Optimal diversity-dependent contributions of genotypes to mixtures

Deployment of genotypes to a production population decisively depends on the measure of diversity, a consideration that parallels genetic gain in the management of genotype mixtures. Optimal diversity-dependent deployment has been developed in this study for a family of diversity indices in the genetical and ecological context. The optimal solution at given diversity was expressed as the relationship between genotype contributions and their genetic performances, which maximized genetic gain. Numerical calculations were performed by using genotypes generated from normal order statistics. An optimal deployment in one situation could be nonoptimum in another. Classical uniform deployment, where superior genotypes equally contribute to the mixtures, was the limit of optimal deployment. Comparisons were made between optimal and uniform deployment and between optimal and nonoptimal deployment where genotypes contributed proportionally to the mixtures in accordance to their genetic superiority. The superiority in gain of optimal deployment over that of uniform deployment increased as the difference between the diversity measure under optimal deployment and the contributing number (N) of genotypes under uniform deployment became large and as the diversity measure and N under optimal deployment increased. The superiority over nonoptimal deployment increased rapidly at low diversity, reaching a maximum somewhere at diversity between 1 and N. Scale of superiority depended on the similitude between optimum and nonoptimum deployment; the larger the distinctiveness, the greater the superiority.