THE UNIT OF SELECTION IN VISCOUS POPULATIONS AND THE EVOLUTION OF ALTRUISM

Group selection can overcome individual selection for selfishness and favour altruism if there is variation among the founders of spatially distinct groups, and groups with many altruists become substantially l arger (or exist longer) than groups with few. Whether altruism can evo lve in populations that do not have an alternation of local population growth and global dispersal (''viscous populations'') has been disput ed for some time. Limited dispersal protects the altruists from the no n-altruists, but also hinders the export of altruism. In this article, we use the Pair Approximation technique (tracking the dynamics of pai rs of neighbours instead of single individuals) to derive explicit inv asion conditions for rare mutants in populations with limited dispersa l. In such viscous populations, invading mutants form clusters, and ul timately, invasion conditions depend on the properties of such cluster s. Thus there is selection on a higher level than that of the individu al; in fact, invasion conditions define the unit of selection in visco us populations. We treat the evolution of altruism as a specific examp le, but the method is of more general interest. In particular, an impo rtant advantage is that spatial aspects can be incorporated into game theory in a straightforward fashion; we will specify the ESS for a mor e general model. The invasion conditions can be interpreted in terms o f inclusive fitness. In contrast with Hamilton's model, the coefficien t of relatedness is not merely a given genetical constant but depends on local population dynamical processes (birth, dispersal and death of individuals). With a simple birth rate function, Hamilton's rule is r ecovered: the cost to the donor should be less than the benefit to the recipient weighted with the coefficient of relatedness. As the coeffi cient of relatedness is roughly inversely proportional to an individua l's number of neighbours, benefits to the recipient must be substantia l to outweight the costs, confirming earlier studies. We discuss the c onsequences for the evolution of dispersal and outline how the method may be extended to study evolution in interacting populations. (C) 199 8 Academic Press.