Theoretical Relations among Single, Three-Way, and Double Cross Hybrids

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Abstract
The proposed model permits the comparison of the means of all possible single, 3-way, and double cross hybrids derived from a fixed set of 4 homozygous lines in terms of additive, dominance, and digenic epistatic effects under the assumption of normal diploid inheritance, no multiple alleles, no linkage, and no recoprocal effects. Five formulas that have been used to predict double cross performance are examined. The expectations of 4 of these are shown to be identical with the expectation of the double cross in the absence of epistasis. A new method of predicting double cross performance when epistasis must be considered, utilizing both single cross and 3-way cross means, is proposed. This method is biased only by a certain portion of the dominance epistatic effects. The analysis of variance among single, 3-way, and double cross means also provides tests for detecting the presence of epistatic effects using non-inbred experimental material.

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