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Evolution and Selection of Quantitative Traits$
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Bruce Walsh and Michael Lynch

Print publication date: 2018

Print ISBN-13: 9780198830870

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198830870.001.0001

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The Infinitesimal Model and Its Extensions

The Infinitesimal Model and Its Extensions

(p.875) 24 The Infinitesimal Model and Its Extensions
Evolution and Selection of Quantitative Traits

Bruce Walsh

Michael Lynch

Oxford University Press

One standard approximation in quantitative genetics is the infinitesimal model, which assumes a large number of loci, each of small effect. In such a setting, the distribution of breeding values in unselected descendants is roughly multivariate normal and most of the (short-term) change in the additive variance under selection is through Bulmer effects (the generation of linkage disequilibrium) rather than by allele-frequency change. A variety of different infinitesimal models are found in the literature, and this chapter examines these different versions and the connections between them. It also examines the theory for moving beyond the infinitesimal approximation. Finally, this chapter shows that the much-debated worry over “missing heritability” simply follows under the infinitesimal setting.

Keywords:   Barton-Turelli equation, Bulmer effect, continuum-of-alleles model, Chebsyshev-Hermite polynominals, cumulants, exchangeable model, Fisher-Bulmer infinitesimal model, Gram-Charlier series, infinite-alleles model, linkage disequilibrium, missing heritability, rare-alleles model

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