Genotype-by-environment interaction (GEI) is an important phenomenon in plant breeding. This paper presents a series of models for describing, exploring, understanding, and predicting GEI. All models depart from a two-way table of genotype by environment means. First, a series of descriptive and explorative models/approaches are presented: Finlay–Wilkinson model, AMMI model, GGE biplot. All of these approaches have in common that they merely try to group genotypes and environments and do not use other information than the two-way table of means. Next, factorial regression is introduced as an approach to explicitly introduce genotypic and environmental covariates for describing and explaining GEI. Finally, QTL modeling is presented as a natural extension of factorial regression, where marker information is translated into genetic predictors. Tests for regression coefficients corresponding to these genetic predictors are tests for main effect QTL expression and QTL by environment interaction (QEI). QTL models for which QEI depends on environmental covariables form an interesting model class for predicting GEI for new genotypes and new environments. For realistic modeling of genotypic differences across multiple environments, sophisticated mixed models are necessary to allow for heterogeneity of genetic variances and correlations across environments. The use and interpretation of all models is illustrated by an example data set from the CIMMYT maize breeding program, containing environments differing in drought and nitrogen stress. To help readers to carry out the statistical analyses, GenStat® programs, 15th Edition and Discovery® version, are presented as “Appendix.”

Associations between markers and complex quantitative traits were investigated in a collection of 146 modern two-row spring barley cultivars, representing the current commercial germ plasm in Europe. Using 236 AFLP markers, associations between markers were found for markers as far apart as 10 cM. Subsequently, for the 146 cultivars the complex traits mean yield, adaptability (Finlay-Wilkinson slope), and stability (deviations from regression) were estimated from the analysis of variety trial data. Regression of those traits on individual marker data disclosed marker-trait associations for mean yield and yield stability. Support for identified associations was obtained from association profiles, i.e., from plots of P-values against chromosome positions. In addition, many of the associated markers were located in regions where earlier QTL were found for yield and yield components. To study the oligogenic genetic base of the traits in more detail, multiple linear regression of the traits on markers was carried out, using stepwise selection. By this procedure, 18-20 markers that accounted for 40-58% of the variation were selected. Our results indicate that association mapping approaches can be a viable alternative to classical QTL approaches based on crosses between inbred lines, especially for complex traits with costly measurements.T HE genetic dissection of complex traits still prepleiotropic effects on a number of performance traits in barley, but Cattivelli et al. (2002) concluded that sents a challenge. The oligo/polygenic character little is known about the regulatory mechanisms controlof complex traits, combined with interactions between ling stress responses, mainly because all stress responses loci, makes the task a priori difficult and intricate. In involve many genes. addition, environmental factors trigger and modify geneThe polygenic basis of complex traits has conseactions and thereby further complicate the analysis.quences for the application of quantitative trait locus Yield is the classical example of a complex trait. Yield (QTL) mapping methodology, as many markers that fluctuations in relation to environmental factors are are associated with the trait need to be identified. Typioften described in terms of adaptability and stability.cally, for QTL mapping, a cross between two inbred The latter can be considered to constitute complex traits lines is made and the cosegregation of alleles of mapped on their own. Parameters quantifying adaptability and marker loci and phenotypic traits allows the identificastability require observations across a range of environtion of linked markers. For complex traits with GE interments for their estimation. The parameters are typically action, this approach implies large-scale testing of spedefined in terms of linear and quadratic functions of cial mapping populations across a range of environments. the genotype by environment (GE) interaction (Lin et

BackgroundGenome-wide association studies (GWAS) based on linkage disequilibrium (LD) provide a promising tool for the detection and fine mapping of quantitative trait loci (QTL) underlying complex agronomic traits. In this study we explored the genetic basis of variation for the traits heading date, plant height, thousand grain weight, starch content and crude protein content in a diverse collection of 224 spring barleys of worldwide origin. The whole panel was genotyped with a customized oligonucleotide pool assay containing 1536 SNPs using Illumina's GoldenGate technology resulting in 957 successful SNPs covering all chromosomes. The morphological trait "row type" (two-rowed spike vs. six-rowed spike) was used to confirm the high level of selectivity and sensitivity of the approach. This study describes the detection of QTL for the above mentioned agronomic traits by GWAS.ResultsPopulation structure in the panel was investigated by various methods and six subgroups that are mainly based on their spike morphology and region of origin. We explored the patterns of linkage disequilibrium (LD) among the whole panel for all seven barley chromosomes. Average LD was observed to decay below a critical level (r2-value 0.2) within a map distance of 5-10 cM. Phenotypic variation within the panel was reasonably large for all the traits. The heritabilities calculated for each trait over multi-environment experiments ranged between 0.90-0.95. Different statistical models were tested to control spurious LD caused by population structure and to calculate the P-value of marker-trait associations. Using a mixed linear model with kinship for controlling spurious LD effects, we found a total of 171 significant marker trait associations, which delineate into 107 QTL regions. Across all traits these can be grouped into 57 novel QTL and 50 QTL that are congruent with previously mapped QTL positions.ConclusionsOur results demonstrate that the described diverse barley panel can be efficiently used for GWAS of various quantitative traits, provided that population structure is appropriately taken into account. The observed significant marker trait associations provide a refined insight into the genetic architecture of important agronomic traits in barley. However, individual QTL account only for a small portion of phenotypic variation, which may be due to insufficient marker coverage and/or the elimination of rare alleles prior to analysis. The fact that the combined SNP effects fall short of explaining the complete phenotypic variance may support the hypothesis that the expression of a quantitative trait is caused by a large number of very small effects that escape detection. Notwithstanding these limitations, the integration of GWAS with biparental linkage mapping and an ever increasing body of genomic sequence information will facilitate the systematic isolation of agronomically important genes and subsequent analysis of their allelic diversity.

