Animal group forces resulting from predator avoidance and competition minimization

A new model to explain animal spacing, based on a trade-off between foragin g efficiency and predation risk, is derived from biological principles. The model is able to explain not only the general tendency for animal groups t o form, but some of the attributes of real groups. These include the indepe ndence of mean animal spacing from group population, the observed variation of animal spacing with resource availability and also with the probability of predation, and the decline in group stability with group size. The appe arance of "neutral zones" within which animals are not motivated to adjust their relative positions is also explained. The model assumes that animals try to minimize a cost potential combining the loss of intake rate due to f oraging interference and the risk from exposure to predators. The cost pote ntial describes a hypothetical field giving rise to apparent attractive and repulsive forces between animals. Biologically based functions are given f or the decline in interference cost and increase in the cost of predation r isk with increasing animal separation. Predation risk is calculated from th e probabilities of predator attack and predator detection as they vary with distance. Using example functions for these probabilities and foraging int erference, we calculate the minimum cost potential for regular lattice arra ngements of animals before generalizing to finite-sized groups and random a rrangements of animals, showing optimal geometries in each case and describ ing how potentials vary with animal spacing. (C) 1999 Academic Press.