Mathematics of kin- and group-selection: Formally equivalent?

Evolution

Volumn 64, Issue 2, 2010, Pages 316-323

  Traulsen, Arne ^a  

^a MAX PLANCK INSTITUTE FOR EVOLUTIONARY BIOLOGY   (Germany)

Author keywords

Evolutionary game theory; Inclusive fitness; Mathematical biology; Multilevel selection

Indexed keywords

EVOLUTIONARY BIOLOGY; EVOLUTIONARY THEORY; GROUP SELECTION; INCLUSIVE FITNESS; KIN SELECTION; NUMERICAL MODEL;

ARTICLE; EVOLUTION; GAME; GENETIC SELECTION; MATHEMATICS;

EVOLUTION; GAME THEORY; MATHEMATICS; SELECTION, GENETIC;

EID: 75149175729     PISSN: 00143820     EISSN: 15585646     Source Type: Journal    
DOI: 10.1111/j.1558-5646.2009.00899.x     Document Type: Article

References (85)

1. Altrock, P. M., and A. Traulsen. 2009. Deterministic evolutionary game dynamics in finite populations. Phys. Rev. E 80 : 011909.
2. Antal, T., M. A. Nowak, and A. Traulsen. 2009a. Strategy abundance in 2×2 games for arbitrary mutation rates. J. Theor. Biol. 257 : 340 344.
3. Antal, T., H. Ohtsuki, J. Wakeley, P. D. Taylor, and M. A. Nowak. 2009b. Evolution of cooperation by phenotypic similarity. Proc. Natl. Acad. Sci. USA 106 : 8597 8600.
4. Antal, T., A. Traulsen, H. Ohtsuki, C. E. Tarnita, and M. A. Nowak. 2009c. Mutation-selection equilibrium in games with multiple strategies. J. Theor. Biol. 258 : 614 622.
5. Barton, N. H., and M. Turelli. 1987. Adaptive landscapes, genetic distance and the evolution of quantitative characters. Genet. Res. 49 : 157 173.
6. Bijma, P., and M. J. Wade. 2008. The joint effects of kin, multilevel selection and indirect genetic effects on response to genetic selection. J. Evol. Biol. 21 : 1175 1188.
7. Bomze, I., and C. Pawlowitsch. 2008. One-third rules with equality: second-order evolutionary stability conditions in finite populations. J. Theor. Biol. 254 : 616 620.
8. Cavalli-Sforza, L. L., and M. W. Feldman. 1978. Darwinian selection and "altruism." Theor. Pop. Biol. 14 : 268 280.
9. Dawkins, R. 1979. Twelve misunderstandings of kin selection. Z. Tierpsychologie 51 : 184 200.
10. Dirac, P. A. M. 1930. The Principles of quantum mechanics. Clarendon, Oxford, UK.
11. Dreber, A., D. G. Rand, D. Fudenberg, and M. A. Nowak. 2008. Winners don't punish. Nature 452 : 348 351.
12. Dugatkin, L. A., and H. K. Reeve. 1994. Behavioral ecology and the levels of selection: dissolving the group selection controversy. Adv. Study Behav. 23 : 101 133.
13. Ewens, W. J. 2004. Mathematical population genetics. Springer, New York.
14. Fletcher, J. A., and M. Doebeli. 2009. A simple and general explanation for the evolution of altruism. Proc. R. Soc. Lond. B 276 : 13 19.
15. Fletcher, J. A., M. Zwick, M. Doebeli, and D. S. Wilson. 2006. What's wrong with inclusive fitness Trends Ecol. Evol. 21 : 597 598.
16. Frank, S. A. 1997. The Price equation, Fischer's fundamental theorem, kin selection, and causal analysis. Evolution 51 : 1712 1729.
17. Frank, S. A. 1998. Foundations of social evolution. Princeton Univ. Press, Princeton.
18. Fudenberg, D., and C. Harris. 1992. Evolutionary dynamics with aggregate shocks. J. Econ. Theory 57 : 420 441.
19. Gardner, A. 2008. The Price equation. Curr. Biol. 18 : R198 R202.
20. Goodnight, C. J. 1997. Experimental studies of groups selection: what do they tell us about group selection in nature Am. Nat. 150 : S59 S79.
21. Grafen, A. 1985. Hamilton's rule ok. Nature 318 : 310 311.
22. Hamilton, W. D. 1964. The genetical evolution of social behavior I and II. J. Theor. Biol. 7 : 1 16 + 17-52.
23. Hamilton, W. D. 1975. Innate social aptitudes of man: an approach from evolutionary genetics. Pp. 133 155, in R. Fox, ed. Biosocial anthropology. Wiley, New York.
24. Heisenberg, W. 1925. Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33 : 879 893.
25. Hofbauer, J., and K. Sigmund. 1998. Evolutionary games and population dynamics. Cambridge Univ. Press, Cambridge.
26. Hölldobler, B., and E. O. Wilson. 1990. The Ants. Belknap Press, Cambridge, MA.
