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Natural selection often simultaneously operates across multiple levels of biological organization, with examples of such cross-scale evolutionary dynamics arising in settings including the evolution of the early cell, the evolution of virulence, and the sustainable management of common-pool resources. These scenarios often present an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to establish cooperation within a group. In this talk, we will explore how evolutionary game theory can be used to explore the evolution of cooperation both within a single group and within a group-structured population. We will then present the recent Luo-Mattingly framework for modeling evolutionary competition at two levels using a nested birth-death process, as well as how to derive a hyperbolic PDE describing the strategic composition of a group-structured population in the limit of infinite population size. We will discuss numerical and analytical approaches for studying the long-time behavior of the resulting PDE, characterizing how long-time support for cooperation depends on the presence of a sufficient strength of between-group competition. Surprisingly, when groups are best off with an intermediate level of cooperation, individual-level competition casts a long shadow on the dynamics of multilevel selection: no level of between-group competition can erase the effects of the individual incentive to defect. We will also conclude the talk with a discussion about applying this PDE framework to a model of the evolution of altruistic punishment via cultural evolution, building off of work by Boyd, Gintis, Bowles, and Richerson. This talk is based on joint work with Yoichiro Mori.

Join on Zoom. https://ucdavis.zoom.us/j/92718892837