Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-08T04:15:34.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Variability in genetic parameters among small populations

Published online by Cambridge University Press:  14 April 2009

P. J. Avery  and
W. G. Hill
P. J. Avery
Affiliation:
Institute of Animal Genetics, Edinburgh EH9 3JN
W. G. Hill
Affiliation:
Institute of Animal Genetics, Edinburgh EH9 3JN
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.

For a model in which quantitative traits are assumed to be determined solely by additive genes at many loci, formulae are developed for the variance among replicated small populations of size N, maintained without selection, of the additive genetic variance, heritability, genetic correlations and similar parameters. The base population is assumed to be in linkage equilibrium, but it is argued that most of the variation in the within-line additive variance (VAt at generation t) is due to linkage disequilibrium caused by sampling. If is the squared correlation of gene frequencies averaged over all pairs of loci at time t, the coefficient of variation (CV) of VAt equals , with similar formulae for other parameters.

The formulae are evaluated for models of loci distributed uniformly along the chromosome but much of the disequilibrium is due to loci on different chromosomes. For unlinked loci CV(VAt) reaches √4/(3(N)), and for mammalian models, this value is not greatly exceeded. The variance in successive generations has a correlation of at least one-half due to the maintenance of linkage disequilibrium. The magnitude of this variance in parameters and their autocorrelation with time shows that accurate predictions cannot be made about genetic parameters in the base population from single replicate results.

Type
Research Article
Information
Genetics Research , Volume 29 , Issue 3 , June 1977 , pp. 193 - 213
Copyright
Copyright © Cambridge University Press 1977

References

REFERENCES

Bodmer, W. F. & Parsons, P. A. (1962). Linkage and Recombination in Evolution. Advances in Genetics 11, 1–87.Google Scholar
Bulmer, M. G. (1976). The effect of selection on genetic variability: a simulation study. Genetical Research 28, 101–118.CrossRefGoogle ScholarPubMed
Crow, J. F. & Kimura, M. (1970). An Introduction to Population Genetics Theory. New York, Evanston and London: Harper and Row.Google Scholar
Falconer, P. S. (1960). Introduction to Quantitative Genetics. Edinburgh and London: Oliver & Boyd.Google Scholar
Green, E. L. and staff of Jackson Laboratory (1966). Biology of the Laboratory Mouse, 2nd edition. New York, Toronto, London, Sydney: McGraw-Hill.Google Scholar
Hill, W. G. (1971). Design and efficiency of selection experiments for estimating genetic parameters. Biometrics 27, 293–311.CrossRefGoogle ScholarPubMed
Hill, W. G. (1974 a). Disequilibrium among several linked neutral genes in finite populations. II. Variances and covariances of disequilibria. Theoretical Population Biology 6, 184–198.Google Scholar
Hill, W. G. (1974 b). Variability of response to selection in genetic experiments. Biometrics 30, 363–366.Google Scholar
Hill, W. G. (1975). Linkage disequilibrium among multiple neutral alleles produced by mutation in finite populations. Theoretical Population Biology 8, 117–126.Google Scholar
Hill, W. G. (1976). Variation in response to selection. Proceedings of International Conference on Quantitative Genetics; Iowa State University Press, Ames (in the Press).Google Scholar
Hill, W. G. & Robertson, A. (1968). Linkage disequilibrium in finite populations. Theoretical and Applied Genetics 38, 226–231.CrossRefGoogle ScholarPubMed
Lindsley, D. L. & Qrell, E. H. (1967). Genetic Variations of Drosophila melanogaster. Washington: Carnegie Institution Press.Google Scholar
Ohta, T. & Kimura, M. (1969). Linkage disequilibrium duo to random genetic drift. Genetical Research 13, 47–55.CrossRefGoogle Scholar
Robertson, A. (1952). The effect of inbreeding on the variation due to recessive genes. Genetics, 37, 189–207.Google Scholar
Robertson, A. (1976). Effects of linkage and population size on selection response and limits. Proceedings of International Conference on Quantitative Genetics; Iowa State University Press, Ames (in the Press).Google Scholar
Strickberger, M. W. (1968). Genetics. London: Collier-Macmillan and New York: Macmillan.Google Scholar
Sved, J. A. & Feldman, M. W. (1973). Correlation and probability methods for 1 and 2 loci. Theoretical Population Biology 4, 129–132.Google Scholar
Tallis, G. M. (1959). Sampling errors of genetic correlation coefficients calculated from analyses of variance and covariance. Australian Journal of Statistics 1, 35–43.Google Scholar
Womack, J. E. (1976). Linkage map of the laboratory mouse. From ‘Mouse Newsletter’ July 1976 (No. 55) (privately circulated).Google Scholar