Short- vs. Long-range Disperser: the Evolutionarily Stable Allocation in a Lattice-Structured Habitat

The population dynamics of two types of organisms in a lattice-structured habitat are studied and the evolutionarily stable allocation between short- and long-range disperser is calculated. Offsprings of short-range dispersal stay in the vicinity of their parent and cause local competition. Using pair approximation, I derive a closed system of ordinary differential equations of global and local densities (or mean crowding), and calculate the condition for one type to invade the population dominated by the other type. The evolutionarily stable strategy (ESS) of resource allocation is derived for the case in which there is a linear trade-off between short- and long-range dispersers. The maximum equilibrium abundance of the population may be achieved by a mixture of both types of dispersers, but it is in general different from the ESS resource allocation calculated from the invasibility condition. For the same parameter values, the ESS invests a larger fraction of resources to short-range disperser than the optimal allocation which maximizes the equilibrium population density. This difference can be explained by the fact that long-range disperser is more effective in the preoccupation of space than short-range disperser. The predictions are confirmed by the direct computer simulations of the lattice stochastic models.