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[This article belongs to Volume - 57, Issue - 06]

Abstract : Our study aims to contribute, in a systematic way, to the development of new genetic diversity by targeting the characteristics of the parents, and the characteristics that can raise the productivity of the resulting offspring. Four genotypes of soft wheat (Triticum aestivum L.) were used as TSI/VEE parents, WeebilliMexipak, and Florence-aurore, to obtain six crosses using the method of crossing half allele. The experiment was carried out in a greenhouse at the Bio-pole Research Center. It is affiliated to the Laboratory for the Development and Valorization of Plant Genetic Resources, University of Mentnouri Brothers Constantine 1 (Algeria).Hybrids were planted with their parents according to the randomized complete block design (RCBD) and at the rate of three replications to study the general ability to compatibility (GAC), the specific ability to compatibility (SAC), the vigor of the hybrid in comparison to the mean of the parents (MP), the best parents (BP) and the degree of heritability in the broad and narrow sense, for some agricultural characteristics. The results revealed the importance of each of the cumulative and non-cumulative genotypes in the inheritance of the studied traits, where the cumulative genotype dominated the inheritance of plant height and the number of grains per spike, the rest of the studied traits were controlled by non-cumulative genotypes, as parents TSI\VEE and Florence Aurore showed better significant and desirable values of general ability to compatibility (GAC) for some adaptive and productive characteristics, therefore it is suggested to use these parents in grain crop improvement programs for their ability to pass on their traits to their offspring. A hybrid with a positive special ability for compatibility (ASC) was obtained as a result of the genetic interaction (cumulative X cumulative) and the bearer of the highest values of hybrid strength, and this is in the hybrid (TSI\VEE X Mexipak).This hybrid can be adopted as an elicited hybrid that has the ability to inherit some characteristics of adaptation and components of yield and follow-up improvement in it through selection in isolated generations to reach a pure strain grown as a stable variety. The degree of heritability in the narrow sense showed high values in seven traits, while the values of the degree of heritability in the broad sense were high in all studied traits.