The infinitesimal model with dominance

Barton NH, Etheridge AM, Véber A. 2023. The infinitesimal model with dominance. Genetics. 225(2), iyad133.

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Barton, Nick HISTA ; Etheridge, Alison M.; Véber, Amandine
The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents’ trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the “shared” and “residual” components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M−−√⁠. We illustrate our results with some numerical examples.
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NHB was supported in part by ERC Grants 250152 and 101055327. AV was partly supported by the chaire Modélisation Mathématique et Biodiversité of Veolia Environment—Ecole Polytechnique—Museum National d’Histoire Naturelle—Fondation X.
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Barton NH, Etheridge AM, Véber A. The infinitesimal model with dominance. Genetics. 2023;225(2). doi:10.1093/genetics/iyad133
Barton, N. H., Etheridge, A. M., & Véber, A. (2023). The infinitesimal model with dominance. Genetics. Oxford Academic.
Barton, Nicholas H, Alison M. Etheridge, and Amandine Véber. “The Infinitesimal Model with Dominance.” Genetics. Oxford Academic, 2023.
N. H. Barton, A. M. Etheridge, and A. Véber, “The infinitesimal model with dominance,” Genetics, vol. 225, no. 2. Oxford Academic, 2023.
Barton NH, Etheridge AM, Véber A. 2023. The infinitesimal model with dominance. Genetics. 225(2), iyad133.
Barton, Nicholas H., et al. “The Infinitesimal Model with Dominance.” Genetics, vol. 225, no. 2, iyad133, Oxford Academic, 2023, doi:10.1093/genetics/iyad133.
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