Rank correlation

Stability (learning theory)

Combinatorics

Correlation

Biplot

Gene–environment interaction

Yield (engineering)

Ranking (information retrieval)

Ammi

Mathematics

Biology

Gene

Statistics

Genotype

Machine learning

Rank (graph theory)

Metallurgy

Materials science

Geometry

Computer science

Genetics

Interaction

The Crop Journal

Several statistical methods have been developed for analyzing genotype × environment (GE) interactions in crop breeding programs to identify genotypes with high yield and stability performances. Four statistical methods, including joint regression analysis (JRA), additive mean effects and multiplicative interaction (AMMI) analysis, genotype plus GE interaction (GGE) biplot analysis, and yield–stability (YSi) statistic were used to evaluate GE interaction in 20 winter wheat genotypes grown in 24 environments in Iran. The main objective was to evaluate the rank correlations among the four statistical methods in genotype rankings for yield, stability and yield–stability. Three kinds of genotypic ranks (yield ranks, stability ranks, and yield–stability ranks) were determined with each method. The results indicated the presence of GE interaction, suggesting the need for stability analysis. With respect to yield, the genotype rankings by the GGE biplot and AMMI analysis were significantly correlated (P < 0.01). For stability ranking, the rank correlations ranged from 0.53 (GGE–YSi; P < 0.05) to 0.97 (JRA–YSi; P < 0.01). AMMI distance (AMMID) was highly correlated (P < 0.01) with variance of regression deviation (S2di) in JRA (r = 0.83) and Shukla stability variance (σ2) in YSi (r = 0.86), indicating that these stability indices can be used interchangeably. No correlation was found between yield ranks and stability ranks (AMMID, S2di, σ2, and GGE stability index), indicating that they measure static stability and accordingly could be used if selection is based primarily on stability. For yield–stability, rank correlation coefficients among the statistical methods varied from 0.64 (JRA–YSi; P < 0.01) to 0.89 (AMMI–YSi; P < 0.01), indicating that AMMI and YSi were closely associated in the genotype ranking for integrating yield with stability performance. Based on the results, it can be concluded that YSi was closely correlated with (i) JRA in ranking genotypes for stability and (ii) AMMI for integrating yield and stability.

Rank correlation among different statistical models in ranking of winter wheat genotypes