12. Two interacting genes (independently assorting) were involved in the same pathway. Absence of either genes function leads to absence of the end product of the pathway. A dihybrid cross involving the two genes is carried out. What fraction of the F2 progeny will show the presence of the end product?
(1) 1/4 (2) 3/4
(3) 9/16 (4) 15/16
Introduction
In genetics, when two independently assorting genes interact in the same biochemical pathway, the absence of function in either gene can result in the absence of the pathway’s end product.
This article explains how to solve dihybrid crosses under such conditions and determine the fraction of F2 progeny displaying the presence of the end product.
Explanation of the Genetic Cross
Two genes independently assort with alleles A/a and B/b. Both genes are necessary in their dominant or functional form to produce the end product.
The genotype combinations that will show the product include all combinations except those homozygous recessive for either gene (aa or bb).
Since each gene independently segregates with a dominant functional allele frequency of 3/4 in the F2 generation (AA or Aa),
the combined probability that both genes have at least one dominant allele is:
(3/4) × (3/4) = 9/16
This means 9/16 of the F2 progeny will show the presence of the end product.
Explanation of Other Options
1/4
This fraction would represent only the double homozygous recessive genotype (aabb), which shows absence of product,
so this option is incorrect for presence.
3/4
This refers to the dominant phenotype for a single gene, not for two interacting genes. Therefore, it is not the correct fraction when both genes are required for product formation.
15/16
This would be the fraction showing presence if only the double recessive genotype lacked function and all others showed the product.
However, since the question states that absence of either gene leads to no product, 15/16 is incorrect.
Correct Answer
The correct fraction of F2 progeny showing the presence of the end product is 9/16.
This is an example of complementary gene action, where both genes must have at least one functional allele for the product to appear.
Thus, the correct answer is (3) 9/16.
Conclusion
This explanation clarifies the epistatic interaction of two genes functioning in the same pathway and how it affects progeny phenotypes in a dihybrid cross.
Understanding such ratios is fundamental to predicting phenotypic outcomes in classical Mendelian and non-Mendelian inheritance patterns.
