Alternative ways of estimating the number of genes in a polygenic system by genotype assay

Abstract

The procedures for estimating k, the number of genes, or more strictly the number of effective factors in a polygenic system by the method of genotype assay have been extended to any number, p, of Fn+2 grand progeny families raised from each Fn individual assayed. Formulae are also derived that would be more appropriate for estimating k if dominance were absent or in the more unlikely event of no internal balancing. The existing and new procedures are illustrated by the analysis of data from a cross between varieties 1 and 5 of Nicotiana rustica which extended to the F8 generation. The structure of these data permitted the estimation of k for flowering time and final height in the F2 from assessments made on the F4 for p = 2, from F5 to F8 for p = 4 and from joint consideration of the F4 to F8assessments. All these assays of the F2 gave low estimates for k. On the other hand, using the same F5 to F8 data to assay the F3 to F6 generations respectively for p = 2 gave estimates of k that increased rapidly with generation so that for every one detected in the F2 there were ten on average in the F6. Checks and controls of the material and method, including using the same procedures to estimate k for a known single major gene difference segregating in this cross, leave no doubt that the rise in the estimate is genuine. Furthermore, it is expected from the nature of effective factors and the linkage disequilibrium that is generated on making this cross and subsequently resolved over successive rounds of recombination. These analyses confirm the overwhelming superiority of genotype assay over the other methods of estimating k that are available in all but a few species.