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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
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Summary

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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

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