Fruit color in a particular plant is controlled by a set of three quantitative trait loci (i.e., QTLs or polygenes), that work in an equal and additive manner. Each QTL has two alleles (i.e., A and a); each allele represented by a capital letter produces one dose of yellow pigment, while alleles represented with lower case letters do not produce any pigment at all. A trihybrid plant (A/a; B/b; C/c) is selfed. Assuming no effects of the environment, what proportion of the offspring will have the same fruit color phenotype as the trihybrid parent?

Given that the trihybrid parents have AaBbCc genotype for fruit color. The trait is a quantitative trait i.e. each dominant allele will have an additive effect on it. In this case, AaBbCc and AABBCC will not produce same fruit color because AaBbCc has only three loci contributing to the color while in AABBCC all the six loci are contributing to the color. For an offspring to be exactly similar to the AaBbCc parents it should have the same genotype of AaBbCc.

The probability of Aa to come from a cross between Aa and Aa is 2/4 or 1/2

The probability of Bb to come from a cross between Bb and Bb is 2/4 or 1/2

The probability of Cc to come from a cross between Cc and Cc is 2/4 or 1/2

So the collective probability of AaBbCc offspring from a cross between AaBbCc and AaBbCc parents would be=

1/2 * 1/2 * 1/2 = 1/8

Hence, assuming no effects of the environment, 1/8 of the offspring will have the same fruit color phenotype as the trihybrid parent.