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

Nascimento, Moysés; Silva, F. F. e; Resende, Marcos Deon Vilela de; Cruz, Cosme Damião; Nascimento, Ana Carolina Campana; Viana, José Marcelo Soriano; Azevedo, Camila Ferreira; Barroso, Laís Mayara Azevedo

doi:10.4238/gmr16019538

Cited by 13 publications

(16 citation statements)

References 23 publications

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“…The ability to choose the "best" relationship between the phenotype and markers increases the predictive performance of the model. According to the authors of [11] and [12], when the conditional distributions of Y are non-normal (for instance, skewed), the mean might not be the best way to describe the functional relationship between the variables.…”

Section: Discussionmentioning

confidence: 99%

“…This feature allows QR to examine all of the conditional distributions, in order to investigate skewness and heteroscedasticity. From a GS viewpoint, we can choose the "best" conditional quantile to represent the relationship between the dependent and independent variables, thus increasing the accuracy of the genomic estimated breeding value (GEBV) prediction of individual genetic merits [12]. However, because of the high dimensionality commonly found in GS studies, a variation of QR, denoted by regularized quantile regression (RQR) [13] should be considered.…”

Section: Introductionmentioning

confidence: 99%

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Quantile Regression Applied to Genome-Enabled Prediction of Traits Related to Flowering Time in the Common Bean

Nascimento

Azevedo

et al. 2019

Agronomy

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Genomic selection (GS) aims to incorporate molecular information directly into the prediction of individual genetic merit. Regularized quantile regression (RQR) can be used to fit models for all portions of a probability distribution of the trait, enabling the conditional quantile that “best” represents the functional relationship between dependent and independent variables to be chosen. The objective of this study was to predict the individual genetic merits of the traits associated with flowering time (DFF—days to first flower; DTF—days to flower) in the common bean using RQR and to compare the predictive abilities obtained from Random Regression Best Linear Unbiased Predictor (RR-BLUP), Bayesian LASSO (BLASSO), BayesB, and RQR for predicting the genetic merit. GS was performed using 80 genotypes of common beans genotyped for 380 single nucleotide polymorphism (SNP) markers. Considering the “best” RQR fit models (RQR0.3 for DFF, and RQR0.2 for DTF), the gains in predictive ability in relation to BLASSO, BayesB, and RR-BLUP were 18.75%, 22.58%, and 15.15% for DFF, respectively, and 15.20%, 24.65%, and 12.55% for DTF, respectively. The potential cultivars selected, considering the RQR “best” models, were among the 5% of cultivars with the lowest genomic estimated breeding value (GEBV) for the DFF and DTF traits—the IAC Imperador, IPR Colibri, Capixaba Precoce, and IPR Andorinha were included in the list of early cycle cultivars.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantile Regression Applied to Genome-Enabled Prediction of Traits Related to Flowering Time in the Common Bean

Nascimento

Azevedo

et al. 2019

Agronomy

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“…To deal with dimensionality problems in GWS studies, which are common in the marker matrix, Li and Zhu [26] proposed the Regularized Quantile Regression (RQR). The use of RQR in a GWS study was proposed by Nascimento et al [27], in order to estimate GEBV for different quantiles of the phenotype of interest [28,29]. In their study, Nascimento et al [27] used RQR to estimate GEBV from simulated data with scenarios with different skewness levels in the phenotype distribution.…”

Section: Introductionmentioning

confidence: 99%

“…The use of RQR in a GWS study was proposed by Nascimento et al [27], in order to estimate GEBV for different quantiles of the phenotype of interest [28,29]. In their study, Nascimento et al [27] used RQR to estimate GEBV from simulated data with scenarios with different skewness levels in the phenotype distribution. The results of the RQR were compared to those of the BLASSO (Bayesian Least Absolute Shrinkage and Selection Operator) method, and the authors observed a lower mean square error of the former.…”

Section: Introductionmentioning

confidence: 99%

Quantile regression in genomic selection for oligogenic traits in autogamous plants: A simulation study

Oliveira

Nascimento

et al. 2021

PLoS ONE

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This study assessed the efficiency of Genomic selection (GS) or genome‐wide selection (GWS), based on Regularized Quantile Regression (RQR), in the selection of genotypes to breed autogamous plant populations with oligogenic traits. To this end, simulated data of an F2 population were used, with traits with different heritability levels (0.10, 0.20 and 0.40), controlled by four genes. The generations were advanced (up to F6) at two selection intensities (10% and 20%). The genomic genetic value was computed by RQR for different quantiles (0.10, 0.50 and 0.90), and by the traditional GWS methods, specifically RR-BLUP and BLASSO. A second objective was to find the statistical methodology that allows the fastest fixation of favorable alleles. In general, the results of the RQR model were better than or equal to those of traditional GWS methodologies, achieving the fixation of favorable alleles in most of the evaluated scenarios. At a heritability level of 0.40 and a selection intensity of 10%, RQR (0.50) was the only methodology that fixed the alleles quickly, i.e., in the fourth generation. Thus, it was concluded that the application of RQR in plant breeding, to simulated autogamous plant populations with oligogenic traits, could reduce time and consequently costs, due to the reduction of selfing generations to fix alleles in the evaluated scenarios.

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“… Varona et al (2008) proposed using linear mixed models with asymmetric distributions in the residuals to tackle the problem in the context of animal breeding when pedigree information is available. Nascimento et al (2017) proposed the Regularized Quantile Regression as a way to overcome the issue of non-symmetric distributions when marker information is available.…”

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confidence: 99%

A Bayesian Genomic Regression Model with Skew Normal Random Errors

Pérez‐Rodríguez

Acosta-Pech

Pérez-Elizalde

et al. 2018

G3 Genes|Genomes|Genetics

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Genomic selection (GS) has become a tool for selecting candidates in plant and animal breeding programs. In the case of quantitative traits, it is common to assume that the distribution of the response variable can be approximated by a normal distribution. However, it is known that the selection process leads to skewed distributions. There is vast statistical literature on skewed distributions, but the skew normal distribution is of particular interest in this research. This distribution includes a third parameter that drives the skewness, so that it generalizes the normal distribution. We propose an extension of the Bayesian whole-genome regression to skew normal distribution data in the context of GS applications, where usually the number of predictors vastly exceeds the sample size. However, it can also be applied when the number of predictors is smaller than the sample size. We used a stochastic representation of a skew normal random variable, which allows the implementation of standard Markov Chain Monte Carlo (MCMC) techniques to efficiently fit the proposed model. The predictive ability and goodness of fit of the proposed model were evaluated using simulated and real data, and the results were compared to those obtained by the Bayesian Ridge Regression model. Results indicate that the proposed model has a better fit and is as good as the conventional Bayesian Ridge Regression model for prediction, based on the DIC criterion and cross-validation, respectively. A computing program coded in the R statistical package and C programming language to fit the proposed model is available as supplementary material.

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

Cited by 13 publications

References 23 publications

Quantile Regression Applied to Genome-Enabled Prediction of Traits Related to Flowering Time in the Common Bean

Quantile Regression Applied to Genome-Enabled Prediction of Traits Related to Flowering Time in the Common Bean

Quantile regression in genomic selection for oligogenic traits in autogamous plants: A simulation study

A Bayesian Genomic Regression Model with Skew Normal Random Errors

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