title: Evolution of cooperation through the heterogeneity of random networks.
abstract: We use the standardized variance (nu_{st}) of the degree distribution of a random network as an analytic measure of its heterogeneity. We show that nu_{st} accurately predicts, quantitatively, the success of cooperators in an evolutionary prisoner's dilemma. Moreover, we show how the generating functional expression for nu_{st} suggests an intrinsic interpretation for the heterogeneity of the network that helps explain local mechanisms through which cooperators thrive in heterogeneous populations. Finally, we give a simple relationship between nu_{st} , the cooperation level, and the epidemic threshold of a random network that reveals an appealing connection between epidemic disease models and the evolutionary prisoner's dilemma.
authors.affiliation: Mathematics Department, University of San Francisco2130 Fulton Street, San Francisco, California 94117, USA.
authors.forename: Stephen
authors.initials: S
authors.lastname: Devlin
authors.forename: Thomas
authors.initials: T
authors.lastname: Treloar