Stability of performance of mixtures and multilines

Summary The effect of intra-populational genetic diversity on the stability of performance of equiproportional mixtures, as measured by their variance in yield over a range of environments, was investigated with a simple theoretical model.In the absence of intergenotypic interactions it was found that a mixture will be more stable than the most stable line (V_min) if:{fx405-1} where n is the number of lines in the mixture and {ie405-1} and {ie405-2} are the mean variance and covariance in yield of the component lines. In other words, the yield of multilines will vary less than that of their most invariant component only when the component lines respond quite differently to environmental changes.In the presence of intergenotypic interactions it was found that a mixture will be more stable than its best or better component (V_min) provided:{fx405-2} where n, {ie405-1} and {ie405-2} take the same meaning as before and {ie405-3} and {ie405-4} represent the mean variance and covariance of the interaction effects among the n lines. That is, when the components of a mixture significantly interact, then the dissimilarity in response of each component to environmental fluctuations must be even greater for there to be a stability benefit to mixtures.These findings are discussed in relation to the problem of developing commercially acceptable multiline varieties.