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Hypothesis and Theory ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Genet. | doi: 10.3389/fgene.2019.00054

Orthogonal Decomposition of the Genetic Variance for Epistatic Traits under Linkage Disequilibrium—Applications to the Analysis of Bateson-Dobzhansky-Müller Incompatibilities and Sign Epistasis

  • 1Centro de Investigación en Química Biológica y Materiales Moleculares (CiQUS), Universidad de Santiago de Compostela, Spain

The one-century-old theory of orthogonal genetic variance decomposition originated the field of quantitative genetics and has kept on being improved ever since. Recently, serious concerns about the possibility of attaining a satisfactory implementation of genetic variance decomposition with linkage disequilibrium (LD) and epistasis have been raised. In this paper we dissipate such doubts by completing the classical theory of variance decomposition into additive, dominance and epistasis components with LD. We apply that theory to the analysis of the genotype-to-phenotype maps of two cases of particular evolutionary interest—Bateson-Dobzhansky-Müller incompatibilities and sign epistasis. For the first case we show how negative LD and reduction of heterozygotes may contribute to maintain genetic variability after secondary contact. For the second case we show that LD transforms the set of frequencies leading to an evolutionary plateau into a ridge. Our theoretical developments reassuringly reflect the complexity LD conveys to genetic systems throughout novel properties—as compared with systems under linkage equilibrium. We argue that such particularities might have actually contributed to cause confusion about the feasibility of developing this methodology. In any case, the theory we provide in this paper enables new perspectives in both evolutionary and quantitative genetics studies.

Keywords: genetic variance decomposition, Linkage Disequilibrium, Epistasis, Bateson-Dobzhansky-Müller incompatibilities, Sign epistasis

Received: 20 Jul 2018; Accepted: 23 Jan 2019.

Edited by:

Mariza De Andrade, Mayo Clinic, United States

Reviewed by:

Li Zhang, University of California, San Francisco, United States
Tao Wang, Medical College of Wisconsin, United States
Marylyn D. Ritchie, University of Pennsylvania, United States  

Copyright: © 2019 Álvarez-Castro and Crujeiras. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. José M Álvarez-Castro, Centro de Investigación en Química Biológica y Materiales Moleculares (CiQUS), Universidad de Santiago de Compostela, Santiago de Compostela, Spain,