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.     

Marker-based estimation of the coefficient of coancestry in hybrid breeding programmes

Molecular markers allow to estimate the pairwise relatedness between the members of a breeding pool when their selection history is no longer available or has become too complex for a classical pedigree analysis. The field of population genetics has several estimation procedures at its disposal, but when the genotyped individuals are highly selected inbred lines, their application is not warranted as the theoretical assumptions on which these estimators were built, usually linkage equilibrium between marker loci or even Hardy–Weinberg equilibrium, are not met. An alternative approach requires the availability of a genotyped reference set of inbred lines, which allows to correct the observed marker similarities for their inherent upward bias when used as a coancestry measure. However, this approach does not guarantee that the resulting coancestry matrix is at least positive semi-definite (psd), a necessary condition for its use as a covariance matrix. In this paper we present the weighted alikeness in state (WAIS) estimator. This marker-based coancestry estimator is compared to several other commonly applied relatedness estimators under realistic hybrid breeding conditions in a number of simulations. We also fit a linear mixed model to phenotypical data from a commercial maize breeding programme and compare the likelihood of the different variance structures. WAIS is shown to be psd which makes it suitable for modelling the covariance between genetic components in linear mixed models involved in breeding value estimation or association studies. Results indicate that it generally produces a low root mean squared error under different breeding circumstances and provides a fit to the data that is comparable to that of several other marker-based alternatives. Recommendations for each of the examined coancestry measures are provided.     

Pedigree-Free Estimates of Heritability in the Wild: Promising Prospects for Selfing Populations

Estimating the genetic variance available for traits informs us about a population’s ability to evolve in response to novel selective challenges. In selfing species, theory predicts a loss of genetic diversity that could lead to an evolutionary dead-end, but empirical support remains scarce. Genetic variability in a trait is estimated by correlating the phenotypic resemblance with the proportion of the genome that two relatives share identical by descent (‘realized relatedness’). The latter is traditionally predicted from pedigrees (Φ_A: expected value) but can also be estimated using molecular markers (average number of alleles shared). Nevertheless, evolutionary biologists, unlike animal breeders, remain cautious about using marker-based relatedness coefficients to study complex phenotypic traits in populations. In this paper, we review published results comparing five different pedigree-free methods and use simulations to test individual-based models (hereafter called animal models) using marker-based relatedness coefficients, with a special focus on the influence of mating systems. Our literature review confirms that Ritland’s regression method is unreliable, but suggests that animal models with marker-based estimates of relatedness and genomic selection are promising and that more testing is required. Our simulations show that using molecular markers instead of pedigrees in animal models seriously worsens the estimation of heritability in outcrossing populations, unless a very large number of loci is available. In selfing populations the results are less biased. More generally, populations with high identity disequilibrium (consanguineous or bottlenecked populations) could be propitious for using marker-based animal models, but are also more likely to deviate from the standard assumptions of quantitative genetics models (non-additive variance).     

Least squares interval mapping of quantitative trait loci under the infinitesimal genetic model in outbred populations.

Genetic marker and phenotypic data for a quantitative trait were simulated on 20 paternal half-sib families with 100 progeny to investigate properties of within-family-regression interval mapping of a postulated single quantitative trait locus (QTL) in a marker interval under the infinitesimal genetic model, which has been the basis of the application of quantitative genetics to genetic improvement programs, and to investigate use of the infinitesimal model as null hypothesis in testing for presence of a major QTL. Genetic effects on the marked chromosome were generated based on a major gene model, which simulated a central biallelic QTL, or based on 101 biallelic QTL of equal effect, which approximated the infinitesimal model. The marked chromosome contained 0, 3.3%, 13.3%, or 33.3% of genetic variance and heritability was 0.25 or 0.70. Under the polygenic model with 3.3% of genetic variance on the marked chromosome, which corresponds to the infinitesimal model for the bovine, significant QTL effects were found for individual families. Correlations between estimates of QTL effects and true chromosome substitution effects were 0.29 and 0.47 for heritabilities of 0.25 and 0.70 but up to 0.85 with 33.3% of polygenic variance on the marked chromosome. These results illustrate the potential of marker-assisted selection even under the infinitesimal genetic model. Power of tests for presence of QTL was substantially reduced when the polygenic model with 3.3% of genetic variance on the chromosome was used as a null hypothesis. The ability to determine whether genetic variance on a chromosome was contributed by a single QTL of major effect or a large number of QTL with minor effects, corresponding to the infinitesimal model, was limited.     

