Populations and communities are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and temporal environmental variations that affect coherently the relative fitness of entire populations. We have studied the dynamics of a community of competing species in the presence of both demographic stochasticity (that allows for extinction events) and temporal environmental fluctuations.
Two model have been considered. In the first, the birth rate of conspecific individuals varies in time while the death rate is kept fixed. In this model fluctuations facilitates the invasion of low-abundance species (storage effect). In the second model birth and death are completely anti-correlated and there is no noise induced coexistence state.
We were interested in two basic scenarios. The first is a two-species system (a mutant/invader against a wild-type/resident species), where the relative fitness fluctuates but its mean is nonzero, so one species is (on average) fitter than the other. The second scenario is a high-diversity assemblage in which all species have the same average fitness (a time-averaged neutral model) and the species composition reflects a speciation-extinction equilibrium.
Results/Conclusions
For a two-species system we have calculated the chance of fixation, the time to fixation and the time to absorption (either fixation or loss), in the presence and in the absence of the storage effect.
For a high-diversity community under the time-averaged neutral model we solved for the species richness and the species abundance distribution.
The resulting species abundance distributions (with and without storage) are contrasted with the Fisher log-series distribution that characterizes the neutral model with pure demographic stochasticity.