A general multilocus two-allele model for epistatic selection

Journal of Genetics

Volumn 77, Issue 2-3, 1998, Pages 115-121

  Zhivotovsky, Lev A ^a   Pylkov, Konstantin V ^a  

^a VAVILOV INSTITUTE OF GENERAL GENETICS   (Russian Federation)

Author keywords

Epistasis; Linkage disequilibrium; Multiple loci; Recombination; Sex; Weak selection

Indexed keywords

EID: 0032129182     PISSN: 00221333     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02966597     Document Type: Article

References (55)

1. Allard R. W. 1996 Genetic basis of the evolution of adaptedness in plants. Euphytica 92, 1-11.
2. Allard R. W., Garcia P., Saenz-De-Miera L. E. and De La Vega M. P. 1993 Evolution of multilocus genetic structure in Avena hirtula and Avena barbata. Genetics 135, 1125-1139.
3. Barton N. H. and Turelli M. 1991 Natural and sexual selection on many loci. Genetics 127, 229-255.
4. Bodmer W. and Felsenstein J. 1967 Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics 57, 237-265.
5. Bulmer M. 1974 Linkage disequilibrium and genetic variability. Genet. Res. 23, 281-289.
6. Bulmer M. 1976 The effect of selection on genetic variability: A simulation study. Genet. Res. 28, 101-117.
7. Bulmer M. G. 1980 The mathematical theory of quantitative genetics. Clarendon Press, Oxford.
8. Burt A. 1995 The evolution of fitness. Evolution 49, 1-8.
9. Cabot E. L., Davis A. W., Johnson N. A. and Wu C.-I. 1994 Genetics of reproductive isolation in the Drosophila simulans clade: Complex epistasis underlying hybrid male sterility. Genetics 137, 175-189.
10. Charlesworth B. 1996 Background selection and patterns of genetic diversity in Drosophila melanogaster. Genet. Res. 68, 131-149.
11. Christiansen F. B. 1990a The generalized multiplicative model for viability selection at multiple loci. J. Math. Biol. 29, 99-129.
12. Christiansen F. B. 1990b Simplified models for viability selection at multiple loci. Theor. Pop. Biol. 37, 39-54.
13. Clegg M. T., Allard R. W. and Kahler A. L. 1972 Is a gene the unit of selection? Evidence from two experimental plant populations. Proc. Natl. Acad. Sci. USA 69, 2474-2478.
14. Dobzhansky T. H. 1937 Genetics and the origin of species. Columbia University Press, New York.
15. Dubinin N. P. 1948 An experimental study of hereditary systems integration in the evolutionary processes. Zh. Obshch. Biol. 9, 203-244 (in Russian).
16. Ewens W. and Thompson G. 1977 Properties of equilibria in multi-locus systems. Genetics 87, 807-819.
17. Feldman M., Franklin I. and Thomson G. 1974 Selection in complex genetic systems. I. The symmetric equilibria of the three-locus viability model. Genetics 76, 135-162.
18. Fleming W. H. 1979 Equilibrium distribution of continuous polygeneic traits. SIAM J. Appl. Math. 36, 148-168.
19. Forbes S. H. and Allendorf F. W. 1991 Associations between mitochondrial and nuclear genotypes in cuttrout hybrid swarms. Evolution 45, 1332-1349.
20. Franklin I. and Lewontin R. C. 1970 Is the gene the unit of selection? Genetics 65, 707-734.
21. Gavrilets S. and de Jong G. 1993 Pleiotropic models of polygenic variation, stabilizing selection and epistasis. Genetics 134, 609-625.
22. Gavrilets S. and Hastings A. 1994 Maintenance of multilocus variability under strong stabilizing selection. J. Math. Biol. 32, 287-302.
23. Gimelfarb A. 1996 Some additional results about polymorphisms in models of an additive trait under stabilizing selection. J. Math. Biol. 35, 88-96.
24. Hastings A. 1982 Unexpected behavior in two-locus genetic systems: an analysis of marginal underdominance at a stable equilibrium. Genetics 102, 129-138.
25. Hastings A. 1986 Multilocus population genetics with weak epistasis. II. Equilibrium properties of multilocus models: What is the unit of selection? Genetics 112, 157-171.
26. The Huntington's Disease Collaborative Research Group 1993 A novel gene containing a trinucleotide repeat that is expanded and unstable on Huntington's disease chromosomes. Cell 72, 971-983.
27. Karlin S. 1975 General two-locus selection models: some objectives, results and interpretations. Theor. Pop. Biol. 7, 364-398.
