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Discrete Evolutionary Genetics: Multiplicative Fitnesses and the Mutation-Fitness Balance

DOI: 10.4236/am.2011.21002, PP. 11-22

Keywords: Evolutionary Genetics, Fitness Landscape, Selection, Mutation, Stochastic Models, Quasi-Stationarity

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Abstract:

We revisit the multi-allelic mutation-fitness balance problem especially when fitnesses are multiplicative. Using ideas arising from quasi-stationary distributions, we analyze the qualitative differences between the fitness-first and mutation-first models, under various schemes of the mutation pattern. We give some stochastic domination relations between the equilibrium states resulting from these models.

References

[1]  W. J. Ewens, “Mathematical Population Genetics. I. Theoretical Introduction,” 2nd Edition, Interdisciplinary Applied Mathematics, Springer-Verlag, New York, Vol. 27, 2004.
[2]  R. Bürger, “The Mathematical Theory of Selection, Recombination, and Mutation,” Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2000.
[3]  S. Karlin, “Mathematical Models, Problems, and Controversies of Evolutionary Theory,” Bulletin of the American Mathematical Society (N.S.), Vol. 10, No. 2, 1984, pp. 221-273.
[4]  J. F. C. Kingman, “Mathematics of Genetic Diversity,” CBMS-NSF Regional Conference Series in Applied Mathematics, 34. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1980.
[5]  J. Hermisson, O. Redner, H. Wagner and E. Baake “Mutation-Selection Balance: Ancestry, Load and Maximum Principle,” Theoretical Population Biology, Vol. 62, No. 1, 2002, pp. 9-46. doi:10.1006/tpbi.2002.1582
[6]  E. Baake and H.-O. Georgii, “Mutation, Selection, and Ancestry in Branching Models: A Variational Approach,” Journal of Mathematical Biology, Vol. 54, No. 2, 2007, pp. 257-303. doi:10.1007/s00285-006-0039-5
[7]  G. Sella and A. E. Hirsh, “The Application of Statistical Physics to Evolutionary Biology,” Proceedings of the National Academy of Sciences, Vol. 102, No. 27, 2005, pp. 9541-9546. doi:10.1073/pnas.0501865102
[8]  N. Champagnat, R. Ferrière and S. Méleard, “From Individual Stochastic Processes to Macroscopic Models in Adaptive evolution,” Stochastic Models, Vol. 24, Suppl. 1, 2008, pp. 2-44. doi:10.1080/15326340802437710
[9]  S. Shashahani, “A New Mathematical Framework for the Study of Linkage and Selection,” Memoirs of the American Mathematical Society, Vol. 17, No. 211, 1979, pp.1-34.
[10]  Y. M. Svirezhev, “Optimum Principles in Genetics,” Studies on Theoretical Genetics, V. A. Ratner (Ed.), USSR Academy of Science, Novosibirsk, 1972, pp. 86-102.
[11]  J. Hofbauer, “The Selection Mutation Equation,” Journal of Mathematical Biology, Vol. 23, No. 1, 1985, pp. 41-53.
[12]  J. N. Darroch and E. Seneta, “On Quasi-Stationary Distributions in Absorbing Discrete-Time Finite Markov chains,” Journal of Applied Probability, Vol. 2, No. 1, 1965, pp. 88-100. doi:10.2307/3211876
[13]  S. Martínez, “Quasi-Stationary Distributions for Birth-death Chains. Convergence Radii and Yaglom Limit,” Cellular Automata and Cooperative Systems (Les Houches, 1992), NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, 396, Kluwer Academic Publishers, Dordrecht, 1993, pp. 491-505.
[14]  S. Martínez and M. E. Vares, “A Markov Chain Associated with the Minimal Quasi-Stationary Distribution of Birth-Death Chains,” Journal of Applied Probability, Vol. 32, No. 1, 1995, pp. 25-38. doi:10.2307/3214918

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