Global Migration Can Lead to Stronger Spatial Selection than Local Migration

The outcome of evolutionary processes depends on population structure. It is well known that mobility plays an important role in affecting evolutionary dynamics in group structured populations. But it is largely unknown whether global or local migration leads to stronger spatial selection and would therefore favor to a larger extent the evolution of cooperation. To address this issue, we quantify the impacts of these two migration patterns on the evolutionary competition of two strategies in a finite island model. Global migration means that individuals can migrate from any one island to any other island. Local migration means that individuals can only migrate between islands that are nearest neighbors; we study a simple geometry where islands are arranged on a one-dimensional, regular cycle. We derive general results for weak selection and large population size. Our key parameters are: the number of islands, the migration rate and the mutation rate. Surprisingly, our comparative analysis reveals that global migration can lead to stronger spatial selection than local migration for a wide range of parameter conditions. Our work provides useful insights into understanding how different mobility patterns affect evolutionary processes.

[1]  G. Szabó,et al.  Cooperation in the noisy case: Prisoner's dilemma game on two types of regular random graphs. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Tobias Galla,et al.  Intrinsic noise in game dynamical learning. , 2009, Physical review letters.

[3]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[4]  Arne Traulsen,et al.  How mutation affects evolutionary games on graphs. , 2012, Journal of theoretical biology.

[5]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[6]  Ulf Dieckmann,et al.  The Geometry of Ecological Interactions: Simplifying Spatial Complexity , 2000 .

[7]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[8]  F. Rousset.  Genetic Structure and Selection in Subdivided Populations (MPB-40) , 2004 .

[9]  Martin A Nowak,et al.  Multiple strategies in structured populations , 2011, Proceedings of the National Academy of Sciences.

[10]  U. Dieckmann,et al.  The Dynamical Theory of Coevolution : A Derivation from Stochastic Ecological Processes , 1996 .

[11]  C. Hauert,et al.  Coevolutionary dynamics: from finite to infinite populations. , 2004, Physical review letters.

[12]  Y. Iwasa,et al.  The evolution of cooperation in a lattice-structured population. , 1997, Journal of theoretical biology.

[13]  S. Frank.  Foundations of Social Evolution , 2019 .

[14]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

[15]  M. Perc,et al.  Towards effective payoffs in the prisoner’s dilemma game on scale-free networks , 2007, 0711.4028.

[16]  Martin A Nowak,et al.  Evolutionary dynamics in set structured populations , 2009, Proceedings of the National Academy of Sciences.

[17]  M. Nowak,et al.  Mutation-selection equilibrium in games with mixed strategies. , 2009, Journal of theoretical biology.

[18]  P. Richerson,et al.  The evolution of reciprocity in sizable groups. , 1988, Journal of theoretical biology.

[19]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[20]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[21]  T. Reichenbach,et al.  Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games , 2007, Nature.

[22]  R. Durrett,et al.  The Importance of Being Discrete (and Spatial) , 1994 .

[23]  R. Cressman.  Evolutionary Dynamics and Extensive Form Games , 2003 .

[24]  Martin A. Nowak,et al.  Evolution of in-group favoritism , 2012, Scientific Reports.

[25]  T. Maruyama.  Stepping stone models of finite length , 1970, Advances in Applied Probability.

[26]  Feng Qi,et al.  Randomness enhances cooperation: a resonance-type phenomenon in evolutionary games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  R. Axelrod,et al.  Evolutionary Dynamics , 2004 .

[28]  M. Nowak,et al.  Nowak et al. reply , 2011, Nature.

[29]  S. Bornholdt,et al.  Coevolutionary games on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  M. Nowak,et al.  Evolutionary dynamics in structured populations , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[31]  S. Levin.  Dispersion and Population Interactions , 1974, The American Naturalist.

[32]  J. Metz,et al.  Adaptive Dynamics: A Geometrical Study of the Consequences of Nearly Faithful Reproduction , 1995 .

[33]  Francisco C. Santos,et al.  Cooperation Prevails When Individuals Adjust Their Social Ties , 2006, PLoS Comput. Biol..

[34]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[35]  Martin A Nowak,et al.  Multi-player games on the cycle. , 2012, Journal of theoretical biology.

[36]  Paul E. Turner,et al.  Prisoner's dilemma in an RNA virus , 1999, Nature.

