4:00 p.m., Monday (January 15, 2007)

MATH 104

Christoph Hauert
Harvard University

Evolutionary Dynamics: Structured Populations and the Problem of Cooperation

Evolutionary dynamics in finite populations reflects a balance between Darwinian selection and random drift. For a long time population structures were assumed to leave the evolutionary outcome unaffected, i.e. to leave the fixation probability of a single mutant type in a resident population unchanged, provided that the fitness of mutants and residents is constant and independent of the population configuration. This result indeed holds for a certain (large) class of population structures or graphs. Quite intriguingly, however, other structures can tilt the balance to the extent that either selection is eliminated and drift rules or drift is eliminated and only selection matters. These results have recently been extended to include frequency-dependent selection on graphs where individuals engage in game theoretical interactions. The most important case refers to the problem of cooperation in social dilemmas, i.e. to behavioral patterns that are beneficial to the group but costly to the individual. For the prisoner's dilemma, this yields a simple rule under which selection can favor cooperation in structured populations that range from regular lattices to scale-free networks. In well-mixed populations, i.e. in the absence of spatial structure, defectors reign. Spatial structure has long been recognized to support cooperation because it allows cooperators to form clusters and thereby to reduce exploitation by defectors. However, this does not hold for social dilemmas in general. In fact, under relaxed conditions of the social dilemma, i.e. if cooperators and defectors can co-exist in well-mixed populations, spatial structure often turns out to be detrimental and may even eliminate cooperation altogether.

Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge).

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