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Additive variance and average effect with partial selfing

Published online by Cambridge University Press:  14 April 2009

A. J. Wright
A. J. Wright
Affiliation:
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, USA
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Summary

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The covariance of an ancestor and the average of its descendants in generation t(CPt) is formulated for a breeding system which is a mixture of selfing and outcrossing. This covariance is partitioned into least squares additive (σA. At) and non-additive (σD. Dt) components summed over individual loci, and the combined inbreeding effects of all loci (H′), such that CPt = σA. At + (s/2)t[σD. Do + H′]. For the mth locus the covariance mσA. At = 2(1 + F)Σipiα(0)iα(t)i, in which pi is the frequency of the ith allele whose additive effect (α(t)) depends on the generation for which it is defined. For distant descendants α(∞) is equal to half of the derivative of the population mean with respect to the frequency of the allele. The covariance CP∞ = σA. A∞ thus relates directly to permanent selection response measured in the equilibrium population, any additional responses observed in earlier generations being due to temporary disturbances in population genotypic structure. It is only for these distant descendants that the least squares additive component has any direct interpretation in terms of selection response. The definitions of α(0) and α(∞), lead to two distinct definitions of the average effect of an allele substitution for a model with two alleles (Fisher, 1941), and to a clarification of their significance for this breeding system.

Type
Research Article
Information
Genetics Research , Volume 50 , Issue 1 , August 1987 , pp. 63 - 68
Copyright
Copyright © Cambridge University Press 1987

References

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