Best Linear Unbiased Prediction of Genomic Breeding Values Using a Trait-Specific Marker-Derived Relationship Matrix

Background

With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest.

Methodology/Principal Findings

In the framework of mixed model equations, a new best linear unbiased prediction (BLUP) method including a trait-specific relationship matrix (TA) was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP) and BLUP with realized relationship matrix (GBLUP). It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario.

Conclusions/Significance

The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that explain more of the genetic variance in the trait.     

Prediction of breeding values and selection responses with genetic heterogeneity of environmental variance

There is empirical evidence that genotypes differ not only in mean, but also in environmental variance of the traits they affect. Genetic heterogeneity of environmental variance may indicate genetic differences in environmental sensitivity. The aim of this study was to develop a general framework for prediction of breeding values and selection responses in mean and environmental variance with genetic heterogeneity of environmental variance. Both means and environmental variances were treated as heritable traits. Breeding values and selection responses were predicted with little bias using linear, quadratic, and cubic regression on individual phenotype or using linear regression on the mean and within-family variance of a group of relatives. A measure of heritability was proposed for environmental variance to standardize results in the literature and to facilitate comparisons to "conventional" traits. Genetic heterogeneity of environmental variance can be considered as a trait with a low heritability. Although a large amount of information is necessary to accurately estimate breeding values for environmental variance, response in environmental variance can be substantial, even with mass selection. The methods developed allow use of the well-known selection index framework to evaluate breeding strategies and effects of natural selection that simultaneously change the mean and the variance.     

A MARKER-BASED METHOD FOR INFERENCES ABOUT QUANTITATIVE INHERITANCE IN NATURAL POPULATIONS

A marker-based method for studying quantitative genetic characters in natural populations is presented and evaluated. The method involves regressing quantitative trait similarity on marker-estimated relatedness between individuals. A procedure is first given for estimating the narrow sense heritability and additive genetic correlations among traits, incorporating shared environments. Estimation of the actual variance of relatedness is required for heritability, but not for genetic correlations. The approach is then extended to include isolation by distance of environments, dominance, and shared levels of inbreeding. Investigations of statistical properties show that good estimates do not require great marker polymorphism, but rather require significant variation of actual relatedness; optimal allocation generally favors sampling many individuals at the expense of assaying fewer marker loci; when relatedness declines with physical distance, it is optimal to restrict comparisons to within a certain distance; the power to estimate shared environments and inbreeding effects is reasonable, but estimates of dominance variance may be difficult under certain patterns of relationship; and any linkage of markers to quantitative trait loci does not cause significant problems. This marker-based method makes possible studies with long-lived organisms or with organisms difficult to culture, and opens the possibility that quantitative trait expression in natural environments can be analyzed in an unmanipulative way.     

Mixed Model Methods for Genomic Prediction and Variance Component Estimation of Additive and Dominance Effects Using SNP Markers