[37]  Arne Traulsen,et al.  Mixing times in evolutionary game dynamics. , 2012, Physical review letters.

[38]  Arne Traulsen,et al.  Pairwise comparison and selection temperature in evolutionary game dynamics. , 2007, Journal of theoretical biology.

[39]  Robert van Rooij,et al.  The Stag Hunt and the Evolution of Social Structure , 2007, Stud Logica.

[40]  K. Holsinger.  The neutral theory of molecular evolution , 2004 .

[41]  Arne Traulsen,et al.  Stochastic gain in population dynamics. , 2004, Physical review letters.

[42]  D. E. Matthews.  Evolution and the Theory of Games , 1977 .

[43]  Martin A Nowak,et al.  Evolving cooperation. , 2012, Journal of theoretical biology.

[44]  S. M. Verduyn Lunel,et al.  Stochastic and spatial structures of dynamical systems , 1996 .

[45]  J. Lebowitz,et al.  Reaction-diffusion equations for interacting particle systems , 1986 .

[46]  M A Nowak,et al.  Superinfection and the evolution of parasite virulence. , 1994, Proceedings. Biological sciences.

[47]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[48]  Martin A. Nowak,et al.  Calculating Evolutionary Dynamics in Structured Populations , 2009, PLoS Comput. Biol..

[49]  Laurent Lehmann,et al.  Inclusive fitness theory and eusociality , 2011, Nature.

[50]  Martin A Nowak,et al.  Evolutionary games on cycles , 2006, Proceedings of the Royal Society B: Biological Sciences.

[51]  Anthony J McMichael,et al.  Social and environmental risk factors in the emergence of infectious diseases , 2004, Nature Medicine.

[52]  M. Nowak,et al.  Evolution of cooperation by multilevel selection. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[53]  Günther Palm,et al.  Evolutionary stable strategies and game dynamics for n-person games , 1984 .

[54]  M. Nowak,et al.  Evolutionary game dynamics in a Wright-Fisher process , 2006, Journal of mathematical biology.

[55]  Naoki Masuda,et al.  A Theoretical Analysis of Temporal Difference Learning in the Iterated Prisoner’s Dilemma Game , 2009, Bulletin of mathematical biology.

[56]  Eörs Szathmáry,et al.  The Major Transitions in Evolution , 1997 .

[57]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

[58]  Feng Fu,et al.  Invasion and expansion of cooperators in lattice populations: prisoner's dilemma vs. snowdrift games. , 2010, Journal of theoretical biology.

[59]  Peter J Richerson,et al.  Voting with your feet: Payoff biased migration and the evolution of group beneficial behavior. , 2009, Journal of theoretical biology.

[60]  Alex Arenas,et al.  The joker effect: cooperation driven by destructive agents. , 2011, Journal of theoretical biology.

[61]  M. Nowak,et al.  The evolution of stochastic strategies in the Prisoner's Dilemma , 1990 .

[62]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[63]  T. Maruyama,et al.  Effective number of alleles in a subdivided population. , 1970, Theoretical population biology.

[64]  H. Ohtsuki,et al.  Strategy selection in structured populations. , 2009, Journal of theoretical biology.

[65]  Long Wang,et al.  Partner switching stabilizes cooperation in coevolutionary prisoner's dilemma. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[66]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations with strong selection and weak mutation. , 2006, Theoretical population biology.

[67]  Long Wang,et al.  Expectation-driven migration promotes cooperation by group interactions. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[68]  H. Ohtsuki,et al.  Mutation-selection equilibrium in games with multiple strategies. , 2008, Journal of theoretical biology.

[69]  Mauro Mobilia,et al.  Spatial rock-paper-scissors models with inhomogeneous reaction rates. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  Duncan J. Watts,et al.  Cooperation in Evolving Social Networks , 2007, Manag. Sci..

[71]  Pardis C Sabeti,et al.  Detecting recent positive selection in the human genome from haplotype structure , 2002, Nature.

[72]  M. Macy,et al.  Learning dynamics in social dilemmas , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[73]  Feng Fu,et al.  Partner Selection Shapes the Strategic and Topological Evolution of Cooperation , 2011, Dyn. Games Appl..

[74]  M. Kimura.  The Neutral Theory of Molecular Evolution: Introduction , 1983 .

[75]  Martin A Nowak,et al.  Evolutionary shift dynamics on a cycle. , 2012, Journal of theoretical biology.

