Stable group size in cooperative breeders: the role of inheritance and reproductive skew

Recent studies of reproductive skew have revealed great variation in the distribution of direct fitness among group members, yet there have been surprisingly few attempts to explore the consequences of such variation for stable group size, and none that take into account the future benefits of group membership to nonbreeders. This means that the existing theory is not suited to explain the group size of most cooperatively breeding vertebrates and primitively social insects in which group membership involves substantial future benefits. Here we model the group size of such species as social queues in which nonbreeders can inherit a breeding position if they outlive those ahead of them in the queue. We demonstrate, however, that the results can be generalized to systems in which inheritance occurs via scramble competition, rather than via a strict queue. The model predicts that stable group size will depend on the number of breeding positions in the group and the mortality rates of breeders and nonbreeders, but not on the distribution of reproduction among the pool of breeders. This is because deaths occur at random, so that each individual has the same chance of surviving to reach each breeding position. We tested a specific prediction of the model using data on ovarian development in the paper wasp, Polistes dominulus. We found a positive correlation between group size and the proportion of females with fully developed eggs, as predicted. Our results clarify the interaction between the dominance structure and size of animal groups and add to the growing recognition of the potential for inheritance as a major determinant of both individual behavior and group-level characteristics of animal societies.