Fixation probability for a beneficial allele and a mutant strategy in a linear game under weak selection in a finite island model

Theoretical Population Biology

Volumn 72, Issue 3, 2007, Pages 409-425

  Ladret, Véronique ^a   Lessard, Sabin ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Beneficial allele; Coalescence times; Evolutionary game theory; Finite island model; Fixation probability; One third law

Indexed keywords

ALLELE; COALESCENCE; EVOLUTIONARY THEORY; GAME THEORY; GENEALOGY; NUMERICAL MODEL; PROBABILITY; SELECTION;

ALLELE; ARTICLE; BIOLOGICAL MODEL; EVOLUTION; GAME; GENE FREQUENCY; GENETIC DRIFT; GENETIC POLYMORPHISM; GENETIC SELECTION; GENETIC VARIABILITY; GEOGRAPHY; HUMAN; POPULATION DYNAMICS; POPULATION GENETICS; PROBABILITY; STATISTICAL MODEL;

ALLELES; EVOLUTION; GAME THEORY; GENE FREQUENCY; GENETIC DRIFT; GENETICS, POPULATION; GEOGRAPHY; HUMANS; MARKOV CHAINS; MODELS, BIOLOGICAL; MODELS, GENETIC; MODELS, STATISTICAL; POLYMORPHISM, GENETIC; POPULATION DYNAMICS; PROBABILITY; SELECTION (GENETICS); VARIATION (GENETICS);

EID: 34848925447     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2007.04.001     Document Type: Article