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 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 multienvironment 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.T HE 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. 2002Cooper et al. , 2005Cooper et al. , 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;Varga...

Definition of clear criteria for evaluation of the quality of core collections is a prerequisite for selecting high-quality cores. However, a critical examination of the different methods used in literature, for evaluating the quality of core collections, shows that there are no clear guidelines on the choices of quality evaluation criteria and as a result, inappropriate analyses are sometimes made leading to false conclusions being drawn regarding the quality of core collections and the methods to select such core collections. The choice of criteria for evaluating core collections appears to be based mainly on the fact that those criteria have been used in earlier publications rather than on the actual objectives of the core collection. In this study, we provide insight into different criteria used for evaluating core collections. We also discussed different types of core collections and related each type of core collection to their respective evaluation criteria. Two new criteria based on genetic distance are introduced. The consequences of the different evaluation criteria are illustrated using simulated and experimental data. We strongly recommend the use of the distance-based criteria since they not only allow the simultaneous evaluation of all variables describing the accessions, but they also provide intuitive and interpretable criteria, as compared with the univariate criteria generally used for the evaluation of core collections. Our findings will provide genebank curators and researchers with possibilities to make informed choices when creating, comparing and using core collections.Electronic supplementary materialThe online version of this article (doi:10.1007/s00122-012-1971-y) contains supplementary material, which is available to authorized users.

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within-and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.KEYWORDS marker-based estimation of heritability; GWAS; genomic prediction; Arabidopsis thaliana; one-vs. two-stage approaches N ARROW-SENSE heritability is an important parameter in quantitative genetics, determining the response to selection and representing the proportion of phenotypic variance that is due to additive genetic effects (Jacquard 1983;Ritland 1996;Visscher et al. 2006Visscher et al. , 2008Holland et al. 2010;Sillanpaa 2011). This definition of heritability goes back to Fisher (1918) and Wright (1920) almost a century ago. In plant species for which replicates of the same genotype are available (inbred lines, doubled haploids, clones), a different form of heritability, broadsense heritability, is traditionally estimated by the intraclass correlation coefficient for genotypic effects, using estimates for within-and between-genotype variance. Broad-sense heritability is also referred to as repeatability and gives the proportion of phenotypic variance explained by heritable (additive) and nonheritable (dominance, epistasis) genetic variance.With the arrival of high-density genotyping there is growing interest in marker-based estimation of narrow-sense heritability (WTCCC 2007;Yang et al. 2010Yang et al. , 2011Vatti...

BackgroundThe use of whole-genome sequence data can lead to higher accuracy in genome-wide association studies and genomic predictions. However, to benefit from whole-genome sequence data, a large dataset of sequenced individuals is needed. Imputation from SNP panels, such as the Illumina BovineSNP50 BeadChip and Illumina BovineHD BeadChip, to whole-genome sequence data is an attractive and less expensive approach to obtain whole-genome sequence genotypes for a large number of individuals than sequencing all individuals. Our objective was to investigate accuracy of imputation from lower density SNP panels to whole-genome sequence data in a typical dataset for cattle.MethodsWhole-genome sequence data of chromosome 1 (1737 471 SNPs) for 114 Holstein Friesian bulls were used. Beagle software was used for imputation from the BovineSNP50 (3132 SNPs) and BovineHD (40 492 SNPs) beadchips. Accuracy was calculated as the correlation between observed and imputed genotypes and assessed by five-fold cross-validation. Three scenarios S40, S60 and S80 with respectively 40%, 60%, and 80% of the individuals as reference individuals were investigated.ResultsMean accuracies of imputation per SNP from the BovineHD panel to sequence data and from the BovineSNP50 panel to sequence data for scenarios S40 and S80 ranged from 0.77 to 0.83 and from 0.37 to 0.46, respectively. Stepwise imputation from the BovineSNP50 to BovineHD panel and then to sequence data for scenario S40 improved accuracy per SNP to 0.65 but it varied considerably between SNPs.ConclusionsAccuracy of imputation to whole-genome sequence data was generally high for imputation from the BovineHD beadchip, but was low from the BovineSNP50 beadchip. Stepwise imputation from the BovineSNP50 to the BovineHD beadchip and then to sequence data substantially improved accuracy of imputation. SNPs with a low minor allele frequency were more difficult to impute correctly and the reliability of imputation varied more. Linkage disequilibrium between an imputed SNP and the SNP on the lower density panel, minor allele frequency of the imputed SNP and size of the reference group affected imputation reliability.

Association or linkage disequilibrium (LD)-based mapping strategies are receiving increased attention for the identification of quantitative trait loci (QTL) in plants as an alternative to more traditional, purely linkage-based approaches. An attractive property of association approaches is that they do not require specially designed crosses between inbred parents, but can be applied to collections of genotypes with arbitrary and often unknown relationships between the genotypes. A less obvious additional attractive property is that association approaches offer possibilities for QTL identification in crops with hard to model segregation patterns. The availability of candidate genes and targeted marker systems facilitates association approaches, as will appropriate methods of analysis. We propose an association mapping approach based on mixed models with attention to the incorporation of the relationships between genotypes, whether induced by pedigree, population substructure, or otherwise. Furthermore, we emphasize the need to pay attention to the environmental features of the data as well, i.e., adequate representation of the relations among multiple observations on the same genotypes. We illustrate our modeling approach using 25 years of Dutch national variety list data on late blight resistance in the genetically complex crop of potato. As markers, we used nucleotide binding-site markers, a specific type of marker that targets resistance or resistance-analog genes. To assess the consistency of QTL identified by our mixed-model approach, a second independent data set was analyzed. Two markers were identified that are potentially useful in selection for late blight resistance in potato.