Red, white and blue: environmental variance spectra and coexistence in metapopulations

Environmental variability, in the form of disturbance, is critically important for metapopulations. Their spatial subdivision makes possible the regional coexistence of inferior competitors (fugitive species) that are unable to persist locally. It is known that such coexistence depends on the frequency of disturbance relative to the rates of dispersal and competitive exclusion. In this paper, the effects of the spectral “color” of the environmental variation in a simple two-species competition model are considered. A simple two-state Markov chain is developed to describe the environment; its single parameter can be tuned to give a power spectrum that emphasizes low frequencies (red) or high frequencies (blue), or that contains all frequencies equally (white). Coupling this to a nonlinear Markov chain model for two competing species, this study considers the interacting effects of disturbance frequency and the spectrum on the frequency of the losing competitor, local species richness, spatial heterogeneity (beta diversity), and the Smoluchowski recurrence time for patch states. In general, a red spectrum makes coexistence more difficult and reduces local diversity. However, the details of the patterns depend on the rates of dispersal and competition.