Covariance, coexistence and the population dynamics of two competitors using a patchy resource

Abstract

A model is presented for two insect species whose larvae compete on discrete and ephemeral patches of food resource. At the beginning of every generation, eggs from both species are distributed among the patches according to a bivariate negative binomial distribution. This allows one to study the effects of covariance between the distributions of the two species. Results include: (1) Coexistence of competitors is facilitated whenever aggregation within species is greater than aggregation between species. This extends the results obtained by Atkinson & Shorrocks (1981); J. Anim. Ecol. 50, 461) and Ives & May (1985); J. theor. Biol. 115, 65), who considered only the special case when species are distributed independently of each other. (2) Increasing covariance between two species makes coexistence more difficult. However, increased covariance can never make coexistence more difficult than when the individuals from both species are homogeneously distributed among patches. Most models in the literature assume a homogeneous distribution, and therefore they represent the worst case for coexistence. (3) When two species coexist, covariance will affect both equilibrium population densities and population dynamics. With greater positive covariance, the reduction in the population growth rate of a species when perturbed to low densities is greater than the reduction in equilibrium population densities. Therefore, covariance may cause a dynamical fragility, as species are less able to rebound if they approach extinction. However, this fragility is not necessarily reflected by long-term population densities, which may remain little changed by covariance. These three results emphasize that in order to understand population-level interactions, the behavior of female insects searching for oviposition sites must be examined.