2021
DOI: 10.3390/agronomy11112179
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Influential Points in Adaptability and Stability Methods Based on Regression Models in Cotton Genotypes

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 varie… Show more

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Cited by 3 publications
(4 citation statements)
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“…Here, a linear regression analysis (Equation ()) was performed on the individual treatment response as function of an environmental index for that respective response (I, Equation ()), which was calculated as the difference between the measured traits for that particular G‐E‐M combination and the overall grand mean for that trait. The output of this analysis includes an adaptability index (i.e., the slope of the relationship), a stability index (i.e., the model fit statistics), and the mean trait value: Yijbadbreak=0.28emnormalβgoodbreak+normalαIjgoodbreak+δij$$\begin{equation}{Y_{ij}} = \;\beta + \alpha {I_j} + {\delta _{ij}}\end{equation}$$where Y ij is the observation of the i th genotype in the j th environment; β is the general mean of the i th genotype over all environments, α is the regression coefficient that measures the response of i th genotype to different environments, and δ ij is the deviation from regression of the i th genotype in the j th environment; I j is the environmental index (Nascimento et al., 2021) Ijbadbreak=iYijg0.28emgoodbreak−ijYijga$$\begin{equation}{I_j} = \frac{{\mathop \sum \nolimits_i {Y_{ij}}}}{g}\; - \frac{{\mathop \sum \nolimits_i \mathop \sum \nolimits_j {Y_{ij}}}}{{ga}}\end{equation}$$…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Here, a linear regression analysis (Equation ()) was performed on the individual treatment response as function of an environmental index for that respective response (I, Equation ()), which was calculated as the difference between the measured traits for that particular G‐E‐M combination and the overall grand mean for that trait. The output of this analysis includes an adaptability index (i.e., the slope of the relationship), a stability index (i.e., the model fit statistics), and the mean trait value: Yijbadbreak=0.28emnormalβgoodbreak+normalαIjgoodbreak+δij$$\begin{equation}{Y_{ij}} = \;\beta + \alpha {I_j} + {\delta _{ij}}\end{equation}$$where Y ij is the observation of the i th genotype in the j th environment; β is the general mean of the i th genotype over all environments, α is the regression coefficient that measures the response of i th genotype to different environments, and δ ij is the deviation from regression of the i th genotype in the j th environment; I j is the environmental index (Nascimento et al., 2021) Ijbadbreak=iYijg0.28emgoodbreak−ijYijga$$\begin{equation}{I_j} = \frac{{\mathop \sum \nolimits_i {Y_{ij}}}}{g}\; - \frac{{\mathop \sum \nolimits_i \mathop \sum \nolimits_j {Y_{ij}}}}{{ga}}\end{equation}$$…”
Section: Methodsmentioning
confidence: 99%
“…where Y ij is the observation of the ith genotype in the jth environment; β is the general mean of the ith genotype over all environments, α is the regression coefficient that measures the response of ith genotype to different environments, and δ ij is the deviation from regression of the ith genotype in the jth environment; I j is the environmental index (Nascimento et al, 2021)…”
Section: Crop Sciencementioning
confidence: 99%
“…Phenotypic and genotypic data are susceptible to outlier samples, regardless of the cause. Outlier observations have been observed in single-site and multi-environment trials 13 , 14 , DNA-seq 15 , 16 , and RNA-seq 17 data. Therefore, the presence of such observations in the data is inevitable and violates the underlying assumptions of many statistical analyses 18 .…”
Section: Introductionmentioning
confidence: 95%
“…Selection for fiber quality and yield is complicated by the contribution of genotype × environment (G × E) interactions on these traits [ 1 , 10 ]. Generally speaking, breeders select for trait stability across their candidate environments, although yearly fluctuations in weather, precipitation, disease pressure, and random field variation can confound a breeder’s ability to make direct selections on observed phenotype means and relative ranks [ 11 , 12 ]. Understanding how the genetic underpinnings of key traits in cotton vary with respect to the loci of variable effect sizes (small to high) or quantitative trait loci (QTL), and the cumulative effect of many loci (the polygenic effect) in multiple years and locations is crucial for designing more efficient selection schemes [ 13 ].…”
Section: Introductionmentioning
confidence: 99%