Evolving Biodiversity

We formulated a mathematical model to study the evolution of biodiversity. Our model describes a collection of sites and incorporates a simple but explicit description of the competitive processes within a site. In our model the characteristics of component species evolve towards an evolutionarily stable state and in this way an evolutionarily stable assemblage of species is formed. We show that the number of species in these assemblages matches two well-documented patterns in biodiversity: the increase in the number of species towards the equator and the dependence of the number of species on the productivity of habitat: the average number of species rises to a maximum and then falls when plotted against increasing productivity of that habitat. Our results show that population dynamical and evolutionary processes can underlie patterns in biodiversity. The distribution of species over the earth is not even or random but seems to follow certain distinct patterns. Probably the best known example of such a pattern is the increase in the number of species towards the equator (Rosenzweig 1995; Gaston & Williams 1998). Another pattern is the dependence of the number of species on the productivity of habitat; the average number of species rises to a maximum and then falls when plotted against increasing productivity of that habitat (Rosenzweig 1995). Such patterns in biodiversity are well documented but as yet not unequivocally explained. Most species do not exist in isolation but coexist and compete with other species. Although communities of competitive species can harbour a large number of species (Zobel 1992), theoretical results predict that the number of competing species is limited by the number of resources. This apparent paradox has been explained by models that describe a collection of sites or patches in which the different species interact. Competing species that cannot coexist in a single site can coexist in a collection of coupled sites, and in this way many species can coexist in the collection of sites, despite the fact that local competition is for a small number of resources The number of species that can coexist somehow depends on the species' characteristics. In most models for biodiversity these characteristics are predefined constants. In real communities, however, the characteristics to a certain extent are formed through evolution. It is still very much an open question how the properties of competitive communities emerge through the evolution of their component species (Levin et al. 1997). Here, we …