title: Games among relatives revisited.
abstract: We present a simple model for the evolution of social behavior in family-structured, finite sized populations. Interactions are represented as evolutionary games describing frequency-dependent selection. Individuals interact more frequently with siblings than with members of the general population, as quantified by an assortment parameter r, which can be interpreted as "relatedness". Other models, mostly of spatially structured populations, have shown that assortment can promote the evolution of cooperation by facilitating interaction between cooperators, but this effect depends on the details of the evolutionary process. For our model, we find that sibling assortment promotes cooperation in stringent social dilemmas such as the Prisoner's Dilemma, but not necessarily in other situations. These results are obtained through straightforward calculations of changes in gene frequency. We also analyze our model using inclusive fitness. We find that the quantity of inclusive fitness does not exist for general games. For special games, where inclusive fitness exists, it provides less information than the straightforward analysis.
authors.affiliation: Department of Mathematics, Emmanuel College, Boston, MA 02115, United States; Center for Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, United States; Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, United States. Electronic address: benjcallen@gmail.com.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Allen
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, United States; Department of Mathematics, Harvard University, Cambridge, MA 02138, United States; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, United States.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D005195:Family Relations / Q000523:psychology*; D005716:Game Theory; D006801:Humans; D008954:Models, Biological; D011156:Population Density; D012919:Social Behavior
keywords: Evolutionary game theory; Family structure; Fixation probability; Inclusive fitness; Kin selection