Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance

Theoretical Population Biology

Volumn 69, Issue 2, 2006, Pages 165-179

  Rousset, François ^a  

^a INSTITUT DES SCIENCES DE L EVOLUTION   (France)

Author keywords

Coalescence; Diffusion; Inclusive fitness; Quasi equilibrium

Indexed keywords

EVOLUTION;

ARTICLE; BIOLOGICAL MODEL; ECOLOGY; GAME; GENE FREQUENCY; GENETIC SELECTION; MOLECULAR EVOLUTION; PHENOTYPE; POPULATION GENETICS; PROBABILITY; STATISTICS; TIME; STATISTICS AND NUMERICAL DATA;

ECOLOGY; EVOLUTION, MOLECULAR; GAME THEORY; GENE FREQUENCY; GENETICS, POPULATION; MODELS, GENETIC; PHENOTYPE; PROBABILITY; SELECTION (GENETICS); TIME FACTORS; SELECTION, GENETIC;

EID: 85052429970     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2005.08.008     Document Type: Article

References (61)

1. É. Ajar Analysis of disruptive selection in subdivided populations BMC Evol. Biol. 3 2003 22
2. R. Axelrod, and W.D. Hamilton The evolution of cooperation Science 211 1981 1390 1396
3. N.H. Barton, and M. Turelli Natural and sexual selection on many loci Genetics 127 1991 229 255
4. N.H. Bingham, C.M. Goldie, and J.L. Teugels Regular Variation 1987 Cambridge University Press Cambridge, UK
5. M.G. Bulmer Theoretical Evolutionary Ecology 1994 Sinauer Sunderland, MA
6. F.B. Christiansen On conditions for evolutionary stability for a continuously varying character Am. Nat. 138 1991 37 50
7. I. Eshel Evolutionary and continuous stability J. Theor. Biol. 103 1983 99 111
8. I. Eshel On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution J. Math. Biol. 34 1996 485 510
9. S.N. Ethier, and T. Nagylaki Diffusion approximations of Markov chains with two time scales and applications to population genetics Adv. Appl. Probab. 12 1980 14 49
10. W.J. Ewens Mathematical Population Genetics I. Theoretical Introduction second ed 2004 Springer New York
11. S.A. Frank Foundations of Social Evolution 1998 Princeton University Press Princeton
12. S. Gandon, and F. Rousset Evolution of stepping-stone dispersal rates Proc. R. Soc. London B 266 1999 2507 2513
13. S.A.H. Geritz, É Kisdi, G. Meszéna, and J.A.J. Metz Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree Evol. Ecol. 12 1998 35 57
14. W.D. Hamilton The genetical evolution of social behavior. I J. Theor. Biol. 7 1964 1 16
15. W.D. Hamilton Selfish and spiteful behaviour in an evolutionary model Nature 228 1970 1218 1220
16. W.D. Hamilton Innate social aptitudes in man, an approach from evolutionary genetics R. Fox Biosocial Anthropology 1975 Malaby Press London 133 157
17. W.D. Hamilton This week's citation classic Curr. Contents 40 1988 16
18. W.D. Hamilton Narrow Roads to Gene Land vol. 2 2001 Oxford University Press Oxford
19. A.J. Irwin, and P.D. Taylor Evolution of dispersal in a stepping-stone population with overlapping generations Theor. Popul. Biol. 58 2000 321 328
20. M. Kimura On the probability of fixation of mutant genes in a population Genetics 47 1962 713 719
21. M. Kirkpatrick, T. Johnson, and N. Barton General models of multilocus evolution Genetics 161 2002 1727 1750
22. É Kisdi Dispersal: risk spreading versus local adaptation Am. Nat. 159 2002 579 596
23. R. Lande Effective deme sizes during long-term evolution estimated from rates of chromosomal rearrangement Evolution 33 1979 234 251
24. S. Lessard Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory Theor. Popul. Biol. 68 2005 19 27
25. H. Leturque, and F. Rousset Convergence stability, probabilities of fixation, and the ideal free distribution in a class-structured population Theor. Popul. Biol. 62 2002 169 180
26. G. Malécot Un traitement stochastique des problèmes linéaires (mutation, linkage, migration) en génétique de population Ann. de l'Université de Lyon A 14 1951 79 117
27. G. Malécot Heterozygosity and relationship in regularly subdivided populations Theor. Popul. Biol. 8 1975 212 241
28. T. Maruyama Effective number of alleles in a subdivided population Theor. Popul. Biol. 1 1970 273 306
29. T. Maruyama Stochastic theory of population genetics Bull. Math. Biol. 45 1983 521 554
