Performance and stability of mixtures of grain sorghum : I. Relationship between level of genetic diversity and performance.

In the absence of intergenotypic interactions the expected yield of randomly constituted, equiproportional mixtures of genotypes is shown to be independent of the number of components. However, with positive, additive interactions, the expected yield of a mixture is expected to be a monotonically increasing function of the number of components. The observed relationship between level of genetic diversity and mean yield, seed number and seed size for mixtures of inbred lines of grain sorghum closely followed the relationships expected under the assumption of additive interaction effects. However, estimates of the first and higher order components of the total interaction effect among the sorghum lines indicated that higher order interaction effects were often as great or greater than their first order counterparts, and opposite in sign, and that they may thus have had a cancelling effect in mixtures containing three or more components. These findings are discussed in terms of the relationship between level of genetic diversity and performance, and in connection with problems associated with the development of commercial multiline varieties.