A theory of heterosis.

Heterosis refers to the superior performance of a hybrid over its parents. It is the basis for hybrid breeding particularly for maize and rice. Genetically, it is due to interactions between alleles of quantitative trait loci (dominance and epistasis). Despite enormous interest and efforts to study the genetic basis of heterosis, the relative contribution of dominance vs epistasis to heterosis is still not clear. This is because most published studies estimate quantitative trait loci effects in pieces, not able to put them together to assess the overall pattern adequately. We propose a theoretical framework that focuses on the inference of the relationship between genome and traits that includes the identification of multiple quantitative trait loci and estimation of the whole set of quantitative trait loci (additive, dominant, and epistatic) effects. Used for heterosis, it gives a clear genetic definition and interpretation of heterosis. We applied the theory and methods to a large maize dataset with a factorial design of many male and female inbred lines and their hybrid crosses. Heterosis of ear weight in maize is primarily due to quantitative trait loci dominant effects, many are overdominant. The contribution to heterosis due to epistasis is small and diffused. For comparison, we also analyzed a rice dataset that is an F2-type population derived from a cross between 2 inbred lines. The result indicates that dominance is still the main contributor to heterosis, and epistasis contribution is small.