Consequences of fluctuating group size for the evolution of cooperation |
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Authors: | Åke Brännström Thilo Gross Bernd Blasius Ulf Dieckmann |
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Institution: | (1) Department of Bioinformatics, Friedrich Schiller University, Ernst-Abbe-Platz 2, 07743 Jena, Germany;(2) Centre for Systems Biology, School of Biosciences, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK;(3) Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA |
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Abstract: | 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. |
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