Methodology for analysis of adaptability and stability using quantile regression

The objective of this work was to develop and validate a methodology for analyzing phenotypic adaptability and stability based on quantile regression (QR). For this, phenotypic values were simulated with symmetrical distribution and with asymmetrical distribution to the right and to the left, with or without outliers. The proposed methodology was applied to a data set from an experiment with 92 alfalfa (Medicago sativa) genotypes, evaluated in 20 environments, and compared with the methodologies of Eberhart & Russell and nonparametric regression. The QR methodology provided equal or superior results, compared to the evaluated alternative methodologies. However, the occurrence of disagreeing results between methodologies evidences the importance of evaluating symmetry in the distribution of phenotypic values. For symmetric distributions with outliers, QR should be used with estimated quantile value (τ) of 0.50; in the absence of outliers, both the methodology of Eberhart & Russel and QR (τ = 0.50) may be used. For asymmetric distributions, the use of RQ with τ = 0.25 is suggested for asymmetry to the right, and with τ = 0.75 for asymmetry to the left, regardless of the presence of outliers.

Medicago sativa; asymmetrical distribution; genotype x environment interaction; plant breeding; outliers; nonparametric regression.