We established a genomic model of quantitative trait with genomic additive and dominance relationships that parallels the traditional quantitative genetics model, which partitions a genotypic value as breeding value plus dominance deviation and calculates additive and dominance relationships using pedigree information. Based on this genomic model, two sets of computationally complementary but mathematically identical mixed model methods were developed for genomic best linear unbiased prediction (GBLUP) and genomic restricted maximum likelihood estimation (GREML) of additive and dominance effects using SNP markers. These two sets are referred to as the CE and QM sets, where the CE set was designed for large numbers of markers and the QM set was designed for large numbers of individuals. GBLUP and associated accuracy formulations for individuals in training and validation data sets were derived for breeding values, dominance deviations and genotypic values. Simulation study showed that GREML and GBLUP generally were able to capture small additive and dominance effects that each accounted for 0.00005–0.0003 of the phenotypic variance and GREML was able to differentiate true additive and dominance heritability levels. GBLUP of the total genetic value as the summation of additive and dominance effects had higher prediction accuracy than either additive or dominance GBLUP, causal variants had the highest accuracy of GREML and GBLUP, and predicted accuracies were in agreement with observed accuracies. Genomic additive and dominance relationship matrices using SNP markers were consistent with theoretical expectations. The GREML and GBLUP methods can be an effective tool for assessing the type and magnitude of genetic effects affecting a phenotype and for predicting the total genetic value at the whole genome level.     

Estimates of missing heritability for complex traits in Brown Swiss cattle

Background

Genomic 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.

Methods

Two 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).

Results

When 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.

Conclusions

When 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.     

Construction of an SSR and RAD Marker-Based Genetic Linkage Map for Carnation (<Emphasis Type="Italic">Dianthus caryophyllus</Emphasis> L.)

A high-density genetic map, an essential tool for comparative genomic studies and quantitative trait locus fine mapping, can also facilitate genome sequence assembly. The sequence-based marker technology known as restriction site-associated DNA (RAD) enables synchronous, single nucleotide polymorphism marker discovery, and genotyping using massively parallel sequencing. We constructed a high-density linkage map for carnation (Dianthus caryophyllus L.) based on simple sequence repeat (SSR) markers in combination with RAD markers developed by double-digest RAD sequencing (ddRAD-seq). A total of 2404 (285 SSR and 2119 RAD) markers could be assigned to 15 linkage groups spanning 971.5 cM, with an average marker interval of 0.4 cM. The total length of scaffolds with identified map positions was 95.6 Mb, which is equivalent to 15.4 % of the estimated genome size. The generated map is the first SSR and RAD marker-based high-density linkage map reported for carnation. The ddRAD-seq pipeline developed in this study should also help accelerate genetic and genomics analyses and molecular breeding of carnation and other non-model crops.     

Genetic response from marker assisted selection in an outbred population for differing marker bracket sizes and with two identified quantitative trait loci.

Effect of flanking quantitative trait loci (QTL)-marker bracket size on genetic response to marker assisted selection in an outbred population was studied by simulation of a nucleus breeding scheme. In addition, genetic response with marker assisted selection (MAS) from two quantitative trait loci on the same and different chromosome(s) was investigated. QTL that explained either 5% or 10% of phenotypic variance were simulated. A polygenic component was simulated in addition to the quantitative trait loci. In total, 35% of the phenotypic variance was due to genetic factors. The trait was measured on females only. Having smaller marker brackets flanking the QTL increased the genetic response from MAS selection. This was due to the greater ability to trace the QTL transmission from one generation to the next with the smaller flanking QTL-marker bracket, which increased the accuracy of estimation of the QTL allelic effects. Greater negative covariance between effects at both QTL was observed when two QTL were located on the same chromosome compared to different chromosomes. Genetic response with MAS was greater when the QTL were on the same chromosome in the early generations and greater when they were on different chromosomes in the later generations of MAS.     

InterStoreDB:A Generic Integration Resource for Genetic and Genomic Data

Associating phenotypic traits and quantitative trait loci (QTL) to causative regions of the underlying genome is a key goal in agricultural research.InterStoreDB is a suite of integrated databases designed to assist in this process.The individual databases are species independent and generic in design,providing access to curated datasets relating to plant populations,phenotypic traits,genetic maps,marker loci and QTL,with links to functional gene annotation and genomic sequence data.Each component database provides access to associated metadata,including data provenance and parameters used in analyses,thus providing users with information to evaluate the relative worth of any associations identified.The databases include CropStoreDB,for management of population,genetic map,QTL and trait measurement data,SeqStoreDB for sequence-related data and AlignStoreDB,which stores sequence alignment information,and allows navigation between genetic and genomic datasets.Genetic maps are visualized and compared using the CMAP tool,and functional annotation from sequenced genomes is provided via an EnsEMBL-based genome browser.This framework facilitates navigation of the multiple biological domains involved in genetics and genomics research in a transparent manner within a single portal.We demonstrate the value of InterStoreDB as a tool for Brassica research.InterStoreDB is available from:http://www.interstoredb.org     

