title: Evolutionary dynamics of collective action in spatially structured populations.
abstract: Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of spatial structure in biological collective action, the analysis of n-player games games in spatially structured populations has so far proved elusive. We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. This allows to conveniently identify convergence stable strategies and to capture the effect of population structure by a single structure coefficient, namely, the pairwise (scaled) relatedness among interacting individuals. As an application, we use our mathematical framework to investigate collective action problems associated with the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: "public goods" (both providers and shirkers can use the good, e.g., alarm calls), "club goods" (only providers can use the good, e.g., participation in collective hunting), and "charity goods" (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness promotes the evolution of collective action in different ways depending on the kind of collective good and its economies of scale. Our findings highlight the importance of explicitly accounting for relatedness, the kind of collective good, and the economies of scale in theoretical and empirical studies of the evolution of collective action.
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany. Electronic address: pena@evolbio.mpg.de.
authors.forename: Jorge
authors.initials: J
authors.lastname: Peña
authors.affiliation: Faculty of Business and Economics, University of Basel, Peter Merian-Weg 6, 4002 Basel, Switzerland. Electronic address: georg.noeldeke@unibas.ch.
authors.forename: Georg
authors.initials: G
authors.lastname: Nöldeke
authors.affiliation: Department of Ecology and Evolution, University of Lausanne, Le Biophore, 1015 Lausanne, Switzerland. Electronic address: laurent.lehmann@unil.ch.
authors.forename: Laurent
authors.initials: L
authors.lastname: Lehmann
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D005190:Family; D006801:Humans; D007398:Interpersonal Relations; D008962:Models, Theoretical; D011157:Population Dynamics
keywords: Games between relatives; Inclusive fitness; Relatedness; n-player games