A quantitative genetic model for analyzing species differences in outcrossing species

A genetic model based on a two-level intra- and interspecific mating design is proposed to estimate the genetic architecture of species differences and heterosis for outcrossing species. The underlying genetic analyses make use of classical quantitative genetic theories and recent results from molecular genetic studies. Gene effects across different quantitative trait loci (QTL) can be approximated by a geometric series. Under natural selection, gene effects are often associated with allele frequencies in a particular way, which can be approximated by the gamma distribution. By incorporating these approximations into family structural analyses in the mating design, we are able to estimate a number of genetic parameters that contribute to quantitative genetic variation based on a nonlinear optimization approach. These parameters include the number of QTL, their gene effects, and their allele frequencies in the parental populations. We perform simulation studies and illustrate an example to demonstrate the statistical property and procedure of the method.