A revised Fisher model on analysis of quantitative trait loci with multiple alleles

Zeng et al. (2005) proposed a general two-allele (G2A) model to model bi-allelic quantitative trait loci (QTL). Comparing with the classical Fisher model, the G2A model can avoid using redundant parameters and be fitted directly using standard least square (LS) approach. In this study, we further extend the G2A model to general multi-allele (GMA) model. First, we propose a one-locus GMA model for phase known genotypes based on modeling the inheritance of paternal and maternal alleles. Next, we develop a one-locus GMA model for phase unknown genotypes by treating it as a special case of the phase known one-locus GMA model. Thirdly, we extend the one-locus GMA models to multiple loci. We discuss how the genetic variance components can be analyzed using these GMA models in equilibrium as well as disequilibrium populations. Finally, we apply the GMA model to a published experimental data set.