Estimate Marker Effects Research Articles

Editorial [Hot Topic: Genetics Dissection of Complex Traits in the Genomic Era (Guest Editor: Bernardo Ordas)

Editorial [Hot Topic: Genetics Dissection of Complex Traits in the Genomic Era (Guest Editor: Bernardo Ordas)

Long-term response to genomic selection: effects of estimation method and reference population structure for different genetic architectures

BackgroundGenomic selection has become an important tool in the genetic improvement of animals and plants. The objective of this study was to investigate the impacts of breeding value estimation method, reference population structure, and trait genetic architecture, on long-term response to genomic selection without updating marker effects.MethodsThree methods were used to estimate genomic breeding values: a BLUP method with relationships estimated from genome-wide markers (GBLUP), a Bayesian method, and a partial least squares regression method (PLSR). A shallow (individuals from one generation) or deep reference population (individuals from five generations) was used with each method. The effects of the different selection approaches were compared under four different genetic architectures for the trait under selection. Selection was based on one of the three genomic breeding values, on pedigree BLUP breeding values, or performed at random. Selection continued for ten generations.ResultsDifferences in long-term selection response were small. For a genetic architecture with a very small number of three to four quantitative trait loci (QTL), the Bayesian method achieved a response that was 0.05 to 0.1 genetic standard deviation higher than other methods in generation 10. For genetic architectures with approximately 30 to 300 QTL, PLSR (shallow reference) or GBLUP (deep reference) had an average advantage of 0.2 genetic standard deviation over the Bayesian method in generation 10. GBLUP resulted in 0.6% and 0.9% less inbreeding than PLSR and BM and on average a one third smaller reduction of genetic variance. Responses in early generations were greater with the shallow reference population while long-term response was not affected by reference population structure.ConclusionsThe ranking of estimation methods was different with than without selection. Under selection, applying GBLUP led to lower inbreeding and a smaller reduction of genetic variance while a similar response to selection was achieved. The reference population structure had a limited effect on long-term accuracy and response. Use of a shallow reference population, most closely related to the selection candidates, gave early benefits while in later generations, when marker effects were not updated, the estimation of marker effects based on a deeper reference population did not pay off.

A comparison of statistical methods for genomic selection in a mice population

BackgroundThe availability of high-density panels of SNP markers has opened new perspectives for marker-assisted selection strategies, such that genotypes for these markers are used to predict the genetic merit of selection candidates. Because the number of markers is often much larger than the number of phenotypes, marker effect estimation is not a trivial task. The objective of this research was to compare the predictive performance of ten different statistical methods employed in genomic selection, by analyzing data from a heterogeneous stock mice population.ResultsFor the five traits analyzed (W6W: weight at six weeks, WGS: growth slope, BL: body length, %CD8+: percentage of CD8+ cells, CD4+/ CD8+: ratio between CD4+ and CD8+ cells), within-family predictions were more accurate than across-family predictions, although this superiority in accuracy varied markedly across traits. For within-family prediction, two kernel methods, Reproducing Kernel Hilbert Spaces Regression (RKHS) and Support Vector Regression (SVR), were the most accurate for W6W, while a polygenic model also had comparable performance. A form of ridge regression assuming that all markers contribute to the additive variance (RR_GBLUP) figured among the most accurate for WGS and BL, while two variable selection methods ( LASSO and Random Forest, RF) had the greatest predictive abilities for %CD8+ and CD4+/ CD8+. RF, RKHS, SVR and RR_GBLUP outperformed the remainder methods in terms of bias and inflation of predictions.ConclusionsMethods with large conceptual differences reached very similar predictive abilities and a clear re-ranking of methods was observed in function of the trait analyzed. Variable selection methods were more accurate than the remainder in the case of %CD8+ and CD4+/CD8+ and these traits are likely to be influenced by a smaller number of QTL than the remainder. Judged by their overall performance across traits and computational requirements, RR_GBLUP, RKHS and SVR are particularly appealing for application in genomic selection.

