Chapter 22, Problem 12P

Two alleles at one locus produce three distinct phenotypes. Two alleles of two genes lead to five distinct phenotypes. Two alleles of six genes lead to 13 distinct phenotypes. (These statements assume that the alleles at any one locus are codominant or incompletely dominant and that each gene makes an equal contribution to the phenotype.)

a.

Derive a formula to express this relationship. (Let n equal the number of genes.)

b.

Each of the most extreme phenotypes for a trait determined by two alleles at one locus are found in a proportion of 1/4 in the F2 generation. If two alleles of two genes determine the trait, each extreme phenotype will be present in the F2 as 1/16 of the population. In common wheat (Triticum aestivum), kernel color varies from red to white and the genes controlling the color act additively, that is, alleles for each gene are incompletely dominant and each gene contributes equally to the color. A true-breeding red variety is crossed to a true-breeding white variety, and 1/256 of the F2 have red kernels and 1/256 have white kernels. How many genes control kernel color in this cross?