Bi-Co Mathematics Colloquium with Dr. Daniel Cooney

Title: "Modeling Evolution and Cooperation at Multiple Levels of Organization" Abstract: Evolutionary forces like natural selection and cultural transmission can simultaneously operate across multiple levels of organization in complex biological and social systems, with such evolutionary competition 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 emergence and stability of cooperation both within a single group and within a group-structured population. We will show how tools from game theory, differential equations, difference equations, and stochastic processes can be used to explore the spread of traits and behaviors within populations, highlighting how the rules for interactions between individuals shape emergent behavior at the population level. 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 continuum limit of this agent-based model to describe the tug-of-war between individual-level competition favoring cheaters and group-level competition favoring collective cooperation. 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.