Relationship between heterosis and heterozygosity at marker loci: a theoretical computation

In this paper we have studied the linear correlation between a genetic distance index between two parent lines (based on marker loci information) and the heterosis observed in the F1 hybrid from the two lines, for a quantitative character (determined by several loci, or QTL). Theoretical computations of the correlation coefficient (ϱ) between the distance index and the heterosis were made, assuming the biallelic model (defined by Fisher). When the alleles at both marker loci and QTL are equally distributed among the whole population of considered lines, the coefficient ϱ is a function of the squares of linkage disequilibria between alleles at marker loci and alleles at QTL. The QTL that are not marked by marker loci and marker loci that do not mark any QTL play symmetrical roles and can decrease ϱ greatly. We conclude that the prediction of F1 hybrid heterosis based on marker loci would be more efficient if these markers were selected for their relationship to the alleles implicated in the heterotic traits considered.