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Losert, V.; Akin, E.

Dynamics of games and genes: Discrete versus continuous time. (English) Zbl 0519.92014

J. Math. Biol. 17, 241-251 (1983).
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Cited in 1 Review
Cited in 38 Documents

MSC:

92D10 Genetics and epigenetics
91A80 Applications of game theory
92D25 Population dynamics (general)
39A10 Additive difference equations
37-XX Dynamical systems and ergodic theory

Keywords:

Fisher-Wright-Haldane model; population genetics; evolutionary games; convergence to equilibrium; continuous time model; discrete time model

Citations:

Zbl 0493.92018
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Full Text: DOI

References:

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[2] Akin, E.: The geometry of population genetics. Lecture notes in biomathematics, vol. 31. Berlin- Heidelberg-New York: Springer 1979 · Zbl 0437.92016
[3] Akin, E., Hofbauer, J.: Recurrence of the unfit. Math. Biosci. (to appear) (1982) · Zbl 0493.92018
[4] Ginzburg, L. R.: Diversity of fitness and generalized fitness. J. Gen. Biol. 33, 77-81 (1972)
[5] an der Heiden, U.: On manifolds of equilibria in the selection model for multiple alleles. J. Math. Biol. 1, 321-330 (1975) · Zbl 0297.92011
[6] Hines, W. G. S.: Three characterizations of population strategy stability. J. Appl. Prob. 17, 333-340 (1980) · Zbl 0439.92021 · doi:10.2307/3213023
[7] Karlin, S.: A first course in stochastic processes. New York: Academic Press 1966 · Zbl 0139.33804
[8] Karlin, S., Feldman, M. W.: Linkage and selection: Two locus symmetric viability model. J. Theoret. Population Biology 1, 39-71 (1970) · Zbl 0245.92013 · doi:10.1016/0040-5809(70)90041-9
[9] Kingman, J. F. C.: A mathematical problem in population genetics. Proc. Camb. Phil. Soc. 57, 574-582 (1961) · Zbl 0104.38202 · doi:10.1017/S0305004100035635
[10] Lang, S.: Differential manifolds. Reading, Mass.: Addison-Wesley 1972 · Zbl 0239.58001
[11] May, R. M.: Biological populations with nonoverlapping generations: Stable points, stable cycles, and chaos. Science 186, 645-647 (1974) · doi:10.1126/science.186.4164.645
[12] Mulholland, H. P., Smith, C. A. B.: An inequality arising in genetical theory. Am. Math. Mon. 66, 673-683 (1959) · Zbl 0094.00903 · doi:10.2307/2309342
[13] Scheuer, P. A. G., Mandel, S. P. H.: An inequality in population genetics. Heredity 13, 519-524 (1959) · doi:10.1038/hdy.1959.52
[14] Taylor, P., Jonker, L.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145-156 (1978) · Zbl 0395.90118 · doi:10.1016/0025-5564(78)90077-9
[15] Feller, W.: A geometrical analysis of fitness in triply allelic systems. Math. Biosci. 5, 19-38 (1969). · Zbl 0176.50503 · doi:10.1016/0025-5564(69)90033-9
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