Roberto Schonmann: UCLA Department of Mathematics, Sao Paulo University Department of Applied Math

The evolution of cooperation and altruism are fundamental scientific challenges highlighted by their role in the major transitions in
life’s history, when natural selection acted simultaneously on several competing levels. The relevance of basic concepts, including group selection and Hamilton’s rule remain nevertheless controversial.
In this talk I will address these problems by introducing a new framework for modeling evolution in group structured populations, incorporating inter- and intra-group competition and migration. Combining group-centric with gene-centric perspectives in a constructive group/kin selection approach, we build methodology that allows for the analysis of arbitrary non-linear fitness functions, resulting from complex multi-individual interactions accross life cycles. This provides extensions of Hamilton’s rule and reveals conditions under which altruism can evolve when rare, but genetic relatedness in groups is modest. Emphasis on linear public goods games has supported the belief that inter-group selection favoring altruism
could only override intra-group selection favoring selfishness under exceptional conditions. In contrast, we show that for iterated public goods games, in which altruists cooperate or not in each round based on previous outcomes altruism can spread even when groups are large,
selection is weak and migration rates are substantially larger than the
inverse of group size. To obtain this result we show that in the absence of selection, when groups are large, the fraction of group members that are close relatives of a randomly chosen individual has a non-Gaussian distribution with a fat tail. As a consequence, even when altruistic alleles are rare in the population, they have a significant probability of concentrating in some groups, accruing substantial reproductive gains through synergy. (This is joint work with Renato Vicente and Nestor Caticha, from Sao Paulo University.)