Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations

Abstract

Quantitative genetics stems from the theoretical models of genetic effects, which are re-parameterizations of the genotypic values into parameters of biological (genetic) relevance. Different formulations of genetic effects are adequate to address different subjects. We thus need to generalize and unify them under a common framework for enabling researchers to easily transform genetic effects between different biological meanings. The Natural and Orthogonal Interactions (NOIA) model of genetic effects has been developed to achieve this aim. Here, we further implement the statistical formulation of NOIA with multiple alleles under Hardy–Weinberg departures (HWD). We show that our developments are straightforwardly connected to the decomposition of the genetic variance and we point out several emergent properties of multiallelic quantitative genetic models, as compared to the biallelic ones. Further, NOIA entails a natural extension of one-locus developments to multiple epistatic loci under linkage equilibrium. Therefore, we present an extension of the orthogonal decomposition of the genetic variance to multiple epistatic, multiallelic loci under HWD. We illustrate this theory with a graphical interpretation and an analysis of published data on the human acid phosphatase (ACP1) polymorphism.

A revised Fisher model on analysis of quantitative trait loci with multiple alleles

“…For example, based on the observed genotype frequencies, an estimate of V D = 1.15 for the trait of ACP1 enzyme inhibition was reported in Álvarez-Castro and Yang (2011), which is noticeably larger than V D = 0.146 that we obtain above.…”

Why Epistasis Is Important for Selection and Adaptation

“…Although this distinction has its roots in an understanding of the context dependency of (additive) gene effects (e.g., Lewontin , ch. 6; Moreno ; Wagner et al ; Templeton ), it was only toward the end of the century that quantitative geneticists started to consider the effects of (functional) epistasis on the additive variance (e.g., Goodnight , ; Cheverud and Routman ), and we could start to resolve the inconsistencies and develop the tools to investigate the full impact of epistasis in quantitative genetics (e.g., Rice , , ; Wagner et al ; Hansen and Wagner ; Barton and Turelli ; Carter et al ; Demuth and Wade ; Álvarez‐Castro and Carlborg ; Jannink et al ; Pavlicev et al , ; Álvarez‐Castro and Yang ; Gjuvesland et al ; Álvarez‐Castro et al ; Slatkin and Kirkpatrick ).…”

Dissecting genetic effects with imprinting

“…The previous expressions and arguments can be extended to the decomposition of the genetic variance with an imprinting variance component, which can easily be obtained from the model in matrix notation above (10) by following the formulae provided by Álvarez-Castro and Yang (2011). In expressions (12) and (13) of that article, the additive and the dominance variance have been obtained as…”

“…The need to update models of genetic effects for making the most of this new source of information was soon pointed out (Cheverud and Routman, 1995), leading to the development of models of genetic effects depicting the GP map as effects of allele substitutions from individual genotypes (Hansen and Wagner, 2001). This is the context in which the Natural and Orthogonal Interactions (NOIA) model of genetic effects was developed (Álvarez-Castro and Carlborg, 2007;Álvarez-Castro and Yang, 2011).…”