Marker-based Relationship Matrices Research Articles

Genomic Predictions With Nonadditive Effects Improved Estimates of Additive Effects and Predictions of Total Genetic Values in Pinus sylvestris.

Genomic selection study (GS) focusing on nonadditive genetic effects of dominance and the first order of epistatic effects, in a full-sib family population of 695 Scots pine (Pinus sylvestris L.) trees, was undertaken for growth and wood quality traits, using 6,344 single nucleotide polymorphism markers (SNPs) generated by genotyping-by-sequencing (GBS). Genomic marker-based relationship matrices offer more effective modeling of nonadditive genetic effects than pedigree-based models, thus increasing the knowledge on the relevance of dominance and epistatic variation in forest tree breeding. Genomic marker-based models were compared with pedigree-based models showing a considerable dominance and epistatic variation for growth traits. Nonadditive genetic variation of epistatic nature (additive × additive) was detected for growth traits, wood density (DEN), and modulus of elasticity (MOEd) representing between 2.27 and 34.5% of the total phenotypic variance. Including dominance variance in pedigree-based Best Linear Unbiased Prediction (PBLUP) and epistatic variance in genomic-based Best Linear Unbiased Prediction (GBLUP) resulted in decreased narrow-sense heritability and increased broad-sense heritability for growth traits, DEN and MOEd. Higher genetic gains were reached with early GS based on total genetic values, than with conventional pedigree selection for a selection intensity of 1%. This study indicates that nonadditive genetic variance may have a significant role in the variation of selection traits of Scots pine, thus clonal deployment could be an attractive alternative for the species. Additionally, confidence in the role of nonadditive genetic effects in this breeding program should be pursued in the future, using GS.

Updating genetic relationship matrices and their inverses: a methodology note

Most of the calculations for genetic relationship matrices and their inverses utilized in recent (t + 1) evaluations for populations of interest can be avoided by updating these matrices at t evaluations for only new animals. This study describes and develops existing methods for updating pedigree-based and marker-based relationship matrices and their inverses. Updating some of the matrices could benefit from parallel computing.

Performance of pedigree and various forms of marker‐derived relationship coefficients in genomic prediction and their correlations

In recent years, with development and validation of different genotyping panels, several methods have been proposed to build efficient similarity matrices among individuals to be used for genomic selection. Consequently, the estimated genetic parameters from such information may deviate from their counterpart using traditional family information. In this study, we used a pedigree-based numerator relationship matrix (A) and three types of marker-based relationship matrices ( ) including two identical by descent, that is and and one identical by state, as well as four Gaussian kernel ( ) similarity kernels with different smoothing parameters to predict yet to be observed phenotypes. Also, we used different kinship matrices that are a linear combination of marker-derived IBD or IBS matrices with A, constructed as , where the weight ( ) assigned to each source of information varied over a grid of values. A Bayesian multiple-trait Gaussian model was fitted to estimate the genetic parameters and compare the prediction accuracy in terms of predictive correlation, mean square error and unbiasedness. Results show that the estimated genetic parameters (heritability and correlations) are affected by the source of the information used to create kinship or the weight placed on the sources of genomic and pedigree information. The superiority of GK-based model depends on the smoothing parameters (θ) so that with an optimum θ value, the GK-based model statistically yielded better performance (higher predictive correlation, lowest MSE and unbiased estimates) and more stable correlations and heritability than the model with IBD, IBS or kinship matrices or any of the linear combinations.

Average information residual maximum likelihood in practice.

Gilmour, Thompson, and Cullis (Biometrics, 1995, 51, 1440) presented the average information residual maximum likelihood (REML) algorithm for efficient variance parameter estimation in the linear mixed model. That paper dealt specifically with traditional variance component models, but the algorithm was quickly applied to more general models and implemented in several REML packages including ASReml (Gilmour etal., Biometrics, 2015, 51, 1440). This paper outlines the theory with respect to these more general models, describes the main issues encountered in fitting these models and how they have been addressed in the ASReml software. The issues covered are the basics steps in the implementation of the algorithm, keeping parameters within the parameter space, maximizing sparsity, avoiding issues associated with unstructured variance matrices by using the factor-analytic structure and handling singularities in marker-based relationship matrices and current work.

