Evolutionary stability of plant communities and the maintenance of multiple dispersal types

S.A. Levin, D. Cohen, and A. Hastings (1984, Theor. Popul. Biol. 19, 169-200) and D. Cohen and S.A. Levin (1991, Theor. Popul. Biol. 39, 63-99) by analytic solution of the problem of invasion of a single dispersal type by any other, have provided a theory for evolutionarily stable strategies for seed dispersal in a random environment. Here the results of Cohen and Levin are extended to describe evolutionarily stable combinations of dispersal types. Such combinations of two types are coalitions that cannot be invaded by any other, although in isolation either of the types in the combination is invasible by others. These combinations appear when there is a negative correlation between the seed production of sites in successive years, or when environments are spatially heterogeneous, or presumably under other circumstances. In this work, we examine only the case of negative correlations. For this situation the configuration of evolutionarily stable strategies (ESS) and evolutionarily stable combinations (ESC) depends upon the ratio of (precompetitive) survival rates of dispersersing and nondispersing seeds, which is denoted by α. For low values of α, the purely nondispersing type is an ESS. At a somewhat higher value of α, the purely dispersing type can invade the nondispersing type, and the two types form an ESC, i.e., a combination that cannot be invaded by any other type. For still larger values of α, the purely nondispersing type is excluded by the ESC. Finally, for the largest values of α, pure dispersal is the ESS. In cases where a single dispersal type cannot exclude all others, the stationary distribution of types has a large spread. It can be adequately approximated by equations for conditional means of the proportions of various types at a site of a given quality, but these means must be conditioned upon the prior history at each site. For some purposes we have found that the history of as many as 8-10 generations is required for a good approximation. This phenomenon appears to preclude simple analytic approximations for the ESC.