RESUMO
BACKGROUND: A common dataset was simulated and made available to participants of the XVI(th) QTL-MAS workshop. Tasks for the participants were to detect QTLs affecting three traits, to assess their possible pleiotropic effects, and to evaluate the breeding values in a candidate population without phenotypes using genomic information. METHODS: Four generations consisting of 20 males and 1000 females were generated by mating each male with 50 females. The genome consisted of 5 chromosomes, each of 100 Mb size and carrying 2,000 equally distributed SNPs. Three traits were simulated in order to mimic milk yield, fat yield and fat content. Genetic (co)variances were generated from 50 QTLs with pleiotropic effects. Phenotypes for all traits were expressed only in females, and were provided for the first 3 generations. Fourteen methods for detecting single-trait QTL and 3 methods for investigating their pleiotropic nature were proposed. QTL mapping results were compared according to the following criteria: number of true QTL detected; number of false positives; and the proportion of the true genetic variance explained by submitted positions. Eleven methods for estimating direct genomic values of the candidate population were proposed. Accuracies and bias of predictions were assessed by comparing estimated direct genomic values with true breeding values. RESULTS: The number of true detections ranged from 0 to 8 across methods and traits, false positives from 0 to 15, and the proportion of genetic variance captured from 0 to 0.82, respectively. The accuracy and bias of genomic predictions varied from 0.74 to 0.85 and from 0.86 to 1.34 across traits and methods, respectively. CONCLUSIONS: The best results in terms of detection power were obtained by ridge regression that, however, led to a large number of false positives. Good results both in terms of true detections and false positives were obtained by the approaches that fit polygenic effects in the model. The investigation of the pleiotropic nature of the QTL permitted the identification of few additional markers compared to the single-trait analyses. Bayesian and grouped regularized regression methods performed similarly for genomic prediction while GBLUP produced the poorest results.
RESUMO
BACKGROUND: The least absolute shrinkage and selection operator (LASSO) can be used to predict SNP effects. This operator has the desirable feature of including in the model only a subset of explanatory SNPs, which can be useful both in QTL detection and GWS studies. LASSO solutions can be obtained by the least angle regression (LARS) algorithm. The big issue with this procedure is to define the best constraint (t), i.e. the upper bound of the sum of absolute value of the SNP effects which roughly corresponds to the number of SNPs to be selected. Usai et al. (2009) dealt with this problem by a cross-validation approach and defined t as the average number of selected SNPs overall replications. Nevertheless, in small size populations, such estimator could give underestimated values of t. Here we propose two alternative ways to define t and compared them with the "classical" one. METHODS: The first (strategy 1), was based on 1,000 cross-validations carried out by randomly splitting the reference population (2,000 individuals with performance) into two halves. The value of t was the number of SNPs which occurred in more than 5% of replications. The second (strategy 2), which did not use cross-validations, was based on the minimization of the Cp-type selection criterion which depends on the number of selected SNPs and the expected residual variance. RESULTS: The size of the subset of selected SNPs was 46, 189 and 64 for the classical approach, strategy 1 and 2 respectively. Classical and strategy 2 gave similar results and indicated quite clearly the regions were QTL with additive effects were located. Strategy 1 confirmed such regions and added further positions which gave a less clear scenario. Correlation between GEBVs estimated with the three strategies and TBVs in progenies without phenotypes were 0.9237, 0.9000 and 0.9240 for classical, strategy 1 and 2 respectively. CONCLUSIONS: This suggests that the Cp-type selection criterion is a valid alternative to the cross-validations to define the best constraint for selecting subsets of predicting SNPs by LASSO-LARS procedure.
RESUMO
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.
