Direct approach to modeling epistasis.
Genome-wide association studies have recently been conducted in humans and domesticated animals and plants to locate and identify chromosomal regions or genes (quantitative trait loci or QTLs) to select individuals with superior performance and qualities. QTL or genetic effects, including epistatic effects, can be defined at the genotypic (functional) and gene (statistical) levels. In the past, the functional or statistical genetic effects have been defined indirectly, and genotypic values were expressed as linear functions of additive, dominance, and epistatic genetic effects. In this chapter, we propose to reverse the thinking and define genetic effects as linear functions of genotypic values. The direct definition of functional genetic effects is straightforward for well-known gene action models [e.g., unweighted (UW), F2, and F∞ models]. However, the direct definition of statistical genetic effects is based on Fisher's concept of average excess, which is closely related to the well-known concept of the average effect of a gene substitution. These definitions can be easily extended to cases of two or more loci as long as the loci are independent of each other. Two numerical examples are used to illustrate the properties of the direct approach.
Research and Innovation Division, Alberta Agriculture and Rural Development, Edmonton, AB, Canada, T6H 5T6, rong-cai.yang@ualberta.ca.
Rong-Cai
RC
Yang
D000818:Animals; D004843:Epistasis, Genetic; D005787:Gene Frequency; D056426:Genetic Loci; D005821:Genetic Techniques; D005838:Genotype; D006801:Humans; D008957:Models, Genetic; D013223:Statistics as Topic