Group size, energy budgets, and population dynamic complexity

Question: If the size of foraging groups directly influences the probability that individuals starve before reproduction, how does increasing group size affect the consumer population’s dynamic complexity? Key assumptions: We partition a population into foraging groups that must search for food. Food per individual forager varies inversely with population density; social interaction within groups amplifies or attenuates the degree of density-dependent starvation. Mortality from predation increases with forager population density. Individuals surviving both predation and starvation go on to breed. Combining mortality and reproduction yields a generalized Ricker map for the population dynamics. Ranges of key variables: The rate at which an individual finds food clumps decreases with, does not depend on, and then increases with group size. The variance in the food energy per clump is less than, equal to, and then exceeds mean clump size. We also vary the total energy intake required to avert starvation. Conclusions: (1) When foragers interfere with each other’s search for food, and/or when the energy intake required to avoid starving is sufficiently large, increasing foraging group size induces dynamic overcompensation. Consequently, the population dynamics follows the period-doubling route to chaos as group size increases. The cause of overcompensation lies in the inverse relationship between group size and the variance of an individual’s total energy consumption. (2) When foragers enhance each other’s food discovery, larger groups stabilize the population dynamics. Depending on the particular energy requirement, increasing group size generates a period-halving bifurcation, or the dynamics equilibrates at a stable node for each group size evaluated.