Genomic Selection in Plant Breeding: A Comparison of Models

ABSTRACTSimulation and empirical studies of genomic selection (GS) show accuracies sufficient to generate rapid genetic gains. However, with the increased popularity of GS approaches, numerous models have been proposed and no comparative analysis is available to identify the most promising ones. Using eight wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), Arabidopsis thaliana (L.) Heynh., and maize (Zea mays L.) datasets, the predictive ability of currently available GS models along with several machine learning methods was evaluated by comparing accuracies, the genomic estimated breeding values (GEBVs), and the marker effects for each model. While a similar level of accuracy was observed for many models, the level of overfitting varied widely as did the computation time and the distribution of marker effect estimates. Our comparisons suggested that GS in plant breeding programs could be based on a reduced set of models such as the Bayesian Lasso, weighted Bayesian shrinkage regression (wBSR, a fast version of BayesB), and random forest (RF) (a machine learning method that could capture nonadditive effects). Linear combinations of different models were tested as well as bagging and boosting methods, but they did not improve accuracy. This study also showed large differences in accuracy between subpopulations within a dataset that could not always be explained by differences in phenotypic variance and size. The broad diversity of empirical datasets tested here adds evidence that GS could increase genetic gain per unit of time and cost.

Accuracies of genomic breeding values in American Angus beef cattle using K-means clustering for cross-validation

BackgroundGenomic selection is a recently developed technology that is beginning to revolutionize animal breeding. The objective of this study was to estimate marker effects to derive prediction equations for direct genomic values for 16 routinely recorded traits of American Angus beef cattle and quantify corresponding accuracies of prediction.MethodsDeregressed estimated breeding values were used as observations in a weighted analysis to derive direct genomic values for 3570 sires genotyped using the Illumina BovineSNP50 BeadChip. These bulls were clustered into five groups using K-means clustering on pedigree estimates of additive genetic relationships between animals, with the aim of increasing within-group and decreasing between-group relationships. All five combinations of four groups were used for model training, with cross-validation performed in the group not used in training. Bivariate animal models were used for each trait to estimate the genetic correlation between deregressed estimated breeding values and direct genomic values.ResultsAccuracies of direct genomic values ranged from 0.22 to 0.69 for the studied traits, with an average of 0.44. Predictions were more accurate when animals within the validation group were more closely related to animals in the training set. When training and validation sets were formed by random allocation, the accuracies of direct genomic values ranged from 0.38 to 0.85, with an average of 0.65, reflecting the greater relationship between animals in training and validation. The accuracies of direct genomic values obtained from training on older animals and validating in younger animals were intermediate to the accuracies obtained from K-means clustering and random clustering for most traits. The genetic correlation between deregressed estimated breeding values and direct genomic values ranged from 0.15 to 0.80 for the traits studied.ConclusionsThese results suggest that genomic estimates of genetic merit can be produced in beef cattle at a young age but the recurrent inclusion of genotyped sires in retraining analyses will be necessary to routinely produce for the industry the direct genomic values with the highest accuracy.

BREEDING AND GENETICS SYMPOSIUM: Really big data: Processing and analysis of very large data sets1

Modern animal breeding data sets are large and getting larger, due in part to recent availability of high-density SNP arrays and cheap sequencing technology. High-performance computing methods for efficient data warehousing and analysis are under development. Financial and security considerations are important when using shared clusters. Sound software engineering practices are needed, and it is better to use existing solutions when possible. Storage requirements for genotypes are modest, although full-sequence data will require greater storage capacity. Storage requirements for intermediate and results files for genetic evaluations are much greater, particularly when multiple runs must be stored for research and validation studies. The greatest gains in accuracy from genomic selection have been realized for traits of low heritability, and there is increasing interest in new health and management traits. The collection of sufficient phenotypes to produce accurate evaluations may take many years, and high-reliability proofs for older bulls are needed to estimate marker effects. Data mining algorithms applied to large data sets may help identify unexpected relationships in the data, and improved visualization tools will provide insights. Genomic selection using large data requires a lot of computing power, particularly when large fractions of the population are genotyped. Theoretical improvements have made possible the inversion of large numerator relationship matrices, permitted the solving of large systems of equations, and produced fast algorithms for variance component estimation. Recent work shows that single-step approaches combining BLUP with a genomic relationship (G) matrix have similar computational requirements to traditional BLUP, and the limiting factor is the construction and inversion of G for many genotypes. A naïve algorithm for creating G for 14,000 individuals required almost 24 h to run, but custom libraries and parallel computing reduced that to 15 m. Large data sets also create challenges for the delivery of genetic evaluations that must be overcome in a way that does not disrupt the transition from conventional to genomic evaluations. Processing time is important, especially as real-time systems for on-farm decisions are developed. The ultimate value of these systems is to decrease time-to-results in research, increase accuracy in genomic evaluations, and accelerate rates of genetic improvement.