27. Kandori, M., G. J. Mailath, and R. Rob. 1993. Learning, mutation, and long run equilibria in games. Econometrica 61 : 29 56.
28. Kerr, B., and P. Godfrey-Smith. 2002. Individualist and multi-level perspectives on selection in structured populations. Biol. Philos. 17 : 477 517.
29. Kerr, B., M. A. Riley, M. W. Feldman, and B. J. M. Bohannan. 2002. Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature 418 : 171 174.
30. Killingback, T., J. Bieri, and T. Flatt. 2006. Evolution in group-structured populations can resolve the tragedy of the commons. Proc. R. Soc. Lond. B 273 : 1477 1481.
31. Kingman, J. F. C. 1982. The coalescent. Stoch. Proc. Appl. 13 : 235 248.
32. Lehmann, L., and L. Keller. 2006. The evolution of cooperation and altruism - a general framework and a classification of models. J. Evol. Biol. 19 : 1365 1378.
33. Lehmann, L., L. Keller, and D. J. T. Sumpter. 2007a. The evolution of helping and harming on graphs: the return of the inclusive fitness effect. J. Evol. Biol. 20 : 2284 2295.
34. Lehmann, L., L. Keller, S. West, and D. Roze. 2007b. Group selection and kin selection: two concepts but one process. Proc. Natl. Acad. Sci. USA 104 : 6736 6739.
35. Milinski, M. 1987. Tit for tat in sticklebacks and the evolution of cooperation. Nature 325 : 433 435.
36. Milinski, M., J. H. Lüthi, R. Eggler, and G. A. Parker. 1997. Cooperation under predation risk: experiments on costs an benefits. Proc. R. Soc. Lond. B 264 : 831 837.
37. Nowak, M. A. 2006. Five rules for the evolution of cooperation. Science 314 : 1560 1563.
38. Nowak, M. A., and K. Sigmund. 1990. The evolution of stochastic strategies in the prisoner's dilemma. Acta Appl. Math. 20 : 247 265.
39. Nowak, M. A., and K. Sigmund. 2004. Evolutionary dynamics of biological games. Science 303 : 793 799.
40. Nowak, M. A., A. Sasaki, C. Taylor, and D. Fudenberg. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428 : 646 650.
41. Ohtsuki, H., and M. A. Nowak. 2006a. Evolutionary games on cycles. Proc. R. Soc. Lond. B 273 : 2249 2256.
42. Ohtsuki, H., and M. A. Nowak. 2006b. The replicator equation on graphs. J. Theor. Biol. 243 : 86 97.
43. Ohtsuki, H., P. Bordalo, and M. A. Nowak. 2007a. The one-third law of evolutionary dynamics. J. Theor. Biol. 249 : 289 295.
44. Ohtsuki, H., P. Bordalo, and M. A. Nowak. 2007b. Evolutionary graph theory: breaking the symmetry between interaction and replacement. J. Theor. Biol. 246 : 681 694. (Pubitemid 46719263)
45. Ohtsuki, H., C. Hauert, E. Lieberman, and M. A. Nowak. 2006. A simple rule for the evolution of cooperation on graphs. Nature 441 : 502 505.
46. Okasha, S. 2006a. Evolution and the levels of selection. Oxford Univ. Press, Oxford, UK.
47. Okasha, S. 2006b. The levels of selection debate: philosophical issues. Philos. Compass 1 : 74 85.
48. Page, K. M., and M. A. Nowak. 2002. Unifying evolutionary dynamics. J. Theor. Biol. 219 : 93 98.
49. Price, G. R. 1970. Selection and covariance. Nature 227 : 520 521.
50. Queller, D. C. 1985. Kinship, reciprocity, and synergism in the evolution of social behaviour. Nature 318 : 366 367.
51. Reeve, H. K., and B. Hölldobler. 2007. The emergence of a superorganism through intergroup competition. Proc. Natl. Acad. Sci. USA 104 : 9736 9740.
52. Ross-Gillespie, A., A. Gardner, S. A. West, and A. S. Griffin. 2007. Frequency dependence and cooperation: theory and a test with bacteria. Am. Nat. 170 : 331 342.
53. Rousset, F., and S. Billiard. 2000. A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal. J. Evol. Biol. 13 : 814 825.
54. Santos, F. C., J. M. Pacheco, and T. Lenaerts. 2006. Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl. Acad. Sci. USA 103 : 3490 3494.
55. Santos, F. C., M. D. Santos, and J. M. Pacheco. 2008. Social diversity promotes the emergence of cooperation in public goods games. Nature 454 : 213 216.
56. Schrödinger, E. 1926. Quantisierung als Eigenwertproblem. Ann. Phys. 79 : 361 376.