30. H. Matsuda, N. Ogita, A. Sasaki, and K. Satō Statistical mechanics of population Prog. Theor. Phys. 88 1992 1035 1049
31. J. Maynard Smith Evolution and the Theory of Games 1982 Cambridge University Press Cambridge
32. J. Maynard Smith, and G. Price The logic of animal conflict Nature 246 1973 15 18
33. M.A. McPeek, and R.D. Holt The evolution of dispersal in spatially and temporally varying environments Am. Nat. 140 1992 1010 1027
34. J.A.J. Metz, and M. Gyllenberg How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies Proc. R. Soc. London B 268 2001 499 508
35. U. Motro Optimal rates of dispersal I. Haploid populations Theor. Popul. Biol. 21 1982 394 411
36. T. Nagylaki The decay of genetic variability in geographically structured populations Proc. Natl. Acad. Sci. USA 71 1974 2932 2936
37. T. Nagylaki The decay of genetic variability in geographically structured populations II Theor. Popul. Biol. 10 1976 70 82
38. M.A. Nowak, and K. Sigmund Games on grids U. Dieckmann R. Law J.A.J. Metz The Geometry of Ecological Interactions: Simplifying Spatial Complexity 2000 Cambridge University Press Cambridge 135 150
39. M.A. Nowak, A. Sasaki, C. Taylor, and D. Fudenberg Emergence of cooperation and evolutionary stability in finite populations Nature 428 2004 646 650
40. O. Ronce, and M. Kirkpatrick When sources become sinks: migrational meltdown in heterogeneous habitats Evolution 55 2001 1520 1531
41. F. Rousset Genetic differentiation and estimation of gene flow from F -statistics under isolation by distance Genetics 145 1997 1219 1228
42. F. Rousset Genetic differentiation in populations with different classes of individuals Theor. Popul. Biol. 55 1999 297 308
43. F. Rousset Inbreeding and relatedness coefficients: what do they measure? Heredity 88 2002 371 380
44. F. Rousset A minimal derivation of convergence stability measures J. Theor. Biol. 221 2003 665 668
45. F. Rousset Genetic Structure and Selection in Subdivided Populations 2004 Princeton University Press Princeton, New Jersey
46. F. Rousset, and S. Billiard A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal J. Evol. Biol. 13 2000 814 825
47. F. Rousset, and S. Gandon Evolution of the distribution of dispersal distance under distance-dependent cost of dispersal J. Evol. Biol. 15 2002 515 523
48. D. Roze, and F. Rousset Diffusion approximations for selection and drift in subdivided populations: a straightforward method and examples involving dominance, selfing and local extinctions Genetics 165 2003 2153 2166
49. Roze, D., Rousset, F., 2005. Inbreeding depression and the evolution of dispersal rates: a multilocus model. Am. Nat. 166, 708-721.
50. S. Sawyer Results for the stepping stone model for migration in population genetics Ann. Probab. 4 1976 699 728
51. S. Sawyer Asymptotic properties of the equilibrium probability of identity in a geographically structured population Adv. Appl. Probab. 9 1977 268 282
52. M. Slatkin Fixation probabilities and fixation times in a subdivided population Evolution 35 1981 477 488
53. F. Spitzer Principles of Random Walk second ed 1976 Springer Berlin
54. P.D. Taylor Inclusive fitness in a homogeneous environment Proc. R. Soc. London B 249 1992 299 302
55. P.D. Taylor Sex ratio in a stepping stone population with sex-specific dispersal Theor. Popul. Biol. 45 1994 203 218
56. M. van Baalen, and D.A. Rand The unit of selection in viscous populations and the evolution of altruism J. Theor. Biol. 193 1998 631 648
57. J. Wakeley Polymorphism and divergence for island-mainland species Genetics 163 2003 411 420
58. J. Wakeley, and T. Takahashi The many-demes limit for selection and drift in a subdivided population Theor. Popul. Biol. 66 2004 83 91
59. G. Wild, and P.D. Taylor Fitness and evolutionary stability in game theoretic models of finite populations Proc. R. Soc. London B 271 2004 2345 2349
60. S. Wright Evolution in Mendelian populations Genetics 16 1931 97 159
61. S. Wright Evolution and the Genetics of Populations II. The Theory of Gene Frequencies 1969 University of Chicago Press Chicago