Joint modeling of additive and non-additive (genetic line) effects in multi-environment trials

Oakey, Helena; Verbyla, A. P.; Cullis, Brian R; Wei, Xianming; Pitchford, W. S.

doi:10.1007/s00122-007-0515-3

Cited by 78 publications

(103 citation statements)

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“…populations with known pedigrees (Oakey et al 2007), but marker-based estimation of epistatic effects for natural populations appears possible only with more advanced statistical methodology, for example semiparametric mixed models and reproducing kernel Hilbert spaces (Gianola and Van Kaam 2008;Howard et al 2014). Another direction for future research is the estimation of heritability in the presence of additional random effects, which would increase the applicability to agricultural field trials (where the raw data are usually at plot rather than individual plant level).…”

Section: Discussionmentioning

confidence: 99%

“…Differences between such blocks are usually best modeled using random block effects. The definition of heritability in such contexts is, however, far from obvious: Oakey et al (2007) proposed generalized heritability, but for natural populations this definition is not equivalent to the classical definition of heritability (Oakey et al 2007, p. 813). In this case the ratio of the estimated genetic variance over the total phenotypic variance could be used as a lower bound on heritability.…”

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Marker-Based Estimation of Heritability in Immortal Populations

et al. 2014

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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...

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Section: Discussionmentioning

confidence: 99%

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Marker-Based Estimation of Heritability in Immortal Populations

et al. 2014

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Section: Phenotypic Data Analysismentioning

confidence: 99%

“…The variance component associated with the additive genomic relationship matrix estimates additive polygenic genetic variance. The variance component associated with the identically and independently distributed line effects captures any other genotypic variance, which could include nonadditive variance (although dominance variance should be generally very low among highly homozygous lines) and also nonpolygenic variance due to individual genes with large effects (Oakey et al 2006(Oakey et al , 2007.For the purpose of estimating heritability of line mean values, both data sets were also analyzed using the modelwhere Y is the vector of BLUE values of each phenotype, u is a vector of inbred line additive effects, Z is a design matrix, and e is a vector of random residuals. The variance-covariance matrix of u is Var(u) = Gs 2 A ; where s 2 A is the additive genetic variance in the noninbred reference population and G is the realized additive relationship matrix based on all markers.…”

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Genetic Architecture of Domestication-Related Traits in Maize

et al. 2016

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Strong directional selection occurred during the domestication of maize from its wild ancestor teosinte, reducing its genetic diversity, particularly at genes controlling domestication-related traits. Nevertheless, variability for some domestication-related traits is maintained in maize. The genetic basis of this could be sequence variation at the same key genes controlling maize-teosinte differentiation (due to lack of fixation or arising as new mutations after domestication), distinct loci with large effects, or polygenic background variation. Previous studies permit annotation of maize genome regions associated with the major differences between maize and teosinte or that exhibit population genetic signals of selection during either domestication or postdomestication improvement. Genome-wide association studies and genetic variance partitioning analyses were performed in two diverse maize inbred line panels to compare the phenotypic effects and variances of sequence polymorphisms in regions involved in domestication and improvement to the rest of the genome. Additive polygenic models explained most of the genotypic variation for domesticationrelated traits; no large-effect loci were detected for any trait. Most trait variance was associated with background genomic regions lacking previous evidence for involvement in domestication. Improvement sweep regions were associated with more trait variation than expected based on the proportion of the genome they represent. Selection during domestication eliminated large-effect genetic variants that would revert maize toward a teosinte type. Small-effect polygenic variants (enriched in the improvement sweep regions of the genome) are responsible for most of the standing variation for domestication-related traits in maize.KEYWORDS quantitative trait loci; nested association mapping; genome-wide association study; variance components; Zea mays T HE domestication of all major crop plants occurred in a relatively short period in human history, starting 10,000 years ago (Harlan 1992). During the domestication process, seeds of preferred forms were selected and saved to plant subsequent generations. Some alleles favored under domestication may have been neutral or even deleterious for the survival of wild plant species; for example, seed shattering promotes seed dispersal in wild grasses, but alleles for nondisarticulating seed structures were strongly selected for under domestication (Galinat 1983). Consequently, rare alleles favorable for growth and development under agricultural conditions or for traits desired by humans increased in frequency, often reaching fixation and reducing genetic variation very near causal sequence sites (Wang et al. 1999). In addition, domestication was often accompanied by severe genetic bottlenecks from the use of small founder populations. The reduction in effective population sizes also resulted in reduced genetic diversity genome-wide. Population genetics methods to model the strength and duration of bottlenecks provide a means to ...

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“…More factors allow for greater flexibility, but may reduce model parsimony. Multiple researchers have demonstrated that a factor analytic structure can be combined with pedigree information to improve model fit, as measured by information criteria (Crossa et al, 2006;Oakey et al, 2007;Kelly et al, 2009;Beeck et al, 2010). These researchers have analyzed a limited number of real MET data sets; a simulation study could determine if the FA model with a GRM is the most effective model for a much wider range of MET.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Linear Mixed Models for Multiple Environment Plant Breeding Trials

Walker¹,

Pita²,

Campbell³

2011

Conference on Applied Statistics in Agriculture

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Evaluations of multiple environment trials (MET) often reveal substantial genotype by environment interactions, and the effects of genotypes within environments are often estimated using cell means, i.e. the simple mean of the observations of each genotype in each environment. However, these estimates are inaccurate, especially for unreplicated or partially replicated trials, so alternative methods of analysis are necessary. One possible approach utilizes information, often from pedigree data, about relationships among the tested genotypes through the use of a genetic relationship matrix (GRM). Predictive accuracy may also be improved by the use of factor analytic (FA) structures for environmental covariances. In this study, data were simulated to resemble results from a range of MET. These simulated data sets covered a range of scenarios with varying numbers of environments and genotypes, environmental relationship patterns, field trial designs, and magnitudes of experimental error. The simulated data were used to evaluate 20 mixed models, ten of which included GRMs and ten which did not. The models included ten structures for environmental covariances including structures with no environmental correlation, structures with constant correlation among environments, and six FA structures. These models were compared to each other and to cell means and Additive Main effects and Multiplicative Interaction (AMMI) methods in terms of successful convergence and predictive accuracy. For most of the scenarios, models which included a GRM and a compound symmetric, constant variance structure produced the most accurate estimates. Models with GRM and FA structures were more accurate only when used to evaluate scenarios simulated with Toeplitz patterns of relationships and more than 25 genotypes or five environments. Unfortunately, the improved accuracy with the FA structures in these scenarios came at the cost of reduced convergence rates, so FA structures may not be reliable enough for some uses.

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Joint modeling of additive and non-additive (genetic line) effects in multi-environment trials

Cited by 78 publications

References 40 publications

Marker-Based Estimation of Heritability in Immortal Populations

Marker-Based Estimation of Heritability in Immortal Populations

Genetic Architecture of Domestication-Related Traits in Maize

Comparison of Linear Mixed Models for Multiple Environment Plant Breeding Trials

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