Effective Game Matrix and Inclusive Payoff in Group-Structured Populations

Dynamic Games and Applications

Volumn 1, Issue 2, 2011, Pages 301-318

  Lessard, Sabin ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Evolutionary game; Finite island model; Group selection; Inclusive fitness; Matrix game; Relatedness

Indexed keywords

EID: 84869217511     PISSN: 21530785     EISSN: 21530793     Source Type: Journal    
DOI: 10.1007/s13235-011-0014-7     Document Type: Article

References (39)

1. Antal T, Ohtsuki H, Wakeley J, Taylor PD, Nowak MA (2009) Proc Natl Acad Sci USA 106: 8597-8600.
2. Aoki K (1982) A condition for group selection to prevail over counteracting individual selection. Evolution 36: 832-842.
3. Boorman S, Levitt PR (1980) The genetics of altruism. Academic Press, New York.
4. Christiansen F (1975) Hard and soft selection in a subdivided population. Am Nat 109: 11-16.
5. Ewens WJ (1972) The sampling theory of selectively neutral alleles. Theor Popul Biol 3: 87-112.
6. Ferrière R, Michod RE (1980) The evolution of cooperation in spatially heterogeneous populations. Am Nat 147: 692-717.
7. Fisher RA (1930) The genetical theory of natural selection. Clarendon, Oxford.
8. Grafen A (1985) A geometric view of relatedness. Oxf Surv Evol Biol 2: 28-89.
9. Hamilton WD (1964) The genetical evolution of social behaviour I and II. J Theor Biol 7: 1-52.
10. Hauert C, Doebeli M (2004) Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428: 643-646.
11. Hilbe C (2011) Local replicator dynamics: a simple link between deterministic and stochastic models of evolutionary game theory. Bull Math Biol, doi: 10. 1007/s11538-010-9608-2.
12. Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge.
13. Hofbauer J, Sigmund K (2003) Evolutionary game dynamics. Bull Am Math Soc 40: 479-519.
14. Kingman JFC (1982) The coalescent. Stoch Process Appl 13: 235-248.
15. Lessard S (1992) Relatedness and inclusive fitness with inbreeding. Theor Popul Biol 42: 284-307.
16. Lessard S (2005) Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory. Theor Popul Biol 68: 19-27.
17. Lessard S (2009) Diffusion approximations for one-locus multi-allele kin selection, mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics. J Math Biol 59: 659-696.
18. Lessard S, Ladret V (2007) The probability of fixation of a single mutant in an exchangeable selection model. J Math Biol 54: 721-744.
19. Lessard S, Rocheleau G (2004) Kin selection and coefficients of relatedness in family-structured populations with inbreeding. Theor Popul Biol 66: 287-306.
20. Levins R (1970) Extinction. In: Gerstenhaber M (ed) Some mathematical questions in biology. Lectures on mathematics in the life sciences, vol 2. Am Math Soc, Providence, pp 75-107.
21. Lewontin RC (1965) Selection in and of populations. In: Moore JA (ed) Ideas in modern biology. Natural History Press, New York, pp 292-311.
22. Maynard Smith J (1964) Group selection and kin selection. Nature 201: 1145-1147.
23. Michod RE, Hamilton WD (1980) Coefficients of relatedness in sociobiology. Nature 288: 694-697.
24. Nowak MA, Tarnita CE, Antal T (2010a) Evolutionary dynamics in structured populations. Philos Trans R Soc Lond B, Biol Sci 365: 19-30.
25. Nowak MA, Tarnita CE, Wilson EO (2010b) The evolution of eusociality. Nature 466: 1057-1062.
26. Ohtsuki H, Hauert C, Lieberman E, Nowak MA (2006) A simple rule for the evolution of cooperation on graphs and social networks. Nature 441: 502-505.
27. Price GR (1970) Selection and covariance. Nature (London) 227: 520-521.
28. Price GR (1972) Extension of covariance selection mathematics. Am Hum Genet, London 35: 485-490.
29. Rousset F (2006) Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance. Theor Popul Biol 69: 165-179.
30. Rousset F, Billiard S (2000) A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal. J Evol Biol 13: 814-825.
31. Roze D, Rousset F (2003) Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions. Genetics 165: 2153-2166.
32. Roze D, Rousset F (2004) The robustness of Hamilton's rule with inbreeding and dominance: Kin selection and fixation probabilities under partial sib-mating. Am Nat 164: 214-231.
33. Tarnita CE, Antal T, Ohtsuki H, Nowak MA (2009) Proc Natl Acad Sci USA 106: 8601-8604.
34. Taylor PD, Day T, Wild G (2007) Evolution of cooperation in a finite homogeneous graph. Nature 447: 469-472.
35. Taylor PD, Irwin A, Day T (2000) Inclusive fitness in finite deme-structured and stepping-stone populations. Selection 1: 83-93.
36. Taylor PD, Jonker L (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40: 145-156.
37. Traulsen A, Claussen JC (2004) Similarity-based cooperation and spatial segregation. Phys Rev E 70(046128): 1-8.
38. Wright S (1931) Evolution in Mendelian populations. Genetics 16: 97-159.
39. Wright S (1970) Random drift and the shifting balance theory of evolution. In: Kojima K (ed) Mathematical topics in population genetics. Springer, Berlin, pp 1-31.