The purpose of this study was to estimate and compare the genetic gain obtained from the Smith-Hazel index model of selection index with direct selection to enhance the selection efficiency of superior promising families in early segregating generations of the durum wheat population. Two methods of selection were evaluated, namely, direct selection and indirect selection, by the selection index in the yield and its components. A comparison of mean performances for different traits among the four generations (F2, F3, F4, and F5) revealed an increase in mean values for most traits with advanced generations from F2 to F5, with some exceptions due to environmental factors. PCV and GCV were generally larger in magnitude for all studied traits in the F2 generation as compared with the advanced generations F3, F4, and F5, indicating that the magnitude of the genetic variability persisting in this material was sufficient for providing a rather substantial amount of improvement through the selection of superior progeny. High heritability values over 50% for most studied traits across generations indicate a high magnitude of genetic variability and possible success in selection in early generations. Nine out of eleven selection indices were more efficient than direct selection for improving GY/P in the F2 population. The highest predicted genetic gain from F2 generation for GY/P was observed when selection index (IW123) was followed by selection index (IW2) and by selections for (IW12), ( IW23), (IW1), and (IW3). Selection index (IW123), followed by IW12 and direct selection (IXW), gave the highest actual genetic gains from the third generation for trait GY/P. Most indices showed a high discrepancy between predicted and actual genetic gain as GY/P; this was due to the interaction between genetic effects and large effects of environmental factors. The maximum predicted genetic advance from F3 and F4 generations for GY/P was achieved when selecting directly (IXW) in F3 followed by selection indices (I123). While maximum actual genetic advance from F3 and F4 generations for GY and P was achieved when using selection indices (I123), followed by (IW2), and then direct selection (Ixw). Deviations of the actual genetic advance from the predicted advance from the F3 and F4 generations showed positive and large values in most procedures.

The main objective of this investigation was to study gene effects by the analysis generation means for grain yield and its components characters in two bread wheat crosses, (Sids1 x Giza171) and (Shandaweel1 x Sakha94). Randomize complete block design with three replications was used for P1, P2, F1, F2, BC1, and BC2 during 2018/2019, 2019/2020 and 2020/2021 growing seasons. The measurements of gene effect and non-allelic interaction in addition to heterosis, inbreeding depression and heritability of grain yield and yield components in bread wheat were estimated. Scaling test showed significant effect for almost characters in both crosses. The additive (d) gene effect was positive and highly significant for number of kernels/spike and grain yield/plant for the first cross and positive significant with 100-kernel weight in the second cross, but negative significant with first cross. Estimates of dominance (h) effects were highly significant for number of spikes/plant and number of kernels/spike in second cross. Better parent heterobeltiosis, significant and highly significant heterobeltiotic effect positive was found between crosses for grain yield in two crosses and number of kernel/spike for the second cross. Results of inbreeding depression were highly significant positive for all the study traits. Broad sense heritability values ranged from 45.15 to 88.01% for all studied characters in both crosses.

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