The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline
Tóm tắt
The balance between the creation of associations between alleles at different loci by immigration and the convergence to linkage equilibrium due to the recombination process is studied in a theoretical model. The geographical structure of the model is a stepping-stone chain of populations linking two genetically constant source populations. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The gene frequencies at each locus will then show a linear cline through the stepping-stone chain of populations. The deviation from linkage equilibrium through the stepping-stone cline is characterized by an equation for linear measures that provide the linkage disequilibrium measures for a given set of loci in terms of the gene frequencies and the linkage disequilibria in the source populations and in terms of the linkage disequilibrium measures through the cline for lower numbers of loci. Numerical examples of this iterative solution are given, and it is shown that the build-up of the higher order Bennett-disequilibria through the cline is considerably more pronounced than the build-up of two-locus disequilibria.
Tài liệu tham khảo
Bennett J H 1954 On the theory of random mating.Ann. Eugenics 18: 311–317
Bodmer W F and Felsenstein J 1967 Linkage and selection: Theoretical analysis of the deterministic two-locus random mating model.Genetics 57: 237–265
Christiansen F B 1986 The effect of population subdivision on multiple loci without selection. (to appear)
Feldman M W and Christiansen F B 1975 The effect of population subdivision on two loci without selection.Genet. Res. (Camb.) 24: 151–162
Feldman M W, Franklin I R and Thomson G J 1974 Selection in complex genetic systems. I. The symmetric equilibria of the three-locus symmetric viability model.Genetics 76: 135–162
Geiringer H 1944 On the probability theory of linkage in Mendelian heredity.Ann. Math. Stat. 15: 25–57
Holgate P 1976 Direct products of genetic algebras and Markov chains.J. Math. Biol. 6: 289–295
Karlin S and Liberman U 1978 Classifications and comparisons of multilocus recombination distributions.Proc. Natl. Acad. Sci. USA 75: 6332–6336
Karlin S and Liberman U 1979a Central equilibria in multilocus systems. I. Generalized nonepistatic selection regimes.Genetics 91: 777–798
Karlin S and Liberrrvin U 1979b Central equilibria in multilocus systems. II. Bisexual generalized nonepistatic selection models.Genetics 91: 799–816
Karlin S and Liberman U 1979c A natural class of multilocus recombination processes and related measures of crossover interference.Adv. Appl. Probab. 11: 479–501
Nei M and Li W-H 1973 Linkage disequilibrium in subdivided populations.Genetics 75: 213–219
Østergaard H and Christiansen F B 1981 Selection component analysis of natural polymorphisms using population samples including mother-offspring combinations, II.Theor. Popul. Biol. 19: 378–419
Prout T 1973Appendix to: Population genetics of marine pelecypods. III. Epistasis between functionally related isoenzymes inMytilus edulis (by J B Mitten and R C Koehn).Genetics 73: 487–496
Robbins R B 1918 Some applications of mathematics to breeding problems, III.Genetics 3: 375–389
Schnell F W 1961 Some general formulations of linkage effects in inbreeding.Genetics 46: 947–957
Sinnock P and Singh C F 1972 Analysis of multilocus genetic systems in Tecimsek Michigan. II. Consideration of the correlation between non-alleles in gametes.Am. J. Hum. Genet. 24: 393–415
Wahlund S 1928 Zusammensetzung von Populationen und Korrelationserscheinungen vom Standpunkt der Vererbungslehre aus betrachte.Hereditas 11: 65–106