2.4.2. Genetic Parameters

Genetic and environmental effects among the genotypes for traits were measured by using their mean sum of squares [20]. The heritability estimate was categorized as low (0–30%), medium (30–60%), and high (>60%).

(a) Genotypic variance

$$
\sigma^2 \mathbf{g} = \frac{\mathbf{GMS} - \mathbf{EMS}}{\mathbf{r}}
$$

Here, GMS is the genotype mean square and EMS denotes the error mean square, and r is the number of replications of genotypes.

(b) Phenotypic variance

$$
\sigma^2 \mathbf{p} = \sigma^2 \mathbf{g} + \sigma^2 \mathbf{e}
$$

Here, *σ*<sup>2</sup> p is the phenotypic variance, *σ*2g is the genotypic variance, and *σ*2e is the environmental variance.

(c) Environmental variance

$$
\sigma^2 \mathbf{e} = \frac{\mathbf{EMS}}{\mathbf{r}}
$$

Here, *σ*2e is the environmental variance, EMS is the error mean square, and r is the number of replications of genotypes.

(d) H2

$$h\_B^2 = \frac{\sigma^2 \text{g}}{\sigma^2 \text{p}}$$

where *h*<sup>2</sup> *<sup>B</sup>* is the broad-sense heritability, which is equal to the ratio of *<sup>σ</sup>*<sup>2</sup> <sup>g</sup> (genotypic variance) and *σ*2p (phenotypic variance).

#### 2.4.3. Estimation of Stability Parameters

The univariate and multivariate parametric stability analyses were performed to assess genotype yield and yield-related traits across multiple environments and predict stable genotypes. Both univariate and multivariate stability analyses were performed year-wise due to the presence of significant variation between the year effect.

#### 2.4.4. Univariate Stability Analysis

Univariate stability of the 7 genotypes for plant height, number of tillers per plant, grain yield per plant, and straw yield per plant was calculated by using AMMI Stability Value (ASV) [21] and AMMI Stability Index (ASI) [22], Shukla's stability variance (*σ*2) [6] and Wricke's ecovalence (*Wi2*) [3].

1. AMMI Stability Value (ASV)

As suggested by Purchase et al. [21], AMMI Stability Value (ASV) parameter for stability assessment is calculated by the following equation

$$\text{ASV} = \sqrt{\left(\frac{\text{SS}\_{\text{IPCA}}}{\text{SS}\_{\text{IPCA}2}} \quad \left(\text{IPCA}1\right)\right)^2 + \left(\text{IPCA}2\right)^2}$$

SSIPCA1 and SSIPCA2 are the sum of squares in the first two principal component interactions. IPCA1 and IPCA2 are the scores of genotypes in the first and second principal components interactions.

2. AMMI Stability Index (ASI)

Jambhulkar et al. [22] suggested the AMMI-model based AMMI Stability Index (ASI), which is calculated by using the following equation:

$$\text{ASI} = \sqrt{\left[\left(\text{IPCA1} \times \theta\_1^2\right)^2 + \left(\text{IPCA2} \times \theta\_2^2\right)^2\right]^2}$$

IPCA1 and IPCA2 are the values of the first two principal component interactions and *θ*<sup>2</sup> <sup>1</sup> and *<sup>θ</sup>*<sup>2</sup> <sup>2</sup> are the values of the percentage sum of square explained by these two components.

3. Wricke's Ecovalence

Wricke [3] introduced the idea of ecovalence parameter to calculate the share of each genotype to the sum of squares of genotype × environment interaction by using the following equation:

$$\mathcal{W}\_i^2 = \sum (X\_{ij} - \overline{X}\_{i\cdot} - \overline{X}\_{\cdot j} + \overline{X}\_{\cdot \cdot})^2$$

Here, *Xij* represents the mean of *i*th genotype in the *j*th environment, *Xi*. is the mean of the yield of *i*th genotype, *X*.*<sup>j</sup>* is the mean of the yield of the *j*th environment, and *X*.. is the grand mean.

4. Shukla's Stability Variance

Shukla [6] proposed the Shukla's stability variance of genotypes across different environments based on the following equation:

$$\sigma^2 = \left[\frac{\mathbf{P}}{(\mathbf{p}-2)(\mathbf{q}-1)}\right] \mathbf{W}\_i^2 - \frac{\sum W\_i^2}{(\mathbf{p}-1)(\mathbf{p}-2)(\mathbf{q}-1)}$$

Here, p and q represent the genotypes and environments number while *Wi <sup>2</sup>* is the Wricke's ecovalence of the *i*th genotype.

#### 2.4.5. Multivariate Stability Analysis

Multivariate stability analysis; AMMI [23] and GGE biplot [13] were performed to identify the ideal genotype across each testing environment with high performance and stability, mega-environments, and understanding of the genotype × environment interactions.
