Quantifying individual variation in reaction norms using random regression models fitted through Legendre polynomials: application in eucalyptus breeding

Abstract

An accurate, efficient and informative statistical method for analyses of genotype × environment (G × E) interactions is a key requirement for progress in any breeding program. Thus, the objective of this study was to quantify individual variation in reaction norms using random regression models fitted through Legendre polynomials in eucalyptus (Eucalyptus spp.) breeding. To this end, a data set with 215 eucalyptus clones of different species and hybrids evaluated in four environments for diameter at breast height (DBH) and Pilodyn penetration (PP) was used. Variance components were estimated by restricted maximum likelihood, and genetic values were predicted by best linear unbiased prediction. The best-fitted model for DBH and PP was indicated by the Akaike information criterion, and the significance of the genotype effects was tested using the likelihood ratio test. Genetic variability between eucalyptus clones and very high accuracies (r ĝg > 0.90) were detected for both traits. Reaction norms and eigenfunctions generated genetic insights into G × E interactions. This is the first study that quantified individual variation in reaction norms using random regression models fitted through Legendre polynomials in eucalyptus breeding and demonstrated the great potential of this technique.

Multiple-trait, random regression, and compound symmetry models for analyzing multi-environment trials in maize breeding

“…Rhe ) fit heterogeneous residuals (i.e., one residual variance for each environment). Heterogeneous residuals in MET analyses were also reported by Melo et al [ 32 ] in analyzing progeny of the common bean, and Alves et al [ 12 ] in analyzing eucalyptus clones. In this study, CSM, MTM, and RRM provided estimates for 6, 14, and 7 parameters, respectively.…”

“…The selected models (CS.Rhe, MT.Rhe, and RR.2.Rhe) fit heterogeneous residuals (i.e., one residual variance for each environment). Heterogeneous residuals in MET analyses were also reported by Melo et al [32] in analyzing progeny of the common bean, and Alves et al [12] in Reaction norms for grain yield (GY) evaluated for maize hybrids in four environments. "A" presents the reaction norms of the 84 maize hybrids, and "B" presents the reaction norms of around 25% of the 84 maize hybrids, and detach the reaction norms intersections using yellow dots.…”

“…Based on the scale proposed by Resende and Alves [15], GY showed heritabilities of moderate magnitude (0.15<h 2 <0.50) in all environments, independently of the model used. Selective accuracy is one of the most relevant parameters in evaluating the effectiveness of inferences of predicted genetic values [12]. This parameter is defined as the correlation between the predicted and true genotypic values and offers evidence of experimental quality, since it considers residual and genetic variances [14].…”

“…Random regression models (RRM) estimate the same genetic parameters as MTM but with less parameterization [ 9 ] and capture the continuous change of a trait over time or environmental gradient [ 8 , 10 ]. Furthermore, this approach is a powerful tool to predict reaction norms [ 11 , 12 ] and, consequently, predict genotypic values of genotypes for untested environments [ 7 ]. The reaction norms consider the effects of GxE and can identify the underlying causes, as they are plotted over an environmental gradient [ 13 ].…”

Random regression for modeling yield genetic trajectories in Jatropha curcas breeding

“…The areas under the genetic trajectories (A), aiming to rank the clones, were obtained by the following expression [ 24 , 25 ]: where μ is the phenotypic mean and where x m is the is the harvest scaled. Genetic correlations ( ρ g ) between each pair of harvests were obtained by the following expression: where , is the genetic covariance between progenies for the pair of harvests i and j ; and are the genetic variance between progenies for the harvests i and j , respectively.…”