A method for computing inbreeding in advanced generations of synthetic varieties was demonstrated. With a knowledge of the effect of inbreeding on the productivity of a particular crop species, a plant breeder, by applying the formulae derived in this paper, can determine the effect of varying the number of parents used to produce a synthetic variety, the amount of inbreeding of parents, if any, that is desirable, and the synthetic generation that should be utilized for agronomic production.

Formulae for predicting yield of synthetic varieties are useful in two ways. First, they presumably have predictive value, and second, if they have predictive value, the formulae define those factors that control yield. Such formulae give the relationship of one yield factor to another. In this paper I derive prediction formulae which will, I believe, successfully predict yield. These formulae take into account the effects of ploidy, selfing, number of parents, inbreeding of parents, combining ability of parents, relationship between parents, and the generation of multiplication of the synthetic variety.The formulae are based upon the observation that heterosis increases with outbreeding and diminishes with inbreeding. A linear relationship between yield and heterozygosity is assumed but the formulae also should be useful when the relationship between yield and heterozygosis is nonlinear, providing a satisfactory transformation of the yield data to fit the linear relationship can be found. The level of heterozygosis is expressed as the coefficient of inbreeding F.

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