A classical setting for associations between markers and loci affecting quantitative traits

We examine the relationships between a genetic marker and a locus affecting a quantitative trait by decomposing the genetic effects of the marker locus into additive and dominance effects under a classical genetic model. We discuss the structure of the associations between the marker and the trait locus, paying attention to non-random union of gametes, multiple alleles at the marker and trait loci, and non-additivity of allelic effects at the trait locus. We consider that this greater-than-usual level of generality leads to additional insights, in a way reminiscent of Cockerham's decomposition of genetic variance into five terms: three terms in addition to the usual additive and dominance terms. Using our framework, we examine several common tests of association between a marker and a trait.     

Comparison of linkage-disequilibrium methods for localization of genes influencing quantitative traits in humans

Linkage disequilibrium has been used to help in the identification of genes predisposing to certain qualitative diseases. Although several linkage-disequilibrium tests have been developed for localization of genes influencing quantitative traits, these tests have not been thoroughly compared with one another. In this report we compare, under a variety of conditions, several different linkage-disequilibrium tests for identification of loci affecting quantitative traits. These tests use either single individuals or parent-child trios. When we compared tests with equal samples, we found that the truncated measured allele (TMA) test was the most powerful. The trait allele frequencies, the stringency of sample ascertainment, the number of marker alleles, and the linked genetic variance affected the power, but the presence of polygenes did not. When there were more than two trait alleles at a locus in the population, power to detect disequilibrium was greatly diminished. The presence of unlinked disequilibrium (D'*) increased the false-positive error rates of disequilibrium tests involving single individuals but did not affect the error rates of tests using family trios. The increase in error rates was affected by the stringency of selection, the trait allele frequency, and the linked genetic variance but not by polygenic factors. In an equilibrium population, the TMA test is most powerful, but, when adjusted for the presence of admixture, Allison test 3 becomes the most powerful whenever D'*>.15.     

QTL detection with bidirectional and unidirectional selective genotyping: marker-based and trait-based analyses

Selective genotyping of one or both phenotypic extremes of a population can be used to detect linkage between markers and quantitative trait loci (QTL) in situations in which full-population genotyping is too costly or not feasible, or where the objective is to rapidly screen large numbers of potential donors for useful alleles with large effects. Data may be subjected to 'trait-based' analysis, in which marker allele frequencies are compared between classes of progeny defined based on trait values, or to 'marker-based' analysis, in which trait means are compared between progeny classes defined based on marker genotypes. Here, bidirectional and unidirectional selective genotyping were simulated, using population sizes and selection intensities relevant to cereal breeding. Control of Type I error was usually adequate with marker-based analysis of variance or trait-based testing using the normal approximation of the binomial distribution. Bidirectional selective genotyping was more powerful than unidirectional. Trait-based analysis and marker-based analysis of variance were about equally powerful. With genotyping of the best 30 out of 500 lines (6%), a QTL explaining 15% of the phenotypic variance could be detected with a power of 0.8 when tests were conducted at a marker 10 cM from the QTL. With bidirectional selective genotyping, QTL with smaller effects and (or) QTL farther from the nearest marker could be detected. Similar QTL detection approaches were applied to data from a population of 436 recombinant inbred rice lines segregating for a large-effect QTL affecting grain yield under drought stress. That QTL was reliably detected by genotyping as few as 20 selected lines (4.5%). In experimental populations, selective genotyping can reduce costs of QTL detection, allowing larger numbers of potential donors to be screened for useful alleles with effects across different backgrounds. In plant breeding programs, selective genotyping can make it possible to detect QTL using even a limited number of progeny that have been retained after selection.     