Evaluation of genome-wide selection efficiency in maize nested association mapping populations

In comparison to conventional marker-assisted selection (MAS), which utilizes only a subset of genetic markers associated with a trait to predict breeding values (BVs), genome-wide selection (GWS) improves prediction accuracies by incorporating all markers into a model simultaneously. This strategy avoids risks of missing quantitative trait loci (QTL) with small effects. Here, we evaluated the accuracy of prediction for three corn flowering traits days to silking, days to anthesis, and anthesis-silking interval with GWS based on cross-validation experiments using a large data set of 25 nested association mapping populations in maize (Zea mays). We found that GWS via ridge regression-best linear unbiased prediction (RR-BLUP) gave significantly higher predictions compared to MAS utilizing composite interval mapping (CIM). The CIM method may be selected over multiple linear regression to decrease over-estimations of the efficiency of GWS over a MAS strategy. The RR-BLUP method was the preferred method for estimating marker effects in GWS with prediction accuracies comparable to or greater than BayesA and BayesB. The accuracy with RR-BLUP increased with training sample proportion, marker density, and heritability until it reached a plateau. In general, gains in accuracy with RR-BLUP over CIM increased with decreases of these factors. Compared to training sample proportion, the accuracy of prediction with RR-BLUP was relatively insensitive to marker density.

Genomic selection in loblolly pine - from lab to field

Background Tree breeding is logistically complex and expensive, and breeders have long sought to use molecular markers to accelerate breeding. A candidate gene approach based on testing for association between the presence of DNA sequence variation in or near candidate genes, and phenotypic variation in a population has long been explored [1,2]. However, using candidate gene approach (QTLs) has not been successful in breeding [3,4]. QTL-trait associations detected in one genetic background are often not observed in other families, because of recombination of genes during the segregation and low levels of linkage disequilibrium in the population. A new technology called genomic selection (GS) is revolutionizing dairy cattle breeding. In GS, marker effects are first estimated in a large training population (>500) with both phenotypic and genotypic data. Subsequently, estimated marker effects are used to predict breeding values in validation populations for which marker genotypes but not phenotypes are available [4]. Several dairy cattle breeding companies now routinely use GS to select and market bulls. The success of GS in cattle breeding is largely based on bovine genome sequencing and discovery of thousands of SNP markers. GS application, if successful, will have a great impact on forest tree breeding because of their complex and logistically difficult breeding programs. Although, there have been several simulation studies examining the effective population size, linkage disequilibrium, and heritability on the predicted accuracy of GS in tree breeding [5], GS has not yet been demonstrated for forest trees using empirical markers data, mainly due to lack of sufficient dense markers. Methods Biallelic SNP markers provided by the CTGN project (http://dendrome.ucdavis.edu/ctgn/) were used for genotyping. A population of 149 cloned full-sib offspring of loblolly pine (Pinus taeda L.) was phenotyped. Fitting 3406 informative SNP markers simultaneously, we estimated genome-wide breeding values and compared them with breeding values based on pedigree model. Variances explained by the marker additive and dominant effects were obtained.

Marker-Assisted Selection to Pyramid Nematode Resistance and the High Oleic Trait in Peanut

Despite important strides in marker technologies, the use of marker-assisted selection has stagnated for the improvement of quantitative traits. Biparental mating designs for the detection of loci affecting these traits (quantitative trait loci [QTL]) impede their application, and the statistical methods used are ill-suited to the traits' polygenic nature. Genomic selection (GS) has been proposed to address these deficiencies. Genomic selection predicts the breeding values of lines in a population by analyzing their phenotypes and high-density marker scores. A key to the success of GS is that it incorporates all marker information in the prediction model, thereby avoiding biased marker effect estimates and capturing more of the variation due to small-effect QTL. In simulations, the correlation between true breeding value and the genomic estimated breeding value has reached levels of 0.85 even for polygenic low heritability traits. This level of accuracy is sufficient to consider selecting for agronomic performance using marker information alone. Such selection would substantially accelerate the breeding cycle, enhancing gains per unit time. It would dramatically change the role of phenotyping, which would then serve to update prediction models and no longer to select lines. While research to date shows the exceptional promise of GS, work remains to be done to validate it empirically and to incorporate it into breeding schemes.

