Quantitative genetics of allogamous F-2: an origin of randomly fertilized populations

The quantitative genetic properties are derived for the bulk F-2 originatin g from random fertilization (RF) amongst hybrid (F-1) individuals. Only its mean appears to have been derived previously, and that definition is confi rmed (by another method). New general equations are found also for all geno type frequencies, allele frequencies, inbreeding coefficient, the genotypic , additive-genetic and dominance variances, and broad-sense and narrow-sens e heritabilities. The assumption that such an F-2 is a classical RF populat ion is shown to be correct. Indeed, the allogamous F-2 is a natural origin for the RF population. The relationships are given between precedent RF pop ulations (parents) and subsequent RF populations following hybridization (a llogamous F-2). The allogamous F-2 is generally inbred with respect to its parental F-1, the degree depending on the hybrid's parents' allele frequenc ies. At the same time, it is outbred with respect to those original parents , and not inbred at all with respect to the equivalent RF population. The g enotypic variance is generally more than in the F-1, and likewise for herit abilities. These findings make it possible to evaluate the genetic advance from selection and hybridization. The results depend on the allele frequenc ies of the original parents and the degree of overdominance, but generally, selection is more advantageous than hybrid vigour.