Estimating linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.     

Accounting for Genetic Architecture Improves Sequence Based Genomic Prediction for a Drosophila Fitness Trait

The ability to predict quantitative trait phenotypes from molecular polymorphism data will revolutionize evolutionary biology, medicine and human biology, and animal and plant breeding. Efforts to map quantitative trait loci have yielded novel insights into the biology of quantitative traits, but the combination of individually significant quantitative trait loci typically has low predictive ability. Utilizing all segregating variants can give good predictive ability in plant and animal breeding populations, but gives little insight into trait biology. Here, we used the Drosophila Genetic Reference Panel to perform both a genome wide association analysis and genomic prediction for the fitness-related trait chill coma recovery time. We found substantial total genetic variation for chill coma recovery time, with a genetic architecture that differs between males and females, a small number of molecular variants with large main effects, and evidence for epistasis. Although the top additive variants explained 36% (17%) of the genetic variance among lines in females (males), the predictive ability using genomic best linear unbiased prediction and a relationship matrix using all common segregating variants was very low for females and zero for males. We hypothesized that the low predictive ability was due to the mismatch between the infinitesimal genetic architecture assumed by the genomic best linear unbiased prediction model and the true genetic architecture of chill coma recovery time. Indeed, we found that the predictive ability of the genomic best linear unbiased prediction model is markedly improved when we combine quantitative trait locus mapping with genomic prediction by only including the top variants associated with main and epistatic effects in the relationship matrix. This trait-associated prediction approach has the advantage that it yields biologically interpretable prediction models.     

Novel Genomic Tools and Modern Genetic and Breeding Approaches for Crop Improvement

In recent past, genomic tools especially molecular markers have been extensively used for understanding genome dynamics as well for applied aspects in crop breeding. Several new genomics technologies such as next generation sequencing (NGS), high-throughput marker genotyping, -omics technologies have emerged as powerful tools for understanding genome variation in crop species at DNA, RNA as well as protein level. These technologies promise to provide an insight into the way gene(s) are expressed and regulated in cell and to unveil metabolic pathways involved in trait(s) of interest for breeders not only in model-/major- but even for under-resourced crop species which were once considered “orphan” crops. In parallel, genetic variation for a species present not only in cultivated genepool but even in landraces and wild species can be harnessed by using new genetic approaches such as advanced-backcross QTL (AB-QTL) analysis, introgression libraries (ILs), multi-parent advanced generation intercross (MAGIC) population and association genetics. The gene(s) or genomic regions, responsible for trait(s) of interest, identified either through conventional linkage mapping or above mentioned approaches can be introgressed or pyramided to develop superior genotypes through molecular breeding approaches such as marker-assisted back crossing (MABC), marker assisted recurrent selection (MARS) and genome wide selection (GWS). This article provides an overview on some recent genomic tools and novel genetic and breeding approaches as mentioned above with a final aim of crop improvement.     

Estimates of genetic parameters and breeding values from western larch open-pollinated families using marker-based relationship

The availability and affordability of genetic markers made it possible to estimate quantitative genetic parameters without mating designs' structured pedigree. Here, we compared 4-year height's heritability and individuals' breeding values for a western larch common-garden population of 1,418 offspring representing 15 open-pollinated families from a 41-clone seed orchard using (a) classical pedigree models such as half- and full-sib families and (b) a molecular marker-based pedigree-free model using four pair-wise relationship estimation methods using eight informative SSR markers. The results highlighted the commonly observed inflated estimates of genetic parameters often obtained from half-sib analyses, as well as demonstrating some of the full-sib analyses' caveats. The pedigree reconstruction permitted the identification of selfed individuals, thus allowing evaluating the impact of selfing on marker-based genetic parameter estimation. The results demonstrated the utility of marker-based methods as an alternative to the classical pedigree-based approaches. Unlike the pedigree-based methods, the marker-based approach allowed better partitioning the variance components as well as separating the non-additive and additive genetic variance. The theoretical underpinning of the marker-based approach was discussed.