Unstable population dynamics in obligate co-operators.

Cooperation significantly impacts a species' population dynamics as individuals choose others to associate with based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely move between groups. Such an assumption works well for facultative co-operators (e.g. flocking birds, schooling fish, and swarming locusts) but less so for obligate co-operators (e.g. canids, cetaceans, and primates). With obligate co-operators, the fitness consequences from associations are stronger compared to facultative co-operators. Consequently, individuals within a group should be more discerning and selective over their associations, rejecting new members and even removing current members. Incorporating such aspects into population models may better reflect obligately cooperative species. In this paper, we create and analyze a model of the population dynamics of obligate co-operators. In our model, a behavioral game determines within-group population dynamics that then spill over into between-group dynamics. Our analysis shows that group number increases when population dynamics are stable, but additional groups lead to unstable population dynamics and an eventual collapse of group numbers. Using a more general analysis, we identify a fundamental mismatch between the stability of the behavioral dynamics and the stability of the population dynamics. When one is stable, the other is not. Our results suggest that group turnover may be inherent to the population dynamics of obligate co-operators. The instability arises from a non-chaotic deterministic process, and such dynamics should be predictable and testable.