Abstract
A new selectively neutral mutation occurs in a multilocus genetic background that has achieved a stable equilibrium at which there is a linkage disequilibrium. Perturbation techniques are applied to an extension of the branching process formulation of Fisher in order to address the question of extinction probabilities. We show that under appropriate conditions the probability of extinction of the new mutant is increased by the existence of linkage disequilibrium in the genetic background.
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Asmussen, M. A., Clegg, M. T.: Dynamics of the linkage disequilibrium function under models of gene frequency hitchhiking. Genetics 99, 337–356 (1981)
Christiansen, F. B.: Epistasis in the multiple locus symmetric viability model. J. Math. Biol. 26, 595–618 (1988)
Christiansen, F. B.: The multiple locus symmetric fertility model. Theor. Popul. Biol. 35, 337–362 (1989)
Ewens, W. J.: Mathematical Population Genetics. Berlin Heidelberg New York: Springer 1979
Feldman, M. W., Franklin, I. R., Thomson, G. J.: Selection in complex genetic systems I. The symmetric equilibria of the three-locus symmetric viability model. Genetics 76, 135–162 (1974)
Fisher, R. A.: The Genetical Theory of Natural Selection. Oxford: Clarendon 1930
Harris, T.: The Theory of Branching Processes. Berlin Heidelberg New York: Springer 1963
Karlin, S., Feldman, M. W.: Linkage and selection: Two locus symmetric viability model. Theor. Popul. Biol. 1, 39–71 (1970)
Karlin, S., Liberman, U.: Representation of nonepistatic selection models and analysis of multilocus Hardy-Weinberg equilibrium configurations. J. Math. Biol. 7, 353–374 (1979)
Maynard Smith, J., Haigh, J.: The hitch-hiking effect of a favorable gene. Genet. Res. 23, 23–35 (1974).
Moran, P. A. P.: The Statistical Processes of Evolutionary Theory. Oxford: Clarendon 1962.
Nagylaki, T.: The evolution of one- and two-locus systems. Genetics 83, 583–600 (1976)
Ohta, T.: Slightly deleterious mutant substitutions in evolution. Nature 246, 96–97 (1973)
Ohta, T.: Role of very slightly deleterious mutations in molecular evolution and polymorphism. Theor. Popul. Biol. 10, 254–275 (1976)
Thomson, G.: The effect of a selected locus on linked neutral loci. Genetics 85, 753–788 (1977)
Turelli, M., Barton, N. H.: Dynamics of polygenic characters under selection. Theor. Popul. Biol. 38, 1–57 (1990)
Zhivotovsky, L., Gavrilets, S.: Quantitative variability and multilocus polymorphism under epistatic selection. Theor. Popul. Biol. (in press)
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Research supported in part by NIH grant GM 28016
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Zhivotovsky, L.A., Feldman, M.W. On the probability of loss of new mutations in the presence of linkage disequilibrium. J. Math. Biol. 31, 177–188 (1993). https://doi.org/10.1007/BF00171225
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DOI: https://doi.org/10.1007/BF00171225