[76]  Arne Traulsen,et al.  The different limits of weak selection and the evolutionary dynamics of finite populations. , 2007, Journal of theoretical biology.

[77]  C. Hauert,et al.  Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game , 2005 .

[78]  M. Nowak.  Five Rules for the Evolution of Cooperation , 2006, Science.

[79]  H. Ohtsuki,et al.  Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. , 2007, Physical review letters.

[80]  D. Helbing,et al.  The outbreak of cooperation among success-driven individuals under noisy conditions , 2009, Proceedings of the National Academy of Sciences.

[81]  Peter D. Taylor,et al.  Evolution of cooperation in a finite homogeneous graph , 2007, Nature.

[82]  J. Cuesta,et al.  Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma , 2012, Proceedings of the National Academy of Sciences.

[83]  Martin A. Nowak,et al.  Evolution of cooperation by phenotypic similarity , 2008, Proceedings of the National Academy of Sciences.

[84]  Hisashi Ohtsuki,et al.  EVOLUTIONARY GAMES IN WRIGHT'S ISLAND MODEL: KIN SELECTION MEETS EVOLUTIONARY GAME THEORY , 2010, Evolution; international journal of organic evolution.

[85]  Víctor M Eguíluz,et al.  Coevolution of dynamical states and interactions in dynamic networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[86]  Christoph Hauert,et al.  Evolutionary games in deme structured, finite populations. , 2012, Journal of theoretical biology.

[87]  J Gómez-Gardeñes,et al.  Dynamical organization of cooperation in complex topologies. , 2007, Physical review letters.

[88]  M. Kimura,et al.  The Stepping Stone Model of Population Structure and the Decrease of Genetic Correlation with Distance. , 1964, Genetics.

[89]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations , 2004, Bulletin of mathematical biology.

[90]  A. Traulsen,et al.  Deterministic evolutionary game dynamics in finite populations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[91]  H. Ohtsuki,et al.  A simple rule for the evolution of cooperation on graphs and social networks , 2006, Nature.

[92]  P. Taylor.  Altruism in viscous populations — an inclusive fitness model , 1992, Evolutionary Ecology.

[93]  C. Hauert,et al.  Reputation-based partner choice promotes cooperation in social networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[94]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[95]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[96]  M. Baalen,et al.  The Unit of Selection in Viscous Populations and the Evolution of Altruism. , 1998, Journal of theoretical biology.

[97]  G. Szabó,et al.  Evolutionary prisoner's dilemma game on a square lattice , 1997, cond-mat/9710096.

[98]  Martin A. Nowak,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2022 .

[99]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[100]  B Skyrms,et al.  A dynamic model of social network formation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[101]  C. Hauert,et al.  Game theory and physics , 2005 .

[102]  A Grafen,et al.  An inclusive fitness analysis of altruism on a cyclical network , 2007, Journal of evolutionary biology.

[103]  Martin A. Nowak,et al.  Evolutionary dynamics on graphs , 2005, Nature.

[104]  O. Penrose,et al.  Cluster and percolation inequalities for lattice systems with interactions , 1977 .

[105]  F. C. Santos,et al.  Evolutionary dynamics of social dilemmas in structured heterogeneous populations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[106]  T. Killingback,et al.  Evolution in group-structured populations can resolve the tragedy of the commons , 2006, Proceedings of the Royal Society B: Biological Sciences.

[107]  M. Kuperman,et al.  Social games in a social network. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[108]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

[109]  C. Cannings,et al.  Evolutionary Game Theory , 2010 .

[110]  M. Nowak,et al.  The evolution of eusociality , 2010, Nature.

[111]  J. Wakeley.  Coalescent Theory: An Introduction , 2008 .

[112]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[113]  S. Bonhoeffer,et al.  Cooperation and Competition in the Evolution of ATP-Producing Pathways , 2001, Science.

[114]  S Redner,et al.  Evolutionary dynamics on degree-heterogeneous graphs. , 2006, Physical review letters.

[115]  David G. Rand,et al.  Direct reciprocity in structured populations , 2012, Proceedings of the National Academy of Sciences.

[116]  M. Kimura.  Evolutionary Rate at the Molecular Level , 1968, Nature.

[117]  T. Geisel,et al.  The scaling laws of human travel , 2006, Nature.