POPULATION PERSISTENCE AND SPATIALLY LIMITED SOCIAL-INTERACTION

We investigate the persistence of a population composed of socially in teracting individuals living in a lattice structured habitat and the e ffect of spatially limited social interaction, reproduction, and migra tion. Both cooperative interaction (enhancing the survivorship of neig hboring individuals) and competitive interaction (reducing it) are exa mined. Mathematical analysis based on pair approximation (or doublet d ecoupling approximation) and computer simulation are used. Results are : If migration rate is not very large, the population tends to form cl usters 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 p ersist than in the corresponding population without spatial structure, because the shortage of nearest neighbor vacant sites reduces reprodu ction. Migration of individuals reduces the clumping of the spatial pa ttern. Pair approximation predicts the equilibrium density fairly accu rately when the predicted density is sufficiently high (i.e., more tha n 40% sites are occupied). If the predicted density is low however, th e pair approximation overestimates the equilibrium population level. T o overcome this disagreement, we examined improved pair approximation. (C) 1995 Academic Press, Inc.