Competition and species packing in patchy environments

In models of competition in which space is treated as a continuum, and population size as continuous, there are no limits to the number of species that can coexist. For a finite number of sites, N, the results are different. The answer will, of course, depend on the model used to ask the question. In the Tilman-May-Nowak ordinary differential equation model, the number of species is asymptotically C log N with most species packed in at the upper end of the competitive hierarchy. In contrast, for metapopulation models with discrete individuals and stochastic spatial systems with various competition neighborhoods, we find a traditional species area relationship CN(a), with no species clumping along the phenotypic gradient. The exponent a is larger by a factor of 2 for spatially explicit models. In words, a spatial distribution of competitors allows for greater diversity than a metapopulation model due to the effects of recruitment limitation in their competition.