References (65)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions (1965), Dover, New York
2. Abrams P.A., and Matsuda H. Fitness minimization and dynamic instability as a consequence of predator-prey coevolution. Evol. Ecol. 11 (1997) 1-20 (reprinted with corrections from 1996, Evol. Ecol. 10, 167-186)
3. Axelrod R., and Hamilton W.D. The evolution of cooperation. Science 211 (1981) 1390-1396
4. Bahlo M., and Griffiths R.C. Coalescence time for two genes from a subdivided population. J. Math. Biol. 43 (2001) 397-410
5. Barton N.H. The probability of fixation of a favoured allele in a subdivided population. Genet. Res. 62 (1993) 149-158
6. Caballero A., and Hill W.G. Effects of partial inbreeding on fixation rates and variation of mutant genes. Genetics 131 (1992) 493-507
7. Cherry J.L. Selection in a subdivided population with dominance or local frequency dependence. Genetics 163 (2003) 1511-1518
8. Cherry J.L. Selection in a subdivided population with local extinction and recolonization. Genetics 164 (2003) 789-795
9. Cherry J.L., and Wakeley J. A diffusion approximation for selection and drift in a subdivided population. Genetics 163 (2003) 421-428
10. Ewens W.J. Mathematical Population Genetics 1. Theoretical Introduction. Second ed (2004), Springer, New York
11. Fisher R.A. On the dominance ratio. Proc. R. Soc. Edinb. 42 (1922) 321-341
12. Fisher R.A. The Genetical Theory of Natural Selection (1930), Oxford University Press, Oxford
13. Godfray H.C.J. Evolutionary theory of parent-offspring conflict. Nature 376 (1995) 133-138
14. Haldane J.B.S. A mathematical theory of natural and artificial selection. V. Selection and mutation. Proc. Camb. Philos. Soc. 23 (1927) 838-844
15. Hamilton W.D. Extraordinary sex ratios. Science 156 (1967) 477-488
16. Hardy I.C.W. Mother Knows Best: Sons or Daughters? A Review of Sex Ratios. Concepts and Methods (2002), Cambridge University Press, Cambridge
17. Herbots, H.M., 1994. Stochastic models in population genetics: genealogy and genetic differentiation in structured populations. Ph.D. Thesis, University of London, London.
18. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge
19. Imhof L.A., and Nowak M.A. Evolutionary game dynamics in a Wright-Fisher process. J. Math. Biol. 52 (2006) 667-681
20. Kerr B., Riley M., Feldman M., and Bohannan B. Local dispersal and interaction promote coexistence in a real life game of rock-paper-scissors. Nature 418 (2002) 171-174
21. Kimura M. Some problems of stochastic processes in genetics. Ann. Math. 28 (1957) 882-901
22. Kimura M. On the probability of fixation of mutant genes in a population. Genetics 47 (1962) 713-719
23. Kingman J.F.C. The coalescent. Stochast. Proc. Appl. 13 (1982) 235-248
24. Kingman J.F.C. On the genealogy of large populations. J. Appl. Prob. 19A (1982) 27-43
25. Lambert A. Probability of fixation under weak selection: a branching process unifying approach. Theor. Popul. Biol. 69 (2006) 419-441
26. Lessard S. Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory. Theor. Popul. Biol. 68 (2005) 19-27
27. Lessard S., and Ladret V. The probability of fixation of a single mutant in an exchangeable selection model. J. Math. Biol. 54 (2007) 721-744
28. Lessard S., and Wakeley J. The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model. J. Math. Biol. 48 (2004) 275-292
29. Maruyama T. Effective number of alleles in a subdivided population. Theor. Popul. Biol. 1 (1970) 273-306
30. Maruyama T. A simple proof that certain quantities are independent of the geographical structure of the population. Theor. Popul. Biol. 5 (1974) 148-154
31. Maynard Smith J. The theory of games and the evolution of animal conflicts. J. Theor. Biol. 47 (1974) 209-221
32. Maynard Smith J. Evolution and the Theory of Games (1982), Cambridge University Press, Cambridge
33. Maynard Smith J., and Price G.R. The logic of animal conflict. Nature 246 (1973) 15-18
34. Nagylaki T. The strong-migration limit in geographically structured populations. J. Math. Biol. 9 (1980) 101-114
35. Nagylaki T. Geographical invariance in population genetics. J. Theor. Biol. 99 (1982) 159-172
36. Nagylaki T. Geographical invariance and the strong-migration limit in subdivided populations. J. Math. Biol. 41 (2000) 123-142
37. Notohara M. The coalescent and the genalogical process in geographically structured populations. J. Math. Biol. 29 (1990) 59-75
38. Notohara M. The strong-migration limit for the genealogical process in geographically structured populations. J. Math. Biol. 31 (1993) 115-122
39. Notohara M. A perturbation method for the structured coalescent with strong migration. J. Appl. Prob. 37 (2000) 148-167
40. Notohara M. The structured coalescent process with weak migration. J. Appl. Prob. 38 (2001) 1-17
41. Nowak M.A., and Sigmund K. Evolutionary dynamics of biological games. Science 303 (2004) 793-799
42. Nowak M.A., Sasaki A., Taylor C., and Fudenberg D. Emergence of cooperation and evolutionary stability in finite populations. Nature 428 (2004) 646-650
43. Orzack S.H., and Hines W.G.S. The evolution of strategy variation: will an ESS evolve?. Evolution 59 (2005) 1183-1193
44. Rousset F. A minimal derivation of convergence stability measures. J. Theor. Biol. 221 (2003) 665-668
45. Rousset F. Genetic Structure and Selection in Subdivided Populations (2004), Princeton University Press, Princeton
46. Rousset F., and Billiard S. A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal. J. Evol. Biol. 13 (2000) 814-825
47. Roze D., and Rousset F. Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and examples involving dominance, selfing, and local extinctions. Genetics 165 (2003) 2153-2166
48. Roze D., and Rousset F. The robustness of Hamilton's rule with inbreeding and dominance: kin selection and fixation probabilities under partial sib mating. Am. Nat. 164 (2004) 214-231
49. Sinervo B., and Lively C.M. The rock-paper-scissors game and the evolution of alternative male reproductive strategies. Nature 380 (1996) 240-243
50. Slatkin M. Fixation probabilities and fixation times in a subdivided population. Evolution 35 (1981) 477-488
51. Sugden R. The Economics of Rights, Co-operation and Welfare (1986), Blackwell, Oxford
52. Takahata N. Genealogy of neutral genes and spreading of selected mutations in a geographically structured population. Genetics 129 (1991) 585-595
53. Taylor P.D., and Jonker L.B. Evolutionarily stable strategies and game dynamics. Math. Biosci. 40 (1978) 145-156
54. Taylor P.D., Day T., Nagy D., Wild G., André J.B., and Gardner A. The evolutionary consequences of plasticity in host-pathogen interactions. Theor. Popul. Biol. 69 (2006) 323-331
55. Turner P.E., and Chao L. Prisoner's dilemna in an RNA virus. Nature 398 (1999) 441-443
56. Wakeley J. Segregating sites in Wright's island model. Theor. Popul. Biol. 53 (1998) 166-175
57. Wakeley J. Polymorphism and divergence for island model species. Genetics 163 (2003) 411-420
58. Wakeley J. Recent trends in population genetics: more data! more math! simple models?. J. Hered. 95 (2004) 397-405
59. Wakeley J., and Lessard S. Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans. Genetics 164 (2003) 1043-1053
60. Wakeley J., and Takahashi T. The many-demes limit for selection and drift in a subdivided population. Theor. Popul. Biol. 66 (2004) 83-91
61. Whitlock M.C. Fixation probability and time in subdivided populations. Genetics 164 (2003) 767-779
62. Wild G., and Taylor P.D. Fitness and evolutionary stability in game theoretic models of finite populations. Proc. R. Soc. B 271 (2004) 2345-2349
63. Wilkinson-Herbots H. Genealogy and subpopulation in differentiation under various models of population structure. J. Math. Biol. 37 (1998) 535-585
64. Wilkinson-Herbots H.M. Coalescence times and FST values in subdivided populations with symmetric structure. Adv. Appl. Prob. 35 (2003) 665-690
65. Wright S. Evolution in Mendelian populations. Genetics 16 (1931) 97-159