Influential Points in Adaptability and Stability Methods Based on Regression Models in Cotton Genotypes

Moysés Nascimento,Francisco José Correia Farias,Isabela De Castro Sant’Anna,Camila Ferreira Azevedo,Larissa Pereira Ribeiro Teodoro,Paulo Eduardo Teodoro,Helaine Claire Almeida,Luiz Paulo De Carvalho,Ana Carolina Campana Nascimento,Laís Mayara Azevedo Barroso

doi:10.3390/agronomy11112179

Abstract

The aim of this work was to answer the following question: can influential points modify the recommendation of genotypes, based on regression methods, in the presence of genotype × environment (G × E)? Therefore, we compared the parameters of the adaptability and stability of three methodologies based on regression in the presence of influential points. Specifically, were evaluated methods based on simple, non-parametric and quantile (τ = 0.50) regressions. The dataset used in this work corresponds to 18 variety trials of cotton cultivars that were conducted in the 2013–2014 and 2014–2015 crop seasons. The evaluated variable was the cotton fiber yield (kg/ha). Once we noticed that the effect of G × E interaction is significant, the statistical procedures adopted for the adaptability and stability analysis of the genotypes. To verify the presence of a possible influential point, we used the leverage values, studentized residuals (SR), DFBETAS and Cook’s distance. As a result, the influential points can modify the recommendation of genotypes, based on regression methods, in the presence of G × E interaction. The non-parametric and quantile (τ = 0.50) regressions, which are based on median estimators, are less sensitive to the presence of influential points avoiding misleading recommendations of genotypes in terms of adaptability.

Highlights

The knowledge of the genotype × environment (G × E) interaction component is important for plant breeding programs
We seek to answer the following question: can influential points modify the recommendation of genotypes in the presence of a G × E interaction? the aim of this work was to compare the parameters of adaptability and stability of three methodologies based on regression in the presence of influential points
The significance of the G × E interaction effects indicates the differential performance of genotypes in different environments justifying the use of adaptability and stabilities analysis

Summary

Introduction

The knowledge of the genotype × environment (G × E) interaction component is important for plant breeding programs. In the presence of influential points, methodologies based on regression may present inadequate estimates, and overestimate or underestimate the adaptability parameter. Once the recommendation of a genotype is made considering a set of environments, the use of a methodology that does not remove a possible influential point and mitigate some possible differential effect is interesting. Non-parametric regression does not present well-defined statistical properties, since it is based on the calculation of medians from the data set. Another regression approach to adaptability (the differential response of genotypes to different environmental conditions) and stability (the ability of genotypes present predictable behavior as to different environmental conditions) studies is QR [8]. The authors showed the efficiency of the QR to deal with the presence of outliers

Objectives

Methods

Results

Discussion

Conclusion