Genetic evaluation for latent variables derived from factor analysis in broilers.

1. The aim of this study was to investigate the associations between several carcass, performance and meat quality traits in broilers through factor analysis and use the latent variables (i.e. factors) as pseudo-phenotypes in genetic evaluations.2. Factors were extracted using the principal components method and varimax rotation algorithm. Genetic parameters were estimated via Bayesian inference under a multiple-trait animal model.3. All factors taken together explained 71% of the original variance of the data. The first factor, denominated as 'weight', was associated with carcass and body weight traits; and the second factor, defined as 'tenderness', represented traits related to water-holding capacity and shear force. The third factor, 'colour', was associated with traits related to meat colour, whereas the fourth, referenced as 'viscera', was related to heart, liver and abdominal fat.4. The four biological factors presented moderate to high heritability (ranging from 0.35 to 0.75), which may confer genetic gains in this population.5. In conclusion, it seems possible to reduce the number of traits in the genetic evaluation of broilers using latent variables derived from factor analysis.

Using quantile regression methodology to evaluate changes in the shape of growth curves in pigs selected for increased feed efficiency based on residual feed intake.

Growth rate is a major component of feed efficiency when estimating residual feed intake (RFI). Quantile regression (QR) methodology can be used to identify animals with different growth trajectories. The objective of this study was to evaluate the use of QR to identify phenotypic and genetic differences in pigs selected for low RFI. Using performance data on 750 Yorkshire pigs selected for low RFI, individual average daily gain (ADG), average daily feed intake (ADFI), RFI and Gompertz growth curve parameters (asymptotic weight (a), inflection point (b) and decay parameter (c)) were estimated for each pig. Using QR methodology, three Gompertz growth curves were estimated for the whole population for three quantiles (0.1, 0.5 and 0.9) of the BW data. Each animal was classified into one of the quantile regression groups (QRG) based on their overall Euclidian distance between each observed and estimated BW from the quantile growth curves. These three curves were also estimated using only part of the data (generations -1 to 3, and -1 to 4) in order to evaluate the agreement classification rate of animals from later generations into QRGs. We evaluated the effect of QRG on growth parameters and performance traits. Genetic parameters were estimated for these traits, as well as for QRG. In addition, genetic trends for each QRG were estimated. Three distinct growth curves were observed for animals classified into either quantiles 0.1 (QRG0.1), 0.5 (QRG0.5) or 0.9 (QRG0.9). When only part of the data was used to estimate quantile growth curves, all animals from QRG0.1 were correctly classified in their group. Animals in QRG0.1 had significantly lower ADFI, ADG and RFI, and greater a, b and c than animals in the other groups. Quantile regression groups analysed as a trait was highly heritable (0.41) and had high (0.8) and moderate (0.46) genetic correlations with ADG and RFI, respectively. Selection for reduced RFI increased the number of animals classified as QRG0.1 in the population. Overall, downward genetic trends were observed for all traits as a function of selection for reduced RFI. However, QRG0.1 was the only group that had a positive genetic trend for ADG. Altogether, these results indicate that selection for reduced RFI changes the shape of growth curves in Yorkshire in pigs, and that QR methodology was able to identify animals having different genetic potential for feed efficiency, bringing a new opportunity to improve selection for reduced RFI.

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.