Evolutionary stability on graphs

Journal of Theoretical Biology

Volumn 251, Issue 4, 2008, Pages 698-707

  Ohtsuki, Hisashi ^a   Nowak, Martin A ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

ESS; Evolutionary game theory; Evolutionary graph theory; Spatial games; Structured population

Indexed keywords

EVOLUTION; EVOLUTIONARILY STABLE STRATEGY; GAME THEORY; GEOMETRY; POPULATION STRUCTURE; THEORETICAL STUDY;

ANALYTIC METHOD; ARTICLE; BIRTH; DEATH; EVOLUTION; GEOMETRY; POPULATION RESEARCH; PRIORITY JOURNAL;

ANIMALS; COMPUTER SIMULATION; EVOLUTION; GAME THEORY; GENETIC DRIFT; POPULATION DYNAMICS;

EID: 41049094933     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2008.01.005     Document Type: Article

References (89)

1. Axelrod R., and Hamilton W.D. The evolution of cooperation. Science 211 (1981) 1390-1396
2. Binmore K. Game Theory and the Social Contract, Vol. 1. Playing Fair (1994), MIT Press, Cambridge
3. Durrett R., and Levin S.A. The importance of being discrete (and spatial). Theor. Popul. Biol. 46 (1994) 363-394
4. Durrett R., and Levin S.A. Allelopathy in spatially distributed populations. J. Theor. Biol. 185 (1997) 165-171
5. Durrett R., and Levin S.A. Spatial aspects of interspecific competition. Theor. Popul. Biol. 53 (1998) 30-43
6. Ellison G. Learning, local interaction, and coordination. Econometrica 61 (1993) 1047-1071
7. Epperson B.K. Geographical Genetics (2003), Princeton University Press, Princeton
8. Eshel I., Samuelson L., and Shaked A. Altruists, egoists, and hooligans in a local interaction model. Am. Econ. Rev. 88 (1998) 157-179
9. Eshel I., Sansone E., and Shaked A. The emergence of kinship behavior in structured populations of unrelated individuals. Int. J. Game Theory 28 (1999) 447-463
10. Ficici S., and Pollack J. Effects of finite populations on evolutionary stable strategies. In: Whitley D. (Ed). Proceedings of the 2000 Genetic and Evolutionary Computation Conference (2000), Morgan-Kaufmann, San Francisco 927-934
11. Fudenberg D., and Tirole J. Game Theory (1991), MIT Press, Cambridge
12. Haraguchi Y., and Sasaki A. The evolution of parasite virulence and transmission rate in a spatially structured population. J. Theor. Biol. 203 (2000) 85-96
13. Hassell M.P., Comins H.N., and May R.M. Species coexistence and self-organizing spatial dynamics. Nature 370 (1994) 290-292
14. Hauert C. Fundamental clusters in spatial 2 × 2 games. Proc. R. Soc. Lond. B 268 (2001) 761-769
15. Hauert C., and Doebeli M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428 (2004) 643-646
16. Hauert C., De Monte S., Hofbauer J., and Sigmund K. Volunteering as red queen mechanism for cooperation in public goods game. Science 296 (2002) 1129-1132
17. Herz A.V.M. Collective phenomena in spatially extended evolutionary games. J. Theor. Biol. 169 (1994) 65-87
18. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge, UK
19. Hofbauer J., Schuster P., and Sigmund K. A note on evolutionarily stable strategies and game dynamics. J. Theor. Biol. 81 (1979) 609-612
20. Ifti M., Killingback T., and Doebeli M. Effects of neighbourhoodsize and connectivity on the spatial Continuous Prisoner's Dilemma. J. Theor. Biol. 231 (2004) 97-106
21. Irwin A., and Taylor P.D. Evolution of altruism in a stepping-stone population with overlapping generations. Theor. Popul. Biol. 60 (2001) 315-325
22. Iwasa Y., Nakamaru M., and Levin S.A. Allelopathy of bacteria in a lattice population: competition between colicin-sensitive and colicin-producing strains. Evol. Ecol. 12 (1998) 785-802
23. Keeling M.J. The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B 266 (1999) 859-869
24. Killingback T., and Doebeli M. Spatial evolutionary game theory: hawks and doves revisited. Proc. R. Soc. Lond. B 263 (1996) 1135-1144
25. Kimura M. Stepping stone model of population. Ann. Rep. Nat. Inst. Genetics (Japan) 3 (1953) 63-65
26. Kimura M., and Weiss G.H. The stepping stone model of population structure and the decrease of genetical correlation with distance. Genetics 49 (1964) 561-576
