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

Tao Wang

doi:10.3389/fgene.2014.00328

Abstract

Zeng et al. (2005) proposed a general two-allele (G2A) model to model bi-allelic quantitative trait loci (QTL). Comparing with the classical Fisher model, the G2A model can avoid using redundant parameters and be fitted directly using standard least square (LS) approach. In this study, we further extend the G2A model to general multi-allele (GMA) model. First, we propose a one-locus GMA model for phase known genotypes based on modeling the inheritance of paternal and maternal alleles. Next, we develop a one-locus GMA model for phase unknown genotypes by treating it as a special case of the phase known one-locus GMA model. Thirdly, we extend the one-locus GMA models to multiple loci. We discuss how the genetic variance components can be analyzed using these GMA models in equilibrium as well as disequilibrium populations. Finally, we apply the GMA model to a published experimental data set.

Highlights

There are two types of statistical genetic models that are commonly used in genetic analysis of quantitative traits
Given genotypes at targeted quantitative trait loci (QTL) or genetic marker loci, we focus on assessing the variations contributed by the allelic effects and interactions of the QTL or marker loci to the total genotypic variance VG
In the analysis of genetic variance components, a separation of the variations contributed by the additive allelic effects and allelic interactions is complicated by the fact that the observed genotypes are often phase-unknown

Summary

INTRODUCTION

There are two types of statistical genetic models that are commonly used in genetic analysis of quantitative traits. One is the F∞ type models that concentrate on direct modeling of the expected genotypic values at targeted quantitative trait loci (QTL) or genetic markers and association testing for various allelic effects and interactions (Fisher, 1918; Cheverud, 2000; Hansen and Wagner, 2001; Wang, 2011). These genetic variance components do not depend on the sample size, and they can provide additional information on better understanding the genetic etiology and assessing for clinical importance Both the F∞ and the Fisher type models form basis in the analysis of quantitative traits. We derive formulas on partitioning the genotypic variance into the additive and dominance variance components under Hardy-Weinberg equilibrium (HWE) as well as in Hardy-Weinberg disequilibrium (HWD) for both the phase-known and phase-unknown one-locus GMA models. We apply the GMA model to a published experimental data set

METHODS AND RESULTS

ONE-LOCUS MODEL FOR PHASE KNOWN

ONE-LOCUS MODEL FOR PHASE UNKNOWN

MULTI-LOCUS MODELS

EXAMPLE

DISCUSSION