Allele coding in genomic evaluation

BackgroundGenomic data are used in animal breeding to assist genetic evaluation. Several models to estimate genomic breeding values have been studied. In general, two approaches have been used. One approach estimates the marker effects first and then, genomic breeding values are obtained by summing marker effects. In the second approach, genomic breeding values are estimated directly using an equivalent model with a genomic relationship matrix. Allele coding is the method chosen to assign values to the regression coefficients in the statistical model. A common allele coding is zero for the homozygous genotype of the first allele, one for the heterozygote, and two for the homozygous genotype for the other allele. Another common allele coding changes these regression coefficients by subtracting a value from each marker such that the mean of regression coefficients is zero within each marker. We call this centered allele coding. This study considered effects of different allele coding methods on inference. Both marker-based and equivalent models were considered, and restricted maximum likelihood and Bayesian methods were used in inference.ResultsTheoretical derivations showed that parameter estimates and estimated marker effects in marker-based models are the same irrespective of the allele coding, provided that the model has a fixed general mean. For the equivalent models, the same results hold, even though different allele coding methods lead to different genomic relationship matrices. Calculated genomic breeding values are independent of allele coding when the estimate of the general mean is included into the values. Reliabilities of estimated genomic breeding values calculated using elements of the inverse of the coefficient matrix depend on the allele coding because different allele coding methods imply different models. Finally, allele coding affects the mixing of Markov chain Monte Carlo algorithms, with the centered coding being the best.ConclusionsDifferent allele coding methods lead to the same inference in the marker-based and equivalent models when a fixed general mean is included in the model. However, reliabilities of genomic breeding values are affected by the allele coding method used. The centered coding has some numerical advantages when Markov chain Monte Carlo methods are used.

Accuracy of genomic breeding values for residual feed intake in crossbred beef cattle1

The benefit of using genomic breeding values (GEBV) in predicting ADG, DMI, and residual feed intake for an admixed population was investigated. Phenotypic data consisting of individual daily feed intake measurements for 721 beef cattle steers tested over 5 yr was available for analysis. The animals used were an admixed population of spring-born steers, progeny of a cross between 3 sire breeds and a composite dam line. Training and validation data sets were defined by randomly splitting the data into training and testing data sets based on sire family so that there was no overlap of sires in the 2 sets. The random split was replicated to obtain 5 separate data sets. Two methods (BayesB and random regression BLUP) were used to estimate marker effects and to define marker panels and ultimately the GEBV. The accuracy of prediction (the correlation between the phenotypes and GEBV) was compared between SNP panels. Accuracy for all traits was low, ranging from 0.223 to 0.479 for marker panels with 200 SNP, and 0.114 to 0.246 for marker panels with 37,959 SNP, depending on the genomic selection method used. This was less than accuracies observed for polygenic EBV accuracies, which ranged from 0.504 to 0.602. The results obtained from this study demonstrate that the utility of genetic markers for genomic prediction of residual feed intake in beef cattle may be suboptimal. Differences in accuracy were observed between sire breeds when the random regression BLUP method was used, which may imply that the correlations obtained by this method were confounded by the ability of the selected SNP to trace breed differences. This may also suggest that prediction equations derived from such an admixed population may be useful only in populations of similar composition. Given the sample size used in this study, there is a need for increased feed intake testing if substantially greater accuracies are to be achieved.

Genomic Selection and Prediction in Plant Breeding

The availability of thousands of genome-wide molecular markers has made possible the use of genomic selection in plants and animals. However, the evaluation of models for genomic selection in plant breeding populations remains limited. In this study, we provide an overview of several models for genomic selection, whose predictive ability we investigate using two plant data sets. The first data set comprises historical phenotypic records of a series of wheat (Triticum aestivum L.) trials evaluated in 10 environments and recently generated genomic data. The second data set pertains to international maize (Zea mays L.) trials in which two disease traits (Exserohilum turcicum and Cercospora zeae-maydis) of maize lines evaluated in five environments were measured. Results showed that models including marker information yielded important gains in predictive ability relative to that of a pedigree-based model, this with a modest number of markers. Estimates of marker effects were different across environmental conditions, indicating that genotype × environment interaction was an important component of genetic variability. Overall, the study provided evidence from real populations indicating that genomic selection could be an effective tool for improving traits of economic importance in commercial crops.

