Regularized quantile regression for SNP marker estimation of pig growth curves.

BACKGROUND: Genomic growth curves are generally defined only in terms of population mean; an alternative approach that has not yet been exploited in genomic analyses of growth curves is the Quantile Regression (QR). This methodology allows for the estimation of marker effects at different levels of the variable of interest. We aimed to propose and evaluate a regularized quantile regression for SNP marker effect estimation of pig growth curves, as well as to identify the chromosome regions of the most relevant markers and to estimate the genetic individual weight trajectory over time (genomic growth curve) under different quantiles (levels). RESULTS: The regularized quantile regression (RQR) enabled the discovery, at different levels of interest (quantiles), of the most relevant markers allowing for the identification of QTL regions. We found the same relevant markers simultaneously affecting different growth curve parameters (mature weight and maturity rate): two (ALGA0096701 and ALGA0029483) for RQR(0.2), one (ALGA0096701) for RQR(0.5), and one (ALGA0003761) for RQR(0.8). Three average genomic growth curves were obtained and the behavior was explained by the curve in quantile 0.2, which differed from the others. CONCLUSIONS: RQR allowed for the construction of genomic growth curves, which is the key to identifying and selecting the most desirable animals for breeding purposes. Furthermore, the proposed model enabled us to find, at different levels of interest (quantiles), the most relevant markers for each trait (growth curve parameter estimates) and their respective chromosomal positions (identification of new QTL regions for growth curves in pigs). These markers can be exploited under the context of marker assisted selection while aiming to change the shape of pig growth curves.

Regularized quantile regression applied to genome-enabled prediction of quantitative traits.

Genomic selection (GS) is a variant of marker-assisted selection, in which genetic markers covering the whole genome predict individual genetic merits for breeding. GS increases the accuracy of breeding values (BV) prediction. Although a variety of statistical models have been proposed to estimate BV in GS, few methodologies have examined statistical challenges based on non-normal phenotypic distributions, e.g., skewed distributions. Traditional GS models estimate changes in the phenotype distribution mean, i.e., the function is defined for the expected value of trait-conditional on markers, E(Y|X). We proposed an approach based on regularized quantile regression (RQR) for GS to improve the estimation of marker effects and the consequent genomic estimated BV (GEBV). The RQR model is based on conditional quantiles, Qτ(Y|X), enabling models that fit all portions of a trait probability distribution. This allows RQR to choose one quantile function that "best" represents the relationship between the dependent and independent variables. Data were simulated for 1000 individuals. The genome included 1500 markers; most had a small effect and only a few markers with a sizable effect were simulated. We evaluated three scenarios according to symmetrical, positively, and negatively skewed distributions. Analyses were performed using Bayesian LASSO (BLASSO) and RQR considering three quantiles (0.25, 0.50, and 0.75). The use of RQR to estimate GEBV was efficient; the RQR method achieved better results than BLASSO, at least for one quantile model fit for all evaluated scenarios. The gains in relation to BLASSO were 86.28 and 55.70% for positively and negatively skewed distributions, respectively.

Using artificial neural networks to select upright cowpea (Vigna unguiculata) genotypes with high productivity and phenotypic stability.

Cowpea (Vigna unguiculata) is grown in three Brazilian regions: the Midwest, North, and Northeast, and is consumed by people on low incomes. It is important to investigate the genotype x environment (GE) interaction to provide accurate recommendations for farmers. The aim of this study was to identify cowpea genotypes with high adaptability and phenotypic stability for growing in the Brazilian Cerrado, and to compare the use of artificial neural networks with the Eberhart and Russell (1966) method. Six trials with upright cowpea genotypes were conducted in 2005 and 2006 in the States of Mato Grosso do Sul and Mato Grosso. The data were subjected to adaptability and stability analysis by the Eberhart and Russell (1966) method and artificial neural networks. The genotypes MNC99-537F-4 and EVX91-2E-2 provided grain yields above the overall environment means, and exhibited high stability according to both methods. Genotype IT93K-93-10 was the most suitable for unfavorable environments. There was a high correlation between the results of both methods in terms of classifying the genotypes by their adaptability and stability. Therefore, this new approach would be effective in quantifying the GE interaction in upright cowpea breeding programs.

Factor analysis applied to genome prediction for high-dimensional phenotypes in pigs.

