Multiple Stable Age Distributions in a Population at Evolutionary Stability

This paper presents a simple model in which a breeding population can be structured into two classes: one-year-old and older animals. Older animals outcompete one-year-old animals for food. Food obtained can be used in current reproduction or to enhance overwinter survival. Each animal behaves as if current supplies of food to the two age classes were maintained in the future, and allocates optimally on this basis. Since food to an individual depends on the population age structure, allocation varies with the age structure. shown that if all population members follow this allocation rule there can be two stable age distributions. At one all food is allocated to reproduction and the breeding population is composed entirely of one-year-olds. At the other the population contains a mixture of the two age classes. A population at either of these stable dynamical equilibria is also at an evolutionary equilibrium in the sense that the allocation of each population members is optimal given the behaviour of the others. Thus if one observed two different populations, one in each of the stable age distributions, it might appear that they had evolved to two different ESSs (even though environmental conditions were the same for both populations). But this would not be so: animals in both populations would be following the same allocation rule, but the full rule would not be observed unless the populations were perturbed from equilibrium.