Detection and utilization of single genes without DNA assays

Quantitative traits are often assumed to be controlled by a large number of loci that each have a small effect. Under this assumption, the distribution of genotypic and phenotypic values can be adequately modeled by a multivariate normal distribution. Thus, most genetic analyses are based on mixed linear models. Evidence is accumulating, however, for the presence of loci that have large effects on traits of economic importance. If the genotypes for such loci can be observed without error, then-conditional on these observed genotypes-genotypic and phenotypic values follow a multivariate normal distribution, and data from very large pedigrees can be analyzed using a mixed linear model that includes the genotypic effects for these loci as fixed effects. However, when the major genotype is not observed, the genotypic and phenotypic values follow a mixture of multivariate normal distributions, and analyses based on fitting a mixed linear model may not be optimum, especially for populations undergoing selection and nonrandom mating. Several approaches are discussed for the genetic analysis of data when the major genotypes are not known.