General relationships between species diversity and stability in competitive systems

Investigating the effect of biodiversity on the stability of ecological communities is complicated by the numerous ways in which models of community interactions can be formulated. This has led to differences in conclusions and interpretations of how the number of species in a community affects its stability. Here, we derive a simple, general relationship between the coefficient of variation (CV) of combined species densities and the environmentally driven variability in species' per capita population growth rates. For a given level of environmentally driven variability in per capita population growth rates, increasing the number of species in a community decreases the CV of combined species densities, provided that species do not respond to environmental fluctuations in a perfectly correlated way. Thus, a community with more species of competitors will be more stable (have lower CV in combined species densities for a given level of environmental variability) than a species-poor community, provided that the species in both communities show equal variability in per capita population growth rates and provided that species within each community do not show strongly correlated responses to environmental fluctuations. This conclusion also applies to "non-interactive" models in which there is no competition between species.