The effect of population structure on the relationship between heterosis and heterozygosity at marker loci.

The relationship between heterozygosity at neutral marker loci and heterosis of F1 hybrids is investigated using a theoretical model. Results emphasize that linkage disequilibrium between the markers and the loci implicated in heterosis [quantitative trait loci (QTLs) that exhibit dominance effects] is a necessary condition to finding a correlation (ϱ mh ) between heterozygosity at marker loci and the heterosis. The effect of population structure, in which the parental inbred lines of the hybrids belong to different heterotic groups, is considered. ϱ mh is investigated for: (1) hybrids between lines that belong to the same heterotic group (within-group hybrids); (2) hybrids between lines that belong to different groups (between-group hybrids); and (3) all hybrids, both within and between-groups. Within a group, significant values of (ϱ mh ) may arise because of linkage disequilibrium generated by drift. At the between-group level, no correlation is expected since link-age disequilibrium should differ randomly from one group to the other, which is consistent with recent experimental results. Possible ways to achieve prediction of the heterosis in this situation are discussed. When all hybrids are considered simultaneously, divergence of allelic frequencies among groups for the markers and the QTLs produces a correlation between heterosis and heterozygosity at marker loci. This correlation increases with the number of markers that are considered.