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.