The Polygenic Model

Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

The standard polygenic model of biometrical genetics can be motivated by considering a quantitative trait determined by a large number of loci acting independently and additively [12]. In a pedigree of m people, let X ini suk be the contribution of locus k to person i. The trait value X i = Σ kX ini suk for person i forms part of a vector X = (X 1,...,X m)t of trait values for the pedigree. If the effects of the various loci are comparable, then the central limit theorem implies that X follows an approximate multivariate normal distribution. (See the references [19, 21] and Appendix B.) Furthermore, independence of the various loci implies Cov(X 1, X j) = Σ k Cov(X ini suk , X ink suk . From our covariance decomposition for two non-inbred relatives at a single locus, it follows that Cov(X 1, X j) = 2Φijσ inα su2 + Δ7ijσ ind su2 , where σ inα su2 and σ ind su2 are the additive and dominance genetic variances summed over all participating loci. These covariances can be expressed collectively in matrix notation as Var(X) = 2σ inα su2 Φ + σ ind su2 Δ7. Again it is convenient to assume that X has mean E(X) = 0. Although it is an article of faith that the assumptions necessary for the central limit theorem actually hold for any given trait, one can check multivariate normality empirically.

Keywords

Quantitative Trait Locus Quantitative Trait Locus Mapping Ridge Count Polygenic Model Observe Information Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag New York, Inc. 2003

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