caa a22 4500 44533018X CHVBK 20180317142734.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00285-010-0367-3 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0367-3 Consequences of fluctuating group size for the evolution of cooperation [Elektronische Daten] [Åke Brännström, Thilo Gross, Bernd Blasius, Ulf Dieckmann] 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. Springer-Verlag, 2010 Brännström Åke Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden aut Gross Thilo Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187, Dresden, Germany aut Blasius Bernd Institute for Chemistry and Biology of Marine Environment, Oldenburg University, 26111, Oldenburg, Germany aut Dieckmann Ulf Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361, Laxenburg, Austria aut Journal of Mathematical Biology Springer-Verlag 63/2(2011-08-01), 263-281 0303-6812 63:2<263 2011 63 285 https://doi.org/10.1007/s00285-010-0367-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0367-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brännström Åke Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden aut NATIONALLICENCE 700 1- Gross Thilo Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187, Dresden, Germany aut NATIONALLICENCE 700 1- Blasius Bernd Institute for Chemistry and Biology of Marine Environment, Oldenburg University, 26111, Oldenburg, Germany aut NATIONALLICENCE 700 1- Dieckmann Ulf Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361, Laxenburg, Austria aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/2(2011-08-01), 263-281 0303-6812 63:2<263 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer