The different limits of weak selection and the evolutionary dynamics of finite populations

Journal of Theoretical Biology

Volumn 247, Issue 2, 2007, Pages 382-390

  Wild, Geoff ^a   Traulsen, Arne ^b  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Evolutionary game theory; Finite population; Fixation probability; Kin selection; Moran model; Weak selection

Indexed keywords

EVOLUTIONARY THEORY; FITNESS; GAME THEORY; KIN SELECTION; PARAMETERIZATION;

ARTICLE; EVOLUTION; FITNESS; GENETIC DISTANCE; GENETIC SELECTION; KIN SELECTION; MATHEMATICAL MODEL; PHENOTYPE; POPULATION DYNAMICS; PRIORITY JOURNAL; REPRODUCTION;

ANIMALS; EVOLUTION; GAME THEORY; MODELS, GENETIC; REPRODUCTION; SELECTION (GENETICS);

EID: 34249789300     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.03.015     Document Type: Article

References (33)

1. Antal T., and Scheuring I. Fixation of strategies for an evolutionary game in finite populations. Bull. Math. Biol. 68 (2006) 1923-1944
2. Carson H.L., and Templeton A.R. Genetic revolutions in relation to speciation phenomena-the founding of new populations. Annu. Rev. Ecol. Syst. 15 (1984) 97-131
3. Christiansen F.B. On the conditions for evolutionary stability for a continuously varying character. Am. Nat. 138 (1991) 37-50
4. Dieckmann U., and Law R. The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34 (1996) 579-612
5. Doebeli M., and Hauert C. Limit's of Hamilton's rule. J. Evol. Biol. 19 (2006) 1386-1388
6. Eshel I. Evolutionary and continuous stability. J. Theor. Biol. 103 (1983) 99-111
7. Ewens W.J. Mathematical Population Genetics (2004), Springer, New York
8. Fletcher J., and Zwick M. Unifying the theories of inclusive fitness and reciprocal altruism. Am. Nat. 168 (2006) 252-262
9. Fletcher J., and Zwick M. The evolution of altruism: game theory in multilevel selection and inclusive fitness. J. Theor. Biol. 245 1 (2007) 26-36
10. Geritz S.A.H., Kisdi E., Meszéna G., and Metz J.A.J. Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12 (1998) 35-57
11. Grafen A. Hamilton's rule ok. Nature 318 (1985) 310-311
12. Hamilton W.D. The genetical evolution of social behavior I and II. J. Theor. Biol. 7 (1964) 1-52
13. Hamilton W.D. Selfish and spiteful behaviour in an evolutionary model. Nature 228 (1970) 1218-1220
14. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge
15. Imhof L.A., and Nowak M.A. Evolutionary game dynamics in a Wright Fisher process. J. Math. Biol. 52 (2006) 667-681
16. Imhof L.A., Fudenberg D., and Nowak M.A. Evolutionary cycles of cooperation and defection. Proc. Natl Acad. Sci. USA 102 (2005) 10797-10800
17. Kimura M. Evolutionary rate at the molecular level. Nature 217 (1968) 624-626
18. Michod R., and Hamilton W.D. Coefficients of relatedness in sociobiology. Nature 288 (1980) 694-697
19. Moran P.A.P. The effect of selection in haploid genetic populations. Proc. Cambridge Philos. Soc. 54 (1958) 463-474
20. Moran P.A.P. The Statistical Processes of Evolutionary Theory (1962), Clarendon Press, Oxford
21. Nowak M.A., and Sigmund K. The evolution of stochastic strategies in the prisoner's dilemma. Acta Appl. Math. 20 (1990) 247-265
22. Nowak M.A., Sasaki A., Taylor C., and Fudenberg D. Emergence of cooperation and evolutionary stability in finite populations. Nature 428 (2004) 646-650
23. Queller D.C. Kinship, reciprocity, and synergism in the evolution of social behaviour. Nature 318 (1985) 366-367
24. 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
25. Taylor C., Fudenberg D., Sasaki A., and Nowak M.A. Evolutionary game dynamics in finite populations. Bull. Math. Biol. 66 (2004) 1621-1644
26. Taylor P.D. Evolutionary stability in one-parameter models under weak selection. Theor. Popul. Biol. 36 (1989) 125-143
27. Taylor P.D., and Jonker L. Evolutionary stable strategies and game dynamics. Math. Biosci. 40 (1978) 145-156
28. Taylor P.D., Irwin A., and Day T. Inclusive fitness in finite deme-structured and stepping-stone populations. Selection 1 (2000) 83-93
29. Traulsen A., and Nowak M.A. Evolution of cooperation by multi-level selection. Proc. Natl Acad. Sci. USA 103 (2006) 10952-10955
30. Traulsen A., Claussen J.C., and Hauert C. Coevolutionary dynamics: from finite to infinite populations. Phys. Rev. Lett. 95 (2005) 238701
31. Traulsen A., Pacheco J.M., and Imhof L.A. Stochasticity and evolutionary stability. Phys. Rev. E 74 (2006) 021905
32. Traulsen A., Nowak M.A., and Pacheco J.M. Stochastic dynamics of invasion and fixation. Phys. Rev. E 74 (2006) 11909
33. Wild G., and Taylor P.D. Fitness and evolutionary stability in game theoretic models of finite populations. Proc. R. Soc. London B 271 (2004) 2345-2349