Estimating the number of genes in a polygenic system by genotype assay

Abstract

A new method, genotype assay, is described for estimating k the number of genes or more strictly the number of effective factors responsible for variation of a continuous kind. The central feature is the determination of the proportion of individuals in the Fn generation of a cross between two pure breeding lines that are heterozygous at, at least, one locus by an assay of their Fn+2 grand progeny families. The observed proportion is then equated to a theoretical expectation which is a function of the number of genes involved. Expectations generalised to cover any generation n for experimental designs in which every Fn individual is assayed by comparing two Fn+2 grand progeny families have been derived for two limiting cases; one in which all genotypic differences are expressed as phenotypic differences and the other where the expression is minimised by imposing the maximum and relational balancing out of the contributions of individual gene loci. Equating the observed proportion of heterozygotes to these expectations therefore, leads to an upper and a lower estimate of k corresponding with these two limiting conditions. The reliability and sensitivity of the estimates depends primarily on n the generation chosen for study, the number of individuals (m) assayed from that generation and the number of individuals (l) raised in each Fn+2 grand progeny family. The two variables m and l being the principal determinants of the variances of the family means set the lower limit to the size of the gene effects that can be detected. The method is illustrated by assays of the F3 and F5 generations of two crosses between conditioned lines of Nicotiana rustica for three characters. The estimates are, without exception, as great as or greater than those obtained by alternative procedures. They show large, consistent increases between the F3 and F5 that cannot be traced to greater sensitivity of the latter generation and hence are presumably genuine.