Statistics

Machine learning

Programming language

Engineering

Artificial intelligence

Selection (genetic algorithm)

Stability (learning theory)

Aerospace engineering

Biotechnology

Mathematics

Biology

Gene

Trait

Index (typography)

Genotype

Main effect

Computer science

World Wide Web

Biplot

Index selection

Genetics

Differential (mechanical device)

Agronomy Journal

Modeling the genotype × environment interaction (GEI) and quantifying genotypic stability are crucial steps for selecting/recommending genotypes in multi‐environment trials (METs). The efficiency in selection/recommendation could be greater if based on multiple traits, but identifying genotypes that combine high performance and stability across many traits has been a difficult task. In this study, we propose a multi‐trait stability index (MTSI) for simultaneous selection considering mean performance and stability (MPE) in the analysis of METs using both fixed and mixed‐effect models. Data from an MET where 14 traits were assessed in 22 genotypes of Avena sativa L. were used to illustrate the application of the method. The genotypic stability was quantified for each trait using the weighted average of absolute scores from the singular value decomposition of the matrix of best linear unbiased predictions for the GEI effects generated by an linear mixed‐effect model (WAASB) index (lower is better). A superiority index, WAASBY (higher is better) was calculated to consider the MPE. The selection differential for the WAASBY index ranged from 9.7 to 44.6%. Positive selection differential (1.75% ≤ selection differential ≤ 17.8%) were observed for trait means that wanted to increase and negative (–11.7%) for one variable that wanted to reduce. The negative selection differential observed for WAASB (–63% ≤ selection differential ≤ −12%) suggested that the selected genotypes were more stable. The MTSI should be useful for breeders and agronomists who desire a selection for MPE based on multiple traits because it provides a robust and easy‐to‐handle selection process, accounting for the correlation structure of the traits. The application of the MTSI in future studies is facilitated by a step‐by‐step guide and an R package containing useful functions. Core Ideas The genotypic stability was quantified in multi‐environment trials (MET) using mixed models. A superiority index that allows weighting between mean performance and stability was used. A multi‐trait stability index (MTSI) for identifying superior genotypes in MET was proposed. Using a real dataset from a MET, stable and high‐performance genotypes were identified. The MTSI should facilitate the genotype selection in a multi‐trait framework.

Mean Performance and Stability in Multi‐Environment Trials II: Selection Based on Multiple Traits