57. Semmann, D., H. J. Krambeck, and M. Milinski. 2005. Reputation is valuable within and outside one's own social group. Behav. Ecol. Sociobiol. 57 : 611 616.
58. Tarnita, C. E., T. Antal, H. Ohtsuki, and M. A. Nowak. 2009a. Evolutionary dynamics in set structured populations. Proc. Natl. Acad. Sci. USA 106 : 8601 8604.
59. Tarnita, C. E., H. Ohtsuki, T. Antal, F. Fu, and M. A. Nowak. 2009b. Strategy selection in structured populations. J. Theor. Biol. 259 : 570 581.
60. Taylor, P. D., and L. Jonker. 1978. Evolutionary stable strategies and game dynamics. Math. Biosci. 40 : 145 156.
61. Taylor, C., and M. A. Nowak. 2007. Transforming the dilemma. Evolution 61 : 2281 2292.
62. Taylor, C., D. Fudenberg, A. Sasaki, and M. A. Nowak. 2004. Evolutionary game dynamics in finite populations. Bull. Math. Biol. 66 : 1621 1644.
63. Taylor, P. D., T. Day, and G. Wild. 2007a. Evolution of cooperation in a finite bi-transitive graph. Nature 447 : 469 472.
64. Taylor, P. D., T. Day, and G. Wild. 2007b. From inclusive fitness to fixation probability in homogeneous structured populations. J. Theor. Biol. 249 : 101 110.
65. Traulsen, A., and M. A. Nowak. 2006. Evolution of cooperation by multi-level selection. Proc. Natl. Acad. Sci. USA 103 : 10952 10955.
66. Traulsen, A., J. C. Claussen, and C. Hauert. 2006a. Coevolutionary dynamics in large, but finite populations. Phys. Rev. E 74 : 11901.
67. Traulsen, A., J. M. Pacheco, and L. A. Imhof. 2006b. Stochasticity and evolutionary stability. Phys. Rev. E 74 : 021905.
68. Traulsen, A., N. Shoresh, and M. A. Nowak. 2008. Analytical results for individual and group selection of any intensity. Bull. Math. Biol. 70 : 1410 1424.
69. Trivers, R. L., and H. Hare. 1976. Haplodiploidy and the evolution of the social insect. Science 191 : 249 263.
70. Turner, P. E., and L. Chao. 1999. Prisoner's Dilemma in an RNA virus. Nature 398 : 441 443.
71. van Veelen, M. 2005. On the use of the Price equation. J. Theor. Biol. 237 : 412 426.
72. van Veelen, M. 2009. Group selection, kin selection, altruism and cooperation: when inclusive fitness is right and when it can be wrong. J. Theor. Biol. 259 : 589 600.
73. van Veelen, M., and A. Hopfensitz. 2007. In love and war: altruism, norm formation, and two different types of group selection. J. Theor. Biol. 249 : 667 680.
74. Wakeley, J. 2008. Coalescent theory: an introduction. Roberts & Company Publishers Greenwood Village, CO.
75. Wenseleers, T., A. Gardner, and K. R. Foster. 2009. Social evolution theory: a review of methods and approaches. in T. Szekely, J. Komdeur, and A. J. Moore, eds. Social behaviour: genes, ecology and evolution. Cambridge Univ. Press Cambridge, UK.
76. West, S. A., A. S. Griffin, and A. Gardner. 2007a. Evolutionary explanations for cooperation. Curr. Biol. 17 : R661 R672.
77. West, S. A., A. S. Griffin, and A. Gardner. 2007b. Social semantics: altruism, cooperation, mutualism, strong reciprocity and group selection. J. Evol. Biol. 20 : 415 432.
78. West, S. A., A. S. Griffin, and A. Gardner. 2007c. Social semantics: how useful has group selection been J. Evol. Biol. 21 : 374 385.
79. Wild, G., and A. Traulsen. 2007. The different limits of weak selection and the evolutionary dynamics of finite populations. J. Theor. Biol. 247 : 382 390.
80. Wild, G., A. Gardner, and S. A. West. 2009. Adaptation and the evolution of parasite virulence in a connected world. Nature 459 : 983 986.
81. Wilson, E. O. 2008. One giant leap: how insects achieved altruism and colonial life. BioScience 58 : 17 25.
82. Wilson, E. O., and B. Hölldobler. 2005. Eusociality: origin and consequences. Proc. Natl. Acad. Sci. USA 102 : 13367 13371.
83. Wilson, D. S., and E. O. Wilson. 2007. Rethinking the theoretical foundation of sociobiology. Q. Rev. Biol. 82 : 327 348.
84. Yamagishi, T. 1986. The provision of a sanctioning system as a public good. J. Pers. Soc. Psychol. 51 : 110 116.
85. Zeeman, E. C. 1980. Population dynamics from game theory. in Lecture Notes in Mathematics 819 : 471 497.