Opposing effects of frequency-dependent and frequency-independent selection on species abundance distributions

Background/Question/Methods

One of the more fascinating aspects of ecological communities is the extent and nature of differentiation between species, which makes especially surprising the apparent success of a mathematical model which explicitly ignores this differentiation. The “neutral theory” of ecology encompasses a class of stochastic dynamic models of co-occurring populations that treat every species equivalently. Despite this admittedly invalid assumption, the models yield remarkably realistic expectations for species richness, relative species abundance and species area relationships. However, the utility of the neutral theory is suspect on two accounts: 1) it involves a free parameter that is essentially impossible to estimate a priori, and 2) agreement on diversity patterns does not guarantee the same processes are operating in nature and in the model. In particular, whether the assumption of neutrality is necessary to achieve the match between model and data cannot be determined without perturbing the assumption. We derive and analyze a stochastic community model that avoids the first problem and allows for arbitrarily small deviations from the assumption of neutrality. We assume the state of a spatially homogeneous community can be modeled as a time-homogeneous Markov chain, in which only one birth or death may occur at a given instant, and study the master equation for the process.

Results/Conclusions

The parameter for total community size appearing in many neutral models is typically the free, and inestimable, parameter. Neither community size, nor species richness, are parameters in the model described, both of which respond to the birth, death and mutation rates. By allowing for density-independent and density-dependent variation in birth and death rates, we introduce two forms of “selection” that oppose neutral drift in each population’s size. While analytical solutions are not currently available, simulation studies reveal opposing effects of the two forms of selection. Strengthening intraspecific density-dependence relative to interspecific density-dependence, a signature of niche structure, increases evenness of the equilibrium distribution of species abundance. Subsequently increasing interspecific variation in density-independent rates, however, restores the species abundance distribution to the shape generated under the neutral parameterization. We conclude that agreement between the neutral model and observed species abundance distributions does not depend on the assumption of neutrality, but could result from combined variation in niche use and relative fitness within a community. Consideration of additional model predictions, in particular the distribution of species’ lifetimes, may yield greater ability to distinguish the contribution of neutral and non-neutral processes.