A Mixed-Model Quantitative Trait Loci (QTL) Analysis for Multiple-Environment Trial Data Using Environmental Covariables for QTL-by-Environment Interactions, with an Example in Maize

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ABSTRACT

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F^sub 5^ maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.

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THE incidence of genotype-by-environment interactions (GEI) for quantitative traits has important implications for any attempts to understand the genetic architecture of these traits by mapping quantitative trait loci (QTL) and also for the effectiveness of attempts to improve these traits by both conventional and markerassisted selection (MAS) breeding strategies. The literature on GEI and QTL-by-environment interactions (QEI) for quantitative traits in maize is ambiguous, with evidence in favor (Moreau et al. 2004) and against (Ledeaux et al. 2006) their importance. The diversity of the results for the importance of QEI for quantitative traits in crop plants observed in the literature strongly suggests that explicit testing for their presence, magnitude, and form is a critical step in any attempt to understand the genetic architecture of these traits. Further, theoretical considerations of the impact of different forms of QEI on the outcomes of MAS in plant breeding (Podlich et al. 2004; Cooper et al. 2002, 2005, 2006) motivate the development of methods for explicitly studying the importance of QEI as a component of the genetic architecture of quantitative traits.

When QEI occurs and environmental covariables derived from geographical and weather information are available,QTL effects across environments can be tested for dependence on particular environmental covariables (Crossa et al. 1999;Malosetti et al. 2004; Vargas et al. 2006). More generally, the phenotypic behavior can be modeled in the form of QTL-dependent response curves to the environmental characterizations (Hammer et al. 2006; Malosetti et al. 2006; Van Eeuwijk et al. 2007). These response curves are expected to have nonlinear forms, but limited environmental information will typically allow only linear approximations to these curves.

In this article, we develop a mixed-model framework that can be used to explicitly test for the presence of QEI and investigate its structure for quantitative traits in multiple-environment trials (MET). Our strategy for the analysis of MET is a bottom-up approach, starting with a phenotypic analysis per trial, using no further genotypic and environmental information. This preliminary step serves to select a model for the intraenvironment error structure for each trial, for later use in the METanalysis. …