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.

由于个体根据适应机会选择其他人进行合作，因此合作会对物种的种群动态产生重大影响。这些动力学模型通常假设个人可以在群体之间自由移动。这样的假设对兼职合作者（例如，成群的鸟类，学鱼和蝗虫）非常有效，但对于专职合作者（例如，犬科动物，鲸类和灵长类动物）则不太适用。与专职合作者相比，专职合作者的结社适应性后果更强。因此，一个小组中的个人应该对他们的协会更具洞察力和选择性，拒绝新成员，甚至罢免现有成员。将这些方面纳入种群模型可能会更好地反映专心合作的物种。在本文中，我们创建并分析了专职合作者的人口动态模型。在我们的模型中，行为博弈确定了群体内部的人口动态，然后扩散到群体之间的动态中。我们的分析表明，当种群动态稳定时，种群数量会增加，但是其他种群会导致种群动态不稳定，并最终导致种群数量崩溃。使用更一般的分析，我们确定了行为动力学的稳定性与种群动力学的稳定性之间的根本失配。当一个稳定时，另一个不稳定。我们的研究结果表明，小组营业额可能是专职合作者的人口动态所固有的。这种不稳定性是由非混沌的确定性过程引起的，这种动力学应该是可预测和可测试的。