28. Karlin S. 1978 Theoretical aspects of multi-locus selection balance. I. In Studies in mathematics, Vol. 16, Studies in mathematical biology (ed. S. A. Levin), pp. 503-587. Mathematical Association of America, Washington, DC.
29. Karlin S. and Avni H. 1981 Analysis of central equilibria in multilocus systems: A generalized symmetric viability regime. Theor. Pop. Biol. 20, 241-280.
30. Karlin S. and Feldman M. 1970 Linkage and selection: two-locus symmetric viability model. Theor. Pop. Biol. 1, 39-71.
31. Karlin S. and Liberman U. 1979 Representation of nonepistatic selection models and analysis of multi-locus Hardy-Weinberg equilibrium configurations. J. Math. Biol. 7, 353-374.
32. Kimura M. 1965 Attainment of quasi-linkage equilibrium when gene frequencies are changing by natural selection. Genetics 52, 875-890.
33. Kirby D. A. and Stephan W. 1996 Multi-locus selection and the structure of variation at the white gene of Drosophila melanogaster. Genetics 144, 635-645.
34. Lande R. 1975 The maintenance of genetic variability by mutation in polygenic character with linked loci. Genet. Res. 26, 221-235.
35. Lewontin R. C. 1964 The interaction of selection and linkage. II. Optimum models. Genetics 50, 757-782.
36. Ljubich Y. I. 1983 Mathematical structures in population genetics (in Russian). Naukova Dumka, Kiev.
37. Mather K. 1942 The balance of polygenic combinations. J. Genet. 43, 309-336.
38. Mukai T. 1964 The genetic structure of natural populations of Drosophila melanogaster. I. Spontaneous mutation rate of polygenes controlling viability. Genetics 50, 1-19.
39. Nagylaki T. 1993 The evolution of multilocus systems under weak selection. Genetics 134, 627-647.
40. Palopoli M. F. and Wu C.-I. 1996 Rapid evolution of a coadapted gene complex: Evidence from the Segregation Distorter (SD) system of meiotic drive in Drosophila melanogaster. Genetics 143, 1675-1688.
41. Passekov V. 1994 A perturbation analysis of a neutral multilocus model in population genetics. In Operation research (models, systems, solutions) (ed. Y. Ivanilov), pp. 51-87. Computational Center RAS, Moscow.
42. Pylkov K., Zhivotovsky L. A. and Feldman M. W. 1998 Migration vs mutation in the evolution of recombination under multilocus selection. Genet. Res. 71, 247-256.
43. Schmalhausen I. 1986 Factors of evolution: the theory of stabilizing selection. University of Chicago Press, Chicago.
44. Slatkin M. 1972 On treating a chromosome as the unit of selection. Genetics 72, 157-168.
45. Turelli M. 1984 Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theor. Pop. Biol. 25, 138-193.
46. Turelli M. and Barton N. H. 1994 Genetic and statistical analyses of strong selection on polygenic traits: what, me normal? Genetics 138, 913-941.
47. Waddington C. H. 1959 Canalisation of development and genetic assimilation of acquired characters. Nature 183, 1654-1655.
48. Weir B. S. and Cockerham C. C. 1989 Complete characterization of disequilibrium at two loci. In Mathematical evolutionary theory (ed. M. W. Feldman), pp. 86-110. Princeton University Press, Princeton.
49. Wright S. 1969 Evolution and the genetics of populations, Vol. 2, The theory of gene frequencies. University of Chicago Press, Chicago.
50. Zhivotovsky L. A. and Christiansen F. B. 1995 The selection barrier between populations subject to stabilizing selection. Evolution 49, 490-501.
51. Zhivotovsky L. A. and Feldman M. W. 1992 On models of quantitative genetic variability: a stabilizing selection-balance model. Genetics 130, 947-955.
52. Zhivotovsky L. A. and Gavrilets S. 1990 Stabilizing selection and linkage disequilibrium (English translation). Sov. Genet. 26, 222-231.
53. Zhivotovsky L. A. and Gavrilets S. 1992 Quantitative variability and multilocus polymorphism under epistatic selection. Theor. Pop. Biol. 42, 254-283.
54. Zhivotovsky L. A. and Yanushpolsky I.I. 1976 The dynamics of the population-genetic parameters and their estimates under selection on quantitative traits. Genetika 12, 139-146 (in Russian).
55. Zhivotovsky L. A., Feldman M. W. and Bergman A. 1996 On the evolution of phenotypic plasticity in a spatially heterogeneous environment. Evolution 50, 547-558.