Methodology

Kang's Rank Sum Method

Kang's rank sum method is a non-parametric approach used to identify stable and high-yielding genotypes across environments. In this method, the rank for each genotype is calculated based on yield performance and stability across multiple environments. The genotypes are ranked based on their mean yield, with the lowest rank assigned to the highest-yielding genotype. Similarly, the genotypes are ranked based on their yield stability, where the stability is assessed using the coefficient of variation or any other stability parameter. The two ranks are summed for each genotype, and the genotype with the lowest total rank is considered the best in terms of yield performance and stability.

Shukla's Stability Variance

Shukla's stability variance is a parametric method used to measure the stability of genotypes across different environments. It calculates the variance of genotype performance, adjusted for environmental effects, and provides an unbiased estimate of genotype stability. A smaller value of Shukla's stability variance indicates greater stability of a genotype across environments. The stability variance is calculated as the deviation of the genotype's performance from the expected performance under the assumption of additive environmental effects. Genotypes with lower stability variance are considered to be more stable and adaptable to varying environmental conditions.

Rank Based Stability Index (RSI)

The proposed algorithm utilizes a linear combination of the rank of RS (Rank Sum) and Si(2) (Variance Method Rank). This combination is denoted as the Rank Based Stability Index (RSI). The formula for RSI is as follows:

RSI = (r_RS + r_Si(2)) / 2

In this formula:

• r_RS represents the rank of the statistic based on the rank-sum method.
• r_Si(2) represents the rank of the statistic based on the variance method (Si(2)).

Lower values of the rank for both the RS and Si(2) statistics indicate a more stable variety. However, these two statistics may assign different ranks for the same experiments, reflecting the distinct nature of each method. By combining the two rankings into the RSI, the algorithm provides a more comprehensive measure of stability across genotypes and environments.

The lower the RSI value, the more stable the variety is considered to be.

Biplot Analysis Using the PCA analysis

The Additive Main Effects and Multiplicative Interaction (AMMI) model is widely used for analyzing genotype by environment interaction (GEI). It combines analysis of variance (ANOVA) to partition the additive effects (genotypes and environments) and principal component analysis (PCA) to capture the multiplicative interaction effects between genotypes and environments. The biplot generated from the AMMI model is a graphical representation that shows both genotypes and environments on the same plot, which helps to interpret the GEI more effectively.

The biplot visually represents the interaction by plotting the principal component scores of the genotypes and environments. Genotypes that are located near the origin of the biplot are considered to have less interaction, indicating stability across environments. Environments located far from the origin are indicative of high interaction, showing a greater environmental effect on genotype performance. The direction and proximity of genotype points relative to environment points provide insight into how well a genotype performs in a specific environment.

References