Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T00:00:46.707Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of finite population size on models of linked overdominant loci

Published online by Cambridge University Press:  14 April 2009

P. J. Avery
P. J. Avery
Affiliation:
Institute of Animal Genetics, West Mains Road, Edinburgh EH9 3JN, Scotland
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Models of two linked overdominant loci in moderately large, but finite, populations are examined by looking at the variance-covariance matrix of the two gene frequencies and the linkage disequilibrium around stable deterministic equilibrium points. In particular, the effect of genetic drift is examined in cases where, in infinite populations, two stable equilibria with non-zero linkage disequilibrium, D, are maintained. Theoretical formulae are produced and checked by computer simulation. In general, the results show that unless the population size is very large indeed, genetic drift causes the values of D to vary considerably about the equilibrium values and that for many models, where stable equilibria exist at non-zero D values, a wide range of values of D have a high probability. Thus it is very difficult to draw conclusions about the selection regime by measuring Linkage disequilibrium in a finite population.

Type
Research Article
Information
Genetics Research , Volume 31 , Issue 3 , June 1978 , pp. 239 - 254
Copyright
Copyright © Cambridge University Press 1978

References

REFERENCES

Avery, P. J. & Hill, W. G. (1978). Variance in quantitative traits due to linked dominant genes and variance in heterozygosity in small populations. (Submitted to Genetics.)Google Scholar
Bodmer, W. F. & Felsenstein, J. (1967). Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics 57, 237–265.CrossRefGoogle ScholarPubMed
Bulmer, M. G. (1976). The effect of selection on genetic variability: a simulation study. Genetical Research 28, 101–117.CrossRefGoogle ScholarPubMed
Felsenstein, J. (1974). Uncorrelated genetic drift of gene frequencies and linkage disequilibrium in some models of linked overdominant polymorphisms. Genetical Research 24, 281–294.CrossRefGoogle ScholarPubMed
Franklin, I. & Lewontin, R. C. (1970). Is the gene the unit of selection? Genetics 65, 707–734.CrossRefGoogle ScholarPubMed
Hill, W. G. (1969). Maintenance of segregation at linked genes in finite populations. Proceedings of the Xllth International Congress of Genetics, vol. III. Japanese Journal of Genetics 44, Supplement 1, 144–151.Google Scholar
Hill, W. G. & Robertson, A. (1968). Linkage disequilibrium in finite populations. Theoretical and Applied Genetics 38, 226–231.CrossRefGoogle ScholarPubMed
Karlin, S. (1975). General two-locus selection models: some objectives, results and interpretations. Theoretical Population Biology 7, 364–398.CrossRefGoogle ScholarPubMed
Karlin, S. & Carmelli, D. (1975). Numerical studies on two loci selection models with general viabilities. Theoretical Population Biology 7, 399–421.CrossRefGoogle ScholarPubMed
Levin, B. R. (1969). Simulation of genetic systems. In Computer Applications in Genetics (ed. Morton, N.), pp. 28–46. Honolulu: University of Hawaii Press.Google Scholar
Lewontin, R. C. & Kojima, K. (1960). The evolutionary dynamics of complex polymorphisms. Evolution 14, 458–472.Google Scholar
Ohta, T. & Kimura, M. (1969). Linkage disequilibrium at steady state determined by random genetic drift and recurrent mutation. Genetics 63, 229–238.CrossRefGoogle ScholarPubMed
Pederson, D. G. (1973). An approximate method of sampling a multinomial population. Biometrics 29, 814–821.CrossRefGoogle ScholarPubMed
Sved, J. (1968). The stability of linked systems of loci with a small population size. Genetics 59, 543–563.CrossRefGoogle ScholarPubMed
Yamazaki, T. (1977). The effects of overdominance on linkage in a multilocus system. Genetics 86, 227–236.CrossRefGoogle Scholar