How informative is Wright's estimator of the number of genes affecting a quantitative character?

Abstract

S. Wright suggested an estimator, m̄, of the number of loci, m, contributing to the difference in a quantitative character between two differentiated populations, which is calculated from the phenotypic means and variances in the two parental populations and their F1 and F2 hybrids. The same method can also be used to estimate m contributing to the genetic variance within a single population, by using divergent selection to create differentiated lines from the base population. In this paper we systematically examine the utility and problems of this technique under the influences of unequal allelic effects and initial allele frequencies, and linkage, which are known to lead m̄ to underestimate m. In addition, we examine the effects of population size and selection intensity during the generations of selection. During selection, the estimator m̄ rapidly approaches its expected value at the selection limit. With reasonable assumptions about unequal allelic effects and initial allele frequencies, the expected value of m̄ without linkage is likely to be on the order of one-third of the number of genes. The estimates suffer most seriously from linkage. The practical maximum expectation of m̄ is just about the number of chromosomes, considerably less than the 'recombination index' which has been assumed to be the upper limit. The estimates are also associated with large sampling variances. An estimator of the variance of m̄ derived by R. Lande substantially underestimates the actual variance. Modifications to the method can ameliorate some of the problems. These include using F3 or later generation variances or the genetic variance in the base population, and replicating the experiments and estimation procedure. However, even in the best of circumstances, information from m̄ is very limited and can be misleading.