Consequences of fluctuating group size for the evolution of cooperation
Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.
Mathematics Subject Classification (2000)00A69 92B05 92D15
Unable to display preview. Download preview PDF.
- Axelrod R (1984) The Evolution of Cooperation. Basic Books, New York, USAGoogle Scholar
- Buss LW (1982) Somatic cell parasitism and the evolution of somatic tissue compatibility. Proc R Soc Lond Ser B 79: 5337–5341Google Scholar
- Dao DN, Kessin RH, Ennis HL (2000) Developmental cheating and the evolutionary biology of Dictyostelium and Myxococcus. Microbiology 146: 1505–1512Google Scholar
- Kagel JH, Roth AE (1995) The Handbook of Experimental Economics. Princeton University Press, Princeton, NJ, USAGoogle Scholar
- Maynard Smith J, Szathmáry E (1995) The Major Transitions in Evolution. W. H. Freeman & Co., Oxford, UKGoogle Scholar
- Metz JAJ, Geritz SAH, Meszéna G, Jacobs FJA, van Heerwaarden JS (1996) Adaptive dynamics: a geometrical study of the consequences of nearly faithful reproduction. In: Strien SJ, Lunel SMV (eds) Stochastic and spatial structures of dynamical systems. North Holland, Amsterdam, pp 183–231Google Scholar
- Parvinen K (2010) Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction. Proc R Soc Lond Ser B (in press)Google Scholar
- Raper KB (1984) The Dictyostelids. Princeton University Press, Princeton, NJ, USAGoogle Scholar
- Sugden SR (1986) The Economics of Rights, Cooperation and Welfare. Blackwell Publishing, Oxford, UKGoogle Scholar
- Wilson DS (1980) The Natural Selection of Populations and Communities. Benjamin-Cummings, Menlo Park, CA, USAGoogle Scholar