Evolutionary Dynamics on Any Population Structure

Overview

Journal Nature

Specialty Science

Date 2017 Mar 30

PMID 28355181

Citations 124

Authors

Benjamin Allen

Gabor Lippner

Yu-Ting Chen

Babak Fotouhi

Naghmeh Momeni

Shing-Tung Yau

Martin A Nowak

Affiliations

Soon will be listed here.

Abstract

Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours. The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm. Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times of random walks. We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure-graph surgery-affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

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References

Krapivsky P, Redner S . Organization of growing random networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2001; 63(6 Pt 2):066123. DOI: 10.1103/PhysRevE.63.066123. View

Ohtsuki H, Hauert C, Lieberman E, Nowak M . A simple rule for the evolution of cooperation on graphs and social networks. Nature. 2006; 441(7092):502-5. PMC: 2430087. DOI: 10.1038/nature04605. View

Barabasi , ALBERT . Emergence of scaling in random networks. Science. 1999; 286(5439):509-12. DOI: 10.1126/science.286.5439.509. View

Nowak M, Tarnita C, Antal T . Evolutionary dynamics in structured populations. Philos Trans R Soc Lond B Biol Sci. 2009; 365(1537):19-30. PMC: 2842709. DOI: 10.1098/rstb.2009.0215. View

Debarre F, Hauert C, Doebeli M . Social evolution in structured populations. Nat Commun. 2014; 5:3409. DOI: 10.1038/ncomms4409. View

Taylor P, Day T, Wild G . Evolution of cooperation in a finite homogeneous graph. Nature. 2007; 447(7143):469-72. DOI: 10.1038/nature05784. View

Hill A, Rand D, Nowak M, Christakis N . Infectious disease modeling of social contagion in networks. PLoS Comput Biol. 2010; 6(11):e1000968. PMC: 2973808. DOI: 10.1371/journal.pcbi.1000968. View

Holme P, Kim B . Growing scale-free networks with tunable clustering. Phys Rev E Stat Nonlin Soft Matter Phys. 2002; 65(2 Pt 2):026107. DOI: 10.1103/PhysRevE.65.026107. View

Santos F, Pacheco J . Scale-free networks provide a unifying framework for the emergence of cooperation. Phys Rev Lett. 2005; 95(9):098104. DOI: 10.1103/PhysRevLett.95.098104. View

10.

Sade D . Sociometrics of Macaca mulatta. I. Linkages and cliques in grooming matrices. Folia Primatol (Basel). 1972; 18(3):196-223. DOI: 10.1159/000155480. View

11.

Allen B, Sample C, Dementieva Y, Medeiros R, Paoletti C, Nowak M . The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure. PLoS Comput Biol. 2015; 11(2):e1004108. PMC: 4342344. DOI: 10.1371/journal.pcbi.1004108. View

12.

Konno T . A condition for cooperation in a game on complex networks. J Theor Biol. 2010; 269(1):224-33. DOI: 10.1016/j.jtbi.2010.10.033. View

13.

Sundaresan S, Fischhoff I, Dushoff J, Rubenstein D . Network metrics reveal differences in social organization between two fission-fusion species, Grevy's zebra and onager. Oecologia. 2006; 151(1):140-9. DOI: 10.1007/s00442-006-0553-6. View

14.

Christakis N, Fowler J . The spread of obesity in a large social network over 32 years. N Engl J Med. 2007; 357(4):370-9. DOI: 10.1056/NEJMsa066082. View

15.

Tarnita C, Ohtsuki H, Antal T, Fu F, Nowak M . Strategy selection in structured populations. J Theor Biol. 2009; 259(3):570-81. PMC: 2710410. DOI: 10.1016/j.jtbi.2009.03.035. View

16.

Nowak M, Michor F, Iwasa Y . The linear process of somatic evolution. Proc Natl Acad Sci U S A. 2003; 100(25):14966-9. PMC: 299861. DOI: 10.1073/pnas.2535419100. View

17.

Hauert C, Michor F, Nowak M, Doebeli M . Synergy and discounting of cooperation in social dilemmas. J Theor Biol. 2005; 239(2):195-202. PMC: 2891160. DOI: 10.1016/j.jtbi.2005.08.040. View

18.

Lozano S, Arenas A, Sanchez A . Mesoscopic structure conditions the emergence of cooperation on social networks. PLoS One. 2008; 3(4):e1892. PMC: 2274863. DOI: 10.1371/journal.pone.0001892. View

19.

Maciejewski W, Fu F, Hauert C . Evolutionary game dynamics in populations with heterogenous structures. PLoS Comput Biol. 2014; 10(4):e1003567. PMC: 3998889. DOI: 10.1371/journal.pcbi.1003567. View

20.

Slatkin M . Inbreeding coefficients and coalescence times. Genet Res. 1991; 58(2):167-75. DOI: 10.1017/s0016672300029827. View