The aim of the present study was to propose and evaluate the use of factor analysis (FA) in obtaining latent variables (factors) that represent a set of pig traits simultaneously, for use in genome-wide selection (GWS) studies. We used crosses between outbred F2 populations of Brazilian Piau X commercial pigs. Data were obtained on 345 F2 pigs, genotyped for 237 SNPs, with 41 traits. FA allowed us to obtain four biologically interpretable factors: "weight", "fat", "loin", and "performance". These factors were used as dependent variables in multiple regression models of genomic selection (Bayes A, Bayes B, RR-BLUP, and Bayesian LASSO). The use of FA is presented as an interesting alternative to select individuals for multiple variables simultaneously in GWS studies; accuracy measurements of the factors were similar to those obtained when the original traits were considered individually. The similarities between the top 10% of individuals selected by the factor, and those selected by the individual traits, were also satisfactory. Moreover, the estimated markers effects for the traits were similar to those found for the relevant factor.

Bayesian forecasting of temporal gene expression by using an autoregressive panel data approach.

We propose and evaluate a novel approach for forecasting gene expression over non-observed times in longitudinal trials under a Bayesian viewpoint. One of the aims is to cluster genes that share similar expression patterns over time and then use this similarity to predict relative expression at time points of interest. Expression values of 106 genes expressed during the cell cycle of Saccharomyces cerevisiae were used and genes were partitioned into five distinct clusters of sizes 33, 32, 21, 16, and 4. After removing the last observed time point, the agreements of signals (upregulated or downregulated) considering the predicted expression level were 72.7, 81.3, 76.2, 68.8, and 50.0%, respectively, for each cluster. The percentage of credibility intervals that contained the true values of gene expression for a future time was ~90%. The methodology performed well, providing a valid forecast of gene expression values by fitting an autoregressive panel data model. This approach is easily implemented with other time-series models and when Poisson and negative binomial probability distributions are assumed for the gene expression data.

Adaptability and phenotypic stability of common bean genotypes through Bayesian inference.

This study used Bayesian inference to investigate the genotype x environment interaction in common bean grown in Mato Grosso do Sul State, and it also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 13 common bean genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian inference was effective for the selection of upright common bean genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. According to Bayesian inference, the EMGOPA-201, BAMBUÍ, CNF 4999, CNF 4129 A 54, and CNFv 8025 genotypes had specific adaptability to favorable environments, while the IAPAR 14 and IAC CARIOCA ETE genotypes had specific adaptability to unfavorable environments.

Artificial intelligence in the selection of common bean genotypes with high phenotypic stability.

Artificial neural networks have been used for various purposes in plant breeding, including use in the investigation of genotype x environment interactions. The aim of this study was to use artificial neural networks in the selection of common bean genotypes with high phenotypic adaptability and stability, and to verify their consistency with the Eberhart and Russell method. Six trials were conducted using 13 genotypes of common bean between 2002 and 2006 in the municipalities of Aquidauana and Dourados. The experimental design was a randomized block with three replicates. Grain yield data were submitted to individual and joint variance analyses. The data were then submitted to analysis of adaptability and stability through the Eberhart and Russell and artificial neural network methods. There was high concordance between the methodologies evaluated for discrimination of phenotypic adaptability of common bean genotypes, indicating that artificial neural networks can be used in breeding programs. Based on both approaches, the genotypes Aporé, Rudá, and CNFv 8025 are recommended for use in unfavorable, general and favorable environments, respectively by the grain yield above the overall average of environments and high phenotypic stability.

Measurements of experimental precision for trials with cowpea (Vigna unguiculata L. Walp.) genotypes.

The aim of this study was to evaluate the suitability of statistics as experimental precision degree measures for trials with cowpea (Vigna unguiculata L. Walp.) genotypes. Cowpea genotype yields were evaluated in 29 trials conducted in Brazil between 2005 and 2012. The genotypes were evaluated with a randomized block design with four replications. Ten statistics that were estimated for each trial were compared using descriptive statistics, Pearson correlations, and path analysis. According to the class limits established, selective accuracy and F-test values for genotype, heritability, and the coefficient of determination adequately estimated the degree of experimental precision. Using these statistics, 86.21% of the trials had adequate experimental precision. Selective accuracy and the F-test values for genotype, heritability, and the coefficient of determination were directly related to each other, and were more suitable than the coefficient of variation and the least significant difference (by the Tukey test) to evaluate experimental precision in trials with cowpea genotypes.

Bayesian approach increases accuracy when selecting cowpea genotypes with high adaptability and phenotypic stability.

This study aimed to verify that a Bayesian approach could be used for the selection of upright cowpea genotypes with high adaptability and phenotypic stability, and the study also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 17 upright cowpea genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian approach was effective for selection of upright cowpea genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions.