Population persistence and spatially limited social interaction.

We investigate the persistence of a population composed of socially interacting individuals living in a lattice structured habitat and the effect of spatially limited social interaction, reproduction, and migration. Both cooperative interaction (enhancing the survivorship of neighboring individuals) and competitive interaction (reducing it) are examined. Mathematical analysis based on pair approximation (or doublet decoupling approximation) and computer simulation are used. Results are: If migration rate is not very large, the population tends to form clusters of individuals (clumped distribution) due to spatially limited reproduction. Although cooperative interaction is more effective in a spatially structured population, the population is more difficult to persist than in the corresponding population without spatial structure, because the shortage of nearest neighbor vacant sites reduces reproduction. Migration of individuals reduces the clumping of the spatial pattern. Pair approximation predicts the equilibrium density fairly accurately when the predicted density is sufficiently high (i.e., more than 40% sites are occupied). If the predicted density is low however, the pair approximation overestimates the equilibrium population level. To overcome this disagreement, we examined improved pair approximation.