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The effect of population subdivision on two loci without selection

  • Marcus W. Feldman (a1) and Freddy Bugge Christiansen (a1)

Summary

This paper is devoted to the study of the effects of population subdivision on the evolution of two linked loci. Two simple deterministic models of population subdivision without selection are investigated. One is a finite linear ‘stepping stone’ model and the other is a finite linear stepping stone chain of populations stretching between two large populations of constant genetic constitution. At equilibrium in the first model the gene frequencies in each population are equal and there is linkage equilibrium in each population. The rate of decay to zero of the linkage disequilibrium functions is the larger of (1 – c) and , where λ1 is the rate of convergence of the gene frequencies to equilibrium and c is the recombination frequency. In the second model at equilibrium there will be a linear cline in gene frequencies connecting the two large constant populations. This cline will be accompanied by a ‘cline’ of linkage disequilibria. The rate of convergence to this equilibrium cline is independent of the recombination frequency, and, in fact, the gene frequencies and the linkage disequilibria converge to equilibrium at the same rate.

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References

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Bodmer, W. F. & Cavalli-Sforza, L. L. (1968). A migration matrix model for the study of random genetic drift. Genetics 59, 565592.
Bodmer, W. F. & Felsenstein, J. (1967). Linkage and selection: Theoretical analysis of the deterministic two locus random mating model. Genetics 57, 237265.
Christiansen, F. B., Frydenberg, O. & Simonsen, V. (1973) Genetics of Zoarces populations. IV. Selection component analysis of an esterase polymorphism using population samples including mother-offspring combinations. Hereditas 73, 291304.
Feller, W. (1957). An introduction to probability theory and its applications, 2nd ed.New York: John Wiley.
Hill, W. G. & Robertson, A. (1968). Linkage disequilibrium in finite populations. Theoretical and Applied Genetics 38, 226231.
Karlin, S. & Feldman, M. W. (1970). Linkage and selection: Two locus symmetric viability model. Theoretical Population Biology 1, 3971.
Kidd, K. & Cavalli-Sforza, L. L. (1974). The role of genetic drift in the differentiation of Icelandic and Norwegian cattle. Evolution (to appear).
Kimura, M. & Weiss, G. H. (1964). The steppibg stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561576.
Lewontin, R. C. & Kojima, K. (1960). The evolutionary dynamics of complex polymorphisms. Evolution 14, 458472.
Lewontin, R. C. & Krakuaer, J. (1973). Distribution of gene frequency as a test of the neutrality of polymorphisms. Genetics 74, 175195.
Malécot, G. (1950). Quelques schémas probabilistés sur la variabilité des populations naturelles. Annales Université de Lyon, Science Section A 13, 3660,
Malécot, G. (1951). Un traitement stochastique des problemes linéares (mutation, linkage et migration en génétique de populations). Annales Université de Lyon, Science Section A 14, 79117.
Malécot, G. (1967). Identical loci and relationship. Proceedings of the 5th Berkeley Symposium in Mathematical Statistics and Probability IV; 317332.
Maruyama, T. (1971). The rate of decrease of heterozygosity in a population occupying a circular or linear habitat. Genetics 67, 437454.
Nei, M. & Li, W. (1973). Linkage disequilibrium in subdivided populations. Genetics 75, 213219.
Ohta, T. (1973). Effect of linkage on behaviour of mutant genes in finite populations. Theoretical Population Biology 4, 145162.
Prout, T. (1973). Appendix to: ′Population genetics of marine pelecypods. III. Epistasis between functionally related isoenzymes Ulytius edulua, by J. B. Mitten and R. C. Koehn. Genetics 73, 487496.
Robbins, R. B. (1918). Some applications of mathematics to breeding problems: II. Genetics 3, 7392.
Sick, K. (1965). Haemoglobin polymorphism of cod in the Baltic and Danish Belt Sea. Hereditas 54, 1948.
Sinnock, P. & Sing, C. F. (1972). Analysis of multilocus genetic systems in Tecimsek Michigan. II. Consideration of the correlation between non-alleles in gametes. American Journal of Human Genetics 24, 393415.
Sved, J. (1971). Linkage disequilibrium and homozygosity of chromosome segments in finite populations. Theoretical Population Biology 2, 125141.
Wahlund, S. (1928). Zusammensetzung von Populationen und Korrelations-escheinungen vom Standpunkt der Vererbungslehre aus betrachtet. Hereditas 11, 65106.
Wright, S. (1943). Isolation by distance. Genetics 28, 114138.

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