27. Le Galliard J., Ferrière R., and Dieckman U. The adaptive dynamics of altruism in spatially heterogeneous populations. Evolution 57 (2003) 1-17
28. Lehmann, L., Keller, L., Sumpter, D.J.T., The evolution of helping and harming on graphs: the return of the inclusive fitness effect. J. Evol. Biol. 20, 2284-2295.
29. Levin S.A. Dispersion and population interactions. Am. Nat. 108 (1974) 207-228
30. Levin S.A., and Paine R.T. Disturbance, patch formation, and community structure. Proc. Natl Acad. Sci. USA 71 (1974) 2744-2747
31. Lieberman E., Hauert C., and Nowak M.A. Evolutionary dynamics on graphs. Nature 433 (2005) 312-316
32. Lindgren K., and Nordahl M.G. Evolutionary dynamics of spatial games. Physica D 75 (1994) 292-309
33. Luce R.D., and Raiffa H. Games and Decision (1957), Wiley, New York
34. Maruyama T. On the fixation probability of mutant genes in a subdivided population. Gen. Res. 15 (1970) 221-226
35. Maruyama T. An invariance property of a structured population. Gen. Res. 18 (1971) 81-84
36. Matsuda H., Tamachi N., Sasaki A., and Ogita N. A lattice model for population biology. In: Teramot E., and Yamaguti M. (Eds). Mathematical Topics in Biology, Morphogenesis and Neurosciences. Springer Lecture Notes in Biomathematics vol. 71 (1987) 154-161
37. Matsuda H., Ogita N., Sasaki A., and Sato K. Statistical mechanics of population-the lattice Lotka-Volterra model. Prog. Theor. Phys. 88 (1992) 1035-1049
38. May R.M. Network structure and the biology of populations. Trends. Ecol. Evol. 21 (2006) 394-399
39. Maynard Smith J. The theory of games and the evolution of animal conflicts. J. Theor. Biol. 47 (1974) 209-221
40. Maynard Smith J. Evolution and the Theory of Games (1982), Cambridge University Press, Cambridge
41. Maynard Smith J. Can a mixed strategy be stable in a finite population?. J. Theor. Biol. 130 (1988) 247-251
42. Maynard Smith J., and Price G. The logic of animal conflicts. Nature 246 (1973) 15-18
43. Nagylaki T. Theoretical Population Genetics (1992), Springer, Berlin
44. Nakamaru M., and Iwasa Y. The evolution of altruism by costly punishment in the lattice structured population: score-dependent viability versus score-dependent fertility. Evol. Ecol. Res. 7 (2005) 853-870
45. Nakamaru M., Matsuda H., and Iwasa Y. The evolution of cooperation in a lattice structured population. J. Theor. Biol. 184 (1997) 65-81
46. Nakamaru M., Nogami H., and Iwasa Y. Score-dependent fertility model for the evolution of cooperation in a lattice. J. Theor. Biol. 194 (1998) 101-124
47. Nash J.F. Equilibrium points in n-person games. Proc. Natl Acad. Sci. USA 36 (1950) 48-49
48. Neill D.B. Evolutionary stability for large populations. J. Theor. Biol. 227 (2004) 397-401
49. Neuhauser C. Mathematical challenges in spatial ecology. Not. Am. Math. Soc. 48 (2001) 1304-1314
50. Nowak M.A. Evolutionary Dynamics (2006), Harvard University Press, MA
51. Nowak M.A., and May R.M. Evolutionary games and spatial chaos. Nature 359 (1992) 826-829
52. Nowak M.A., and May R.M. The spatial dilemmas of evolution. Int. J. Bifur. Chaos 3 (1993) 35-78
53. Nowak M.A., and Sigmund K. Evolutionary dynamics of biological games. Science 303 (2004) 793-799
54. Nowak M.A., Bonhoeffer S., and May R.M. More spatial games. Int. J. Bifurc. Chaos 4 (1994) 33-56
55. Nowak M.A., Sasaki A., Taylor C., and Fudenberg D. Emergence of cooperation and evolutionary stability in finite populations. Nature 428 (2004) 646-650
56. Ohtsuki H., and Nowak M.A. Evolutionary games on cycles. Proc. R. Soc. B 273 (2006) 2249-2256
57. Ohtsuki H., and Nowak M.A. The replicator equation on graphs. J. Theor. Biol. 243 (2006) 86-97
58. Ohtsuki H., Hauert C., Lieberman E., and Nowak M.A. A simple rule for the evolution of cooperation on graphs and social networks. Nature 441 (2006) 502-505
59. Ohtsuki H., Nowak M.A., and Pacheco J. Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. Phys. Rev. Lett. 98 (2007) 108106