Accuracy of genomic selection in simulated populations mimicking the extent of linkage disequilibrium in beef cattle

BackgroundThe success of genomic selection depends mainly on the extent of linkage disequilibrium (LD) between markers and quantitative trait loci (QTL), the number of animals in the training set (TS) and the heritability (h2) of the trait. The extent of LD depends on the genetic structure of the population and the density of markers. The aim of this study was to calculate accuracy of direct genomic estimated breeding values (DGEBV) using best linear unbiased genomic prediction (GBLUP) for different marker densities, heritabilities and sizes of the TS in simulated populations that mimicked previously reported extent and pattern of LD in beef cattle.ResultsThe accuracy of DGEBV increased significantly (p < 0.05) with the increase in the number of bulls in the TS (480, 960 or 1920), trait h2 (0.10, 0.25 or 0.40) and marker densities (40 k or 800 k). Increasing the number of animals in the TS by 4-fold and using their phenotypes to estimate marker effects was not sufficient to maintain or increase the accuracy of DGEBV obtained using estimated breeding values (EBVs) when the trait h2 was lower than 0.40 for both marker densities. Comparing to expected accuracies of parent average (PA), the gains by using DGEBV would be of 27%, 13% and 10% for trait h2 equal to 0.10, 0.25 and 0.40, respectively, considering the scenario with 40 k markers and 1920 bulls in TS.ConclusionsAs reported in dairy cattle, the size of the TS and the extent of LD have major impact on the accuracy of DGEBV. Based on the findings of this simulation study, large TS, as well as dense marker panels, aiming to increase the level of LD between markers and QTL, will likely be needed in beef cattle for successful implementation of genomic selection.

The use of communal rearing of families and DNA pooling in aquaculture genomic selection schemes

BackgroundTraditional family-based aquaculture breeding programs, in which families are kept separately until individual tagging and most traits are measured on the sibs of the candidates, are costly and require a high level of reproductive control. The most widely used alternative is a selection scheme, where families are reared communally and the candidates are selected based on their own individual measurements of the traits under selection. However, in the latter selection schemes, inclusion of new traits depends on the availability of non-invasive techniques to measure the traits on selection candidates. This is a severe limitation of these schemes, especially for disease resistance and fillet quality traits.MethodsHere, we present a new selection scheme, which was validated using computer simulations comprising 100 families, among which 1, 10 or 100 were reared communally in groups. Pooling of the DNA from 2000, 20000 or 50000 test individuals with the highest and lowest phenotypes was used to estimate 500, 5000 or 10000 marker effects. One thousand or 2000 out of 20000 candidates were preselected for a growth-like trait. These pre-selected candidates were genotyped, and they were selected on their genome-wide breeding values for a trait that could not be measured on the candidates.ResultsA high accuracy of selection, i.e. 0.60-0.88 was obtained with 20000-50000 test individuals but it was reduced when only 2000 test individuals were used. This shows the importance of having large numbers of phenotypic records to accurately estimate marker effects. The accuracy of selection decreased with increasing numbers of families per group.ConclusionsThis new selection scheme combines communal rearing of families, pre-selection of candidates, DNA pooling and genomic selection and makes multi-trait selection possible in aquaculture selection schemes without keeping families separately until individual tagging is possible. The new scheme can also be used for other farmed species, for which the cost of genotyping test individuals may be high, e.g. if trait heritability is low.

Prediction of Genetic Values of Quantitative Traits in Plant Breeding Using Pedigree and Molecular Markers

The availability of dense molecular markers has made possible the use of genomic selection (GS) for plant breeding. However, the evaluation of models for GS in real plant populations is very limited. This article evaluates the performance of parametric and semiparametric models for GS using wheat (Triticum aestivum L.) and maize (Zea mays) data in which different traits were measured in several environmental conditions. The findings, based on extensive cross-validations, indicate that models including marker information had higher predictive ability than pedigree-based models. In the wheat data set, and relative to a pedigree model, gains in predictive ability due to inclusion of markers ranged from 7.7 to 35.7%. Correlation between observed and predictive values in the maize data set achieved values up to 0.79. Estimates of marker effects were different across environmental conditions, indicating that genotype × environment interaction is an important component of genetic variability. These results indicate that GS in plant breeding can be an effective strategy for selecting among lines whose phenotypes have yet to be observed.

