Gene interaction and modified ratios

When the ratio is not 9 : 3 : 3 : 1

In Mendel's dihybrid cross, the two genes control two separate traits, and the F2 shows 9 : 3 : 3 : 1. Some traits are made by two genes together. The two genes still assort independently, and there are still 16 boxes. What changes is how the boxes are sorted into phenotypes.

This lesson goes beyond the NTA syllabus. Gene interaction is taught at A-Level, in IB Biology at Higher Level and at the Olympiad. The papers of this course keep to topics of the NTA syllabus.

Epistasis

Epistasis is the masking of the effect of one gene by a gene at another place. It is not the same as dominance, which is a relation between two alleles of one gene. The gene that masks is epistatic, and the gene that is masked is hypostatic.

Recessive epistasis: 9 : 3 : 4

The coat colour of a Labrador retriever depends on two genes.

• Gene B: black (B) is dominant over brown (b).
• Gene A (called E in many books): A lets the pigment go into the hair. In the genotype aa, no pigment goes into the hair, and the coat is yellow, whatever the B gene is.

An AaBb dog crossed with an AaBb dog gives 9 black (A and B), 3 brown (A and bb) and 4 yellow (aa with any B). The ratio is 9 : 3 : 4. The recessive genotype aa is epistatic over B.

Dominant epistasis: 12 : 3 : 1

In the fruit colour of the summer squash, a dominant allele W gives white fruit and hides the effect of the second gene. Without W, the allele Y gives yellow and yy gives green. The F2 shows 12 white (W with anything) : 3 yellow (ww with Y) : 1 green (wwyy). The ratio is 12 : 3 : 1.

Complementary genes: 9 : 7

Sometimes a trait needs a dominant allele of each of two genes. Without either one, the trait does not appear. In the sweet pea, the purple colour of the flower needs a dominant allele of both gene C and gene P. Two heterozygous plants give 9 purple (C and P) : 7 white. The ratio is 9 : 7.

Duplicate genes: 15 : 1 and 9 : 6 : 1

Two genes may do the same job.

• If one dominant allele of either gene is enough, only aabb differs. The F2 ratio is 15 : 1. An example is the shape of the seed capsule of the shepherd's purse.
• If each dominant allele adds to the trait, there are three classes: both genes dominant, only one gene dominant, and neither. The F2 ratio is 9 : 6 : 1. An example is the shape of the summer squash fruit.

Epistasis in the human blood groups

The Bombay phenotype shows epistasis in a human gene system. A person who is hh cannot make the substance H, on which the A and B sugars are built. Such a person has red cells that look like group O, even if the person carries the allele $I^A$ or $I^B$.

The method

You do not need to remember all the ratios. Use the steps.

1. Write the 16 boxes of AaBb × AaBb.
2. Write the rule of the trait in terms of "has A" and "has B".
3. Count the boxes of each phenotype.

You should see that every ratio is a sorting of the same 16 boxes into 2 or 3 classes.

Try it in Python

The program applies the rule of each kind of interaction to the 16 boxes and prints the ratio.

Practise with new numbers

Common mistakes

• Calling epistasis dominance. Dominance is between two alleles of one gene. Epistasis is between two genes.
• Thinking that the genes assort in another way. They still assort independently. Only the sorting of the phenotypes changes.
• Writing 9 : 3 : 3 : 1 for every cross with two genes. Check whether the two genes act on one trait.
• Adding the classes wrongly. Every ratio of this lesson must add up to 16.

Remember these

• Recessive epistasis: 9 : 3 : 4. Dominant epistasis: 12 : 3 : 1. Complementary genes: 9 : 7.
• Duplicate genes: 15 : 1. With a cumulative effect: 9 : 6 : 1.
• All of them come from the same 16 boxes of AaBb × AaBb.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A cross of two AaBb plants gives 9 purple : 7 white. Name the interaction.

2. Two AaBb Labradors have 48 puppies. How many are black, brown and yellow?

3. Two AaBb squash plants are crossed and give 12 white : 3 yellow : 1 green. Name the kind of interaction.

4. A cross gives 15 : 1. How many kinds of genotype are in the large class?

5. How is epistasis different from dominance?

References

• Clark M. A., Douglas M. and Choi J. (2018). Biology 2e, OpenStax, chapter 12.3 (Laws of inheritance, epistasis).
• NCERT (2023). Biology, Textbook for Class XII, chapter 4 (for the dihybrid cross that this lesson modifies).