Persistence vs Extinction of Cooperation via Multilevel Selection: The Dynamical Shadow of Lower-Level Selection

Natural selection often acts simultaneously upon multilevel levels of biological organization, inducing a tension between traits favoring selfish individuals and traits providing collective benefit for the group. Examples of such conflicts arise in settings including the evolution of the early cell, the evolution of virulence, and the sustainable management of common-pool resources. In this talk, we consider a PDE model for the evolution of a cooperative trait in which competition takes place both within groups through individual-level reproduction and between-groups through a group-level birth-death process. Generalizing previous work from evolutionary game theory, we show that there exists a threshold intensity of between-group competition separating regimes in which cooperation goes extinct or persists in the population. We additional provide bounds on the long-time average payoff of the population, showing that the population cannot outperform the payoff of a full-cooperator group in the long run and allowing us to determine when measure-valued solutions to the multilevel dynamics converge to a steady-state density or forever oscillate. When intermediate levels of cooperation are most favorable to the group, this means that multilevel selection will always promote suboptimal collective outcomes, and no level of between-group competition can erase the shadow of lower-level selection.