Graph-Based Data Selection for the Construction of Genomic Prediction Models

Efficient genomic selection in animals or crops requires the accurate prediction of the agronomic performance of individuals from their high-density molecular marker profiles. Using a training data set that contains the genotypic and phenotypic information of a large number of individuals, each marker or marker allele is associated with an estimated effect on the trait under study. These estimated marker effects are subsequently used for making predictions on individuals for which no phenotypic records are available. As most plant and animal breeding programs are currently still phenotype driven, the continuously expanding collection of phenotypic records can only be used to construct a genomic prediction model if a dense molecular marker fingerprint is available for each phenotyped individual. However, as the genotyping budget is generally limited, the genomic prediction model can only be constructed using a subset of the tested individuals and possibly a genome-covering subset of the molecular markers. In this article, we demonstrate how an optimal selection of individuals can be made with respect to the quality of their available phenotypic data. We also demonstrate how the total number of molecular markers can be reduced while a maximum genome coverage is ensured. The third selection problem we tackle is specific to the construction of a genomic prediction model for a hybrid breeding program where only molecular marker fingerprints of the homozygous parents are available. We show how to identify the set of parental inbred lines of a predefined size that has produced the highest number of progeny. These three selection approaches are put into practice in a simulation study where we demonstrate how the trade-off between sample size and sample quality affects the prediction accuracy of genomic prediction models for hybrid maize.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use.

Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect

BackgroundWhen estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias.MethodsGenomic selection using the Bayesian method, 'BayesB' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations.ResultsAccuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density.ConclusionsIncluding a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.

LASSO with cross-validation for genomic selection

We used a least absolute shrinkage and selection operator (LASSO) approach to estimate marker effects for genomic selection. The least angle regression (LARS) algorithm and cross-validation were used to define the best subset of markers to include in the model. The LASSO-LARS approach was tested on two data sets: a simulated data set with 5865 individuals and 6000 Single Nucleotide Polymorphisms (SNPs); and a mouse data set with 1885 individuals genotyped for 10 656 SNPs and phenotyped for a number of quantitative traits. In the simulated data, three approaches were used to split the reference population into training and validation subsets for cross-validation: random splitting across the whole population; random sampling of validation set from the last generation only, either within or across families. The highest accuracy was obtained by random splitting across the whole population. The accuracy of genomic estimated breeding values (GEBVs) in the candidate population obtained by LASSO-LARS was 0.89 with 156 explanatory SNPs. This value was higher than those obtained by Best Linear Unbiased Prediction (BLUP) and a Bayesian method (BayesA), which were 0.75 and 0.84, respectively. In the mouse data, 1600 individuals were randomly allocated to the reference population. The GEBVs for the remaining 285 individuals estimated by LASSO-LARS were more accurate than those obtained by BLUP and BayesA for weight at six weeks and slightly lower for growth rate and body length. It was concluded that LASSO-LARS approach is a good alternative method to estimate marker effects for genomic selection, particularly when the cost of genotyping can be reduced by using a limited subset of markers.

Prediction of hybrid performance in maize using molecular markers and joint analyses of hybrids and parental inbreds

The identification of superior hybrids is important for the success of a hybrid breeding program. However, field evaluation of all possible crosses among inbred lines requires extremely large resources. Therefore, efforts have been made to predict hybrid performance (HP) by using field data of related genotypes and molecular markers. In the present study, the main objective was to assess the usefulness of pedigree information in combination with the covariance between general combining ability (GCA) and per se performance of parental lines for HP prediction. In addition, we compared the prediction efficiency of AFLP and SSR marker data, estimated marker effects separately for reciprocal allelic configurations (among heterotic groups) of heterozygous marker loci in hybrids, and imputed missing AFLP marker data for marker-based HP prediction. Unbalanced field data of 400 maize dent x flint hybrids from 9 factorials and of 79 inbred parents were subjected to joint analyses with mixed linear models. The inbreds were genotyped with 910 AFLP and 256 SSR markers. Efficiency of prediction (R (2)) was estimated by cross-validation for hybrids having no or one parent evaluated in testcrosses. Best linear unbiased prediction of GCA and specific combining ability resulted in the highest efficiencies for HP prediction for both traits (R (2) = 0.6-0.9), if pedigree and line per se data were used. However, without such data, HP for grain yield was more efficiently predicted using molecular markers. The additional modifications of the marker-based approaches had no clear effect. Our study showed the high potential of joint analyses of hybrids and parental inbred lines for the prediction of performance of untested hybrids.