive term (45–92% R2). However, our results show that empirical species richness peaks do deviate from those of the MDE predictions in 3 dimensions. Variation explained (R2) by MDE predictions generally increased with increasing mean range size of the different biotic groups (from amphibian, to tree, mammal and finally bird data), and decreased with increasing dimensions being accounted for in the models. The results suggest geometric constraints alone can explain much of the variation in species richness with elevation, specifically with respect to the larger-range taxa, birds and mammals. Our analysis addresses many of the recent methodological criticisms directed at studies testing the MDE, and our results support the hypothesis that species diversity patterns are influenced by geometric constraints