Abstract
Cooperative acts is widely observed in nature. Because cooperation allows individuals to choose their associations based on differences in fitness opportunities, such behaviors directly influence population dynamics. Cooperative acts can be classified into two types: facultative and obligate. Facultative cooperation seen in starling murmurations, fish schools, and locust swarms grant the actors full choice over their associations since the consequences of non-cooperation are not severe. Obligate cooperation like that of canids, cetaceans, primates, and eusocial insects only grant partial actor choice as the consequences of non-cooperation are more severe. The population dynamics of facultative cooperative species are well-modeled, but not so for obligate co-operators. In this paper, we model and analyze the population dynamics of obligate cooperators by embedding a game theoretic behavioral dynamic into a within group population dynamic with additional between group dynamics. Our model confirms previous results showing within group cooperation leading to unstable population dynamics and go further by showing that more groups lead to greater population instability. Our behavioral analysis also shows that stable population equilibria will lead to behavioral instabilities. From there, we generalize our results to show that obligate cooperative species can never achieve full stability due to the fundamental mismatch between the stability of the behavioral equilibrium (ESS) and the stability of the population size equilibrium. Our results, general enough to apply to most systems, show that the constant group turnover seen in obligately cooperative species are not necessarily a function of external stochastic events but instead inherent to their dynamics.
Significance Obligately cooperative species show population dynamics of constant group turnover. Through mathematical analysis, we show that these dynamics are intrinsic and unavoidable. Other factors may exacerbate the instability but can only be secondary. Processes like group fusion or costs to group splitting can help further stabilize dynamics though not sufficiently to overcome overall instability. Because the instability arises out of a non-chaotic deterministic process, the dynamics are predictable and can be tested against experiments and simulations. In addition, this instability means cooperative species are particularly vulnerable and require large protected areas compared to their non-cooperative counterparts. We feel this work can prove to be a starting point for further research into the population dynamics of obligately cooperative species.