The mathematical influence on global patterns of biodiversity.

Although we understand how species evolve, we do not appreciate how this process has filled an empty world to create current patterns of biodiversity. Here, we conduct a numerical experiment to determine why biodiversity varies spatially on our planet. We show that spatial patterns of biodiversity are mathematically constrained and arise from the interaction between the species' ecological niches and environmental variability that propagates to the community level. Our results allow us to explain key biological observations such as (a) latitudinal biodiversity gradients (LBGs) and especially why oceanic LBGs primarily peak at midlatitudes while terrestrial LBGs generally exhibit a maximum at the equator, (b) the greater biodiversity on land even though life first evolved in the sea, (c) the greater species richness at the seabed than at the sea surface, and (d) the higher neritic (i.e., species occurring in areas with a bathymetry lower than 200 m) than oceanic (i.e., species occurring in areas with a bathymetry higher than 200 m) biodiversity. Our results suggest that a mathematical constraint originating from a fundamental ecological interaction, that is, the niche-environment interaction, fixes the number of species that can establish regionally by speciation or migration.