Efficiency of genomic prediction across two Eucalyptus nitens seed orchards with different selection histories

Genomic selection is expected to enhance the genetic improvement of forest tree species by providing more accurate estimates of breeding values through marker-based relationship matrices compared with pedigree-based methodologies. When adequately robust genomic prediction models are available, an additional increase in genetic gains can be made possible with the shortening of the breeding cycle through elimination of the progeny testing phase and early selection of parental candidates. The potential of genomic selection was investigated in an advanced Eucalyptus nitens breeding population focused on improvement for solid wood production. A high-density SNP chip (EUChip60K) was used to genotype 691 individuals in the breeding population, which represented two seed orchards with different selection histories. Phenotypic records for growth and form traits at age six, and for wood quality traits at age seven were available to build genomic prediction models using GBLUP, which were compared to the traditional pedigree-based alternative using BLUP. GBLUP demonstrated that breeding value accuracy would be improved and substantial increases in genetic gains towards solid wood production would be achieved. Cross-validation within and across two different seed orchards indicated that genomic predictions would likely benefit in terms of higher predictive accuracy from increasing the size of the training data sets through higher relatedness and better utilization of LD

Relevance of Additive and Nonadditive Genetic Relatedness for Genomic Prediction in Rice Population under Recurrent Selection Breeding

In genomic recurrent selection programs of self-pollinated crops, additive genetic effects (breeding values) are effectively relevant for selection of superior progenies as new parents. However, considering additive and nonadditive genetic effects can improve the prediction of genome-enhanced breeding values (GEBV) of progenies, for quantitative traits. In this study, we assessed the magnitude of additive and nonadditive genetic variances for eight key traits in a rice population under recurrent selection, using marker-based relationship matrices. We then assessed the goodness-to-fit, bias, stability and accuracy of prediction for breeding values and total (additive plus nonadditive) genetic values, in five genomic best linear unbiased prediction (GBLUP) models, ignoring or not nonadditive genetic effects. The models were compared using 6174 single nucleotide polymorphisms (SNP) markers from 174 S1:3 progenies evaluated in field yield trial. We found dominance effects accounting for a substantial proportion of the total genetic variance for the key traits in rice, especially for days to flowering. In average of the traits, the component of variance additive, dominance, and epistatic contributed to about 34%, 14% and 9% for phenotypic variance. Additive genomic models, ignoring nonadditive genetic effects, showed better fit to the data and lower bias, in addition to greater stability and accuracy for predict GEBV of progenies. These results improve our understanding of the genetic architecture of the key traits in rice, evaluated in early-generation testing. Clearly, this study highlighted the advantages of additive models using genome-wide information, for genomic prediction applied to recurrent selection in a self-pollinated crop

Marker-Based Estimates Reveal Significant Nonadditive Effects in Clonally Propagated Cassava (Manihot esculenta): Implications for the Prediction of Total Genetic Value and the Selection of Varieties.

In clonally propagated crops, nonadditive genetic effects can be effectively exploited by the identification of superior genetic individuals as varieties. Cassava (Manihot esculenta Crantz) is a clonally propagated staple food crop that feeds hundreds of millions. We quantified the amount and nature of nonadditive genetic variation for three key traits in a breeding population of cassava from sub-Saharan Africa using additive and nonadditive genome-wide marker-based relationship matrices. We then assessed the accuracy of genomic prediction for total (additive plus nonadditive) genetic value. We confirmed previous findings based on diallel crosses that nonadditive genetic variation is significant for key cassava traits. Specifically, we found that dominance is particularly important for root yield and epistasis contributes strongly to variation in cassava mosaic disease (CMD) resistance. Further, we showed that total genetic value predicted observed phenotypes more accurately than additive only models for root yield but not for dry matter content, which is mostly additive or for CMD resistance, which has high narrow-sense heritability. We address the implication of these results for cassava breeding and put our work in the context of previous results in cassava, and other plant and animal species.

Modeling additive and non-additive effects in a hybrid population using genome-wide genotyping: prediction accuracy implications.

Hybrids are broadly used in plant breeding and accurate estimation of variance components is crucial for optimizing genetic gain. Genome-wide information may be used to explore models designed to assess the extent of additive and non-additive variance and test their prediction accuracy for the genomic selection. Ten linear mixed models, involving pedigree- and marker-based relationship matrices among parents, were developed to estimate additive (A), dominance (D) and epistatic (AA, AD and DD) effects. Five complementary models, involving the gametic phase to estimate marker-based relationships among hybrid progenies, were developed to assess the same effects. The models were compared using tree height and 3303 single-nucleotide polymorphism markers from 1130 cloned individuals obtained via controlled crosses of 13 Eucalyptus urophylla females with 9 Eucalyptus grandis males. Akaike information criterion (AIC), variance ratios, asymptotic correlation matrices of estimates, goodness-of-fit, prediction accuracy and mean square error (MSE) were used for the comparisons. The variance components and variance ratios differed according to the model. Models with a parent marker-based relationship matrix performed better than those that were pedigree-based, that is, an absence of singularities, lower AIC, higher goodness-of-fit and accuracy and smaller MSE. However, AD and DD variances were estimated with high s.es. Using the same criteria, progeny gametic phase-based models performed better in fitting the observations and predicting genetic values. However, DD variance could not be separated from the dominance variance and null estimates were obtained for AA and AD effects. This study highlighted the advantages of progeny models using genome-wide information.

Unraveling additive from nonadditive effects using genomic relationship matrices.

