Table 5.

The equations to select best performing waterlogging stress tolerant sesame genotypes including their strengths and weaknesses, broad sense heritability (h²), selection gain (SG) and factor analysis.

Index	Equations	Equation No.	Reference
Ideotype design and rescaling of traits	$r{X}_{ij}=\frac{{\eta }_{nj}-{\phi }_{nj}}{{\eta }_{oj}-{\phi }_{oj}}\times \left({\theta }_{ij}-{\eta }_{0j}\right)+{\eta }_{nj}$	viii	[13]
Multi trait genotype-ideotype index (MGIDI)	$MGID{I}_i={\left[\sum _{j=1}^f{\left({\gamma }_{ij}-{\gamma }_j\right)}^2\right]}^{0.5}$	ix
Broad sense heritability (h2)	$h^2={\widehat{\sigma }}_a^2/\left({\widehat{\sigma }}_a^2+{\widehat{\sigma }}_{\epsilon }^2/r\right)$	x
Selection differential (SD)	$SD={\bar{X}}_s-{\bar{X}}_o$	xi
Selection gain (SG)	$SG(\%)=\frac{\left({\bar{X}}_s-{\bar{X}}_o\right)\times h^2}{{\bar{X}}_o}\times 100$	xii
Factor analysis	$X=\mu +Lf+\epsilon$	xiii
Factor loadings	$F=Z{\left(A^T{R}^{-1}\right)}^T$	xvi
Strength and weaknesses of selected genotypes	${\omega }_{ij}=\frac{\sqrt{D_{\mathrm{i}j}^2}}{{\sum }_{j=1}^f\sqrt{D_{ij}^2}}$	xv