60. Ohtsuki H., Pacheco J., and Nowak M.A. Evolutionary graph theory: breaking the symmetry between interaction and replacement. J. Theor. Biol. 246 (2007) 681-694
61. Pacheco J.M., Traulsen A., and Nowak M.A. Active linking in evolutionary games. J. Theor. Biol. 243 (2006) 437-443
62. Pacheco J.M., Traulsen A., and Nowak M.A. Coevolution of strategy and structure in complex networks with dynamical linking. Phys. Rev. Lett. 97 (2006) 258103
63. Pastor-Satorras R., and Vespignani A. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86 (2001) 3200-3203
64. Rapoport A., and Chammah A.M. Prisoners Dilemma: A Study in Conflict and Cooperation (1965), The University of Michigan Press, Ann Arbor, MI, USA
65. Rousset F. Genetic Structure and Selection in Subdivided Populations (2004), Princeton University Press, Princeton
66. Samuelson L. Evolutionary Games and Equilibrium Selection (1997), MIT Press, Cambridge
67. Santos F.C., and Pacheco J.M. Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95 (2005) 098104
68. Santos F.C., Pacheco J.M., and Lenaerts T. Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl Acad. Sci. USA 103 (2006) 3490-3494
69. Schaffer M. Evolutionarily stable strategies for a finite population and a variable contest size. J. Theor. Biol. 132 (1988) 469-478
70. Szabó G., and Fáth G. Evolutionary games on graphs. Phys. Rep. 446 (2007) 97-216
71. Szabó G., and Hauert C. Phase transitions and volunteering in spatial public goods games. Phys. Rev. Lett. 89 (2002) 118101
72. Szabó G., and To{combining double acute accent}ke C. Evolutionary prisoner's dilemma game on a square lattice. Phys. Rev. E 58 (1998) 69-73
73. Szabó G., Antal T., Szabó P., and Droz M. Spatial evolutionary prisoner's dilemma game with three strategies and external constraints. Phys. Rev. E 62 (2000) 1095-1103
74. Szabó G., Vukov J., and Szolnoki A. Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. Phys. Rev. E 72 (2005) 047107
75. Tainaka K. Vortices and strings in a model ecosystem. Phys. Rev. E 50 (1994) 3401-3409
76. Taylor P.D. Altruism in viscous populations-an inclusive fitness approach. Evol. Ecol. 6 (1992) 352-356
77. Taylor P.D., and Irwin A.J. Overlapping generations can promote altruistic behavior. Evolution 54 (2000) 1135-1141
78. Taylor P.D., and Jonker L. Evolutionary stable strategies and game dynamics. Math. Biosci. 40 (1978) 145-156
79. Taylor P.D., Day T., and Wild G. Evolution of cooperation in a finite homogeneous graph. Nature 447 (2007) 469-472
80. Tilman, D., Karieva, P. (Eds.), 1997. Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Monographs in Population Biology. Princeton University Press, Princeton, NJ.
81. Traulsen A., Pacheco J.M., and Imhof L.A. Stochasticity and evolutionary stability. Phys. Rev. E 74 (2006) 021905
82. van Baalen M. Pair approximations for different spatial geometries. In: Dieckmann U., Law R., and Metz J.A.J. (Eds). The Geometry of Ecological Interactions (2000), Cambridge University Press, Cambridge, UK 359-387
83. van Baalen M., and Rand D.A. The unit of selection in viscous populations and the evolution of altruism. J. Theor. Biol. 193 (1998) 631-648
84. Weibull J. Evolutionary Game Theory (1995), MIT Press, Cambridge
85. Wild G., and Taylor P.D. Fitness and evolutionary stability in game theoretic models of finite populations. Proc. R. Soc. Lond. B 271 (2004) 2345-2349
86. Wilson D.S., Pollock G.B., and Dugatkin L.A. Can altruism evolve in purely viscous populations?. Evol. Ecol. 6 (1992) 331-341
87. Wootton J.T. Local interactions predict large-scale pattern in empirically derived cellular automata. Nature 413 (2001) 841-844
88. Wright S. Isolation by distance. Genetics 28 (1943) 114-138
89. Zeeman E.C. Population dynamics from game theory. In: Nitecki A., and Robinson C. (Eds). Proceedings of an International Conference on Global Theory of Dynamical Systems. Lecture Notes in Mathematics vol. 819 (1980), Springer, Berlin