The application of quantitative genetics in plant and animal breeding has largely focused on additive models, which may also capture dominance and epistatic effects. Partitioning genetic variance into its additive and nonadditive components using pedigree-based models (P-genomic best linear unbiased predictor) (P-BLUP) is difficult with most commonly available family structures. However, the availability of dense panels of molecular markers makes possible the use of additive- and dominance-realized genomic relationships for the estimation of variance components and the prediction of genetic values (G-BLUP). We evaluated height data from a multifamily population of the tree species Pinus taeda with a systematic series of models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance), using either pedigree- or marker-based information. We show that, compared with the pedigree, use of realized genomic relationships in marker-based models yields a substantially more precise separation of additive and nonadditive components of genetic variance. We conclude that the marker-based relationship matrices in a model including additive and nonadditive effects performed better, improving breeding value prediction. Moreover, our results suggest that, for tree height in this population, the additive and nonadditive components of genetic variance are similar in magnitude. This novel result improves our current understanding of the genetic control and architecture of a quantitative trait and should be considered when developing breeding strategies.

Estimates of missing heritability for complex traits in Brown Swiss cattle.

BackgroundGenomic selection estimates genetic merit based on dense SNP (single nucleotide polymorphism) genotypes and phenotypes. This requires that SNPs explain a large fraction of the genetic variance. The objectives of this work were: (1) to estimate the fraction of genetic variance explained by dense genome-wide markers using 54 K SNP chip genotyping, and (2) to evaluate the effect of alternative marker-based relationship matrices and corrections for the base population on the fraction of the genetic variance explained by markers.MethodsTwo alternative marker-based relationship matrices were estimated using 35 706 SNPs on 1086 dairy bulls. Both pedigree- and marker-based relationship matrices were fitted simultaneously or separately in an animal model to estimate the fraction of variance not explained by the markers, i.e. the fraction explained by the pedigree. The phenotypes considered in the analysis were the deregressed estimated breeding values (dEBV) for milk, fat and protein yield and for somatic cell score (SCS).ResultsWhen dEBV were not sufficiently accurate (50 or 70%), the estimated fraction of the genetic variance explained by the markers was around 65% for yield traits and 45% for SCS. Scaling marker genotypes with locus-specific frequencies of heterozygotes slightly increased the variance explained by markers, compared with scaling with the average frequency of heterozygotes across loci. The estimated fraction of the genetic variance explained by the markers using separately both relationships matrices followed the same trends but the results were underestimated. With less accurate dEBV estimates, the fraction of the genetic variance explained by markers was underestimated, which is probably an artifact due to the dEBV being estimated by a pedigree-based animal model.ConclusionsWhen using only highly accurate dEBV, the proportion of the genetic variance explained by the Illumina 54 K SNP chip was approximately 80% for Brown Swiss cattle. These results depend on the SNP chip used and the family structure of the population, i.e. more dense SNPs and closer family relationships are expected to result in a higher fraction of the variance explained by the SNPs.

Correction: Compatibility of pedigree-based and marker-based relationship matrices for single-step genetic evaluation

Correction: Compatibility of pedigree-based and marker-based relationship matrices for single-step genetic evaluation

Compatibility of pedigree-based and marker-based relationship matrices for single-step genetic evaluation

BackgroundSingle-step methods provide a coherent and conceptually simple approach to incorporate genomic information into genetic evaluations. An issue with single-step methods is compatibility between the marker-based relationship matrix for genotyped animals and the pedigree-based relationship matrix. Therefore, it is necessary to adjust the marker-based relationship matrix to the pedigree-based relationship matrix. Moreover, with data from routine evaluations, this adjustment should in principle be based on both observed marker genotypes and observed phenotypes, but until now this has been overlooked. In this paper, I propose a new method to address this issue by 1) adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix instead of the reverse and 2) extending the single-step genetic evaluation using a joint likelihood of observed phenotypes and observed marker genotypes. The performance of this method is then evaluated using two simulated datasets.ResultsThe method derived here is a single-step method in which the marker-based relationship matrix is constructed assuming all allele frequencies equal to 0.5 and the pedigree-based relationship matrix is constructed using the unusual assumption that animals in the base population are related and inbred with a relationship coefficient γ and an inbreeding coefficient γ / 2. Taken together, this γ parameter and a parameter that scales the marker-based relationship matrix can handle the issue of compatibility between marker-based and pedigree-based relationship matrices. The full log-likelihood function used for parameter inference contains two terms. The first term is the REML-log-likelihood for the phenotypes conditional on the observed marker genotypes, whereas the second term is the log-likelihood for the observed marker genotypes. Analyses of the two simulated datasets with this new method showed that 1) the parameters involved in adjusting marker-based and pedigree-based relationship matrices can depend on both observed phenotypes and observed marker genotypes and 2) a strong association between these two parameters exists. Finally, this method performed at least as well as a method based on adjusting the marker-based relationship matrix.ConclusionsUsing the full log-likelihood and adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix provides a new and interesting approach to handle the issue of compatibility between the two matrices in single-step genetic evaluation.