Mid-domain models as predictors of species diversity patterns: bathymetric diversity gradients in the deep sea

Geometric constraints represent a class of null models that describe how species diversity may vary between hard boundaries that limit geographic distributions. Recent studies have suggested that a number of large scale biogeographic patterns of diversity (e.g. latitude, altitude, depth) may reflect boundary constraints. However, few studies have rigorously tested the degree to which mid-domain null predictions match empirical patterns or how sensitive the null models are to various assumptions. We explore how variation in the assumptions of these models alter null depth ranges and consequently bathymetric variation in diversity, and test the extent to which bathymetric patterns of species diversity in deep sea gastropods, bivalves, and polychaetes match null predictions based on geometric constraints. Range-size distributions and geographic patterns of diversity produced by these null models are sensitive to the relative position of the hard boundaries, the specific algorithms used to generate range sizes, and whether species are continuously or patchily distributed between range end points. How well empirical patterns support null expectations is highly dependent on these assumptions. Bathymetric patterns of species diversity for gastropods, bivalves and polychaetes differ substantially from null expectations suggesting that geometric constraints do not account for diversity-depth patterns in the deep sea benthos.