33. Assume that the gene UNC is essential for the coordinated movement of a nematode and that the wild-type allele U is dominant over the mutant allele u. Similarly, the wild-type allele D of another gene DPY, which is responsible for the normal body length, is dominant over the mutant allele d. Assume the UNC and DPY are on two different chromosomes. If a female of genotype UUDD mates with a male of the genotype uudd, the percentage of the F2 progeny that will display uncoordinated movement but will have normal body length is

Dihybrid Cross Probability: Calculating the Percentage of F₂ Progeny with Uncoordinated Movement and Normal Body Length

Introduction

The dihybrid cross is one of the most important concepts in classical genetics because it demonstrates Mendel’s Law of Independent Assortment. According to this law, genes located on different chromosomes assort independently during meiosis, producing new combinations of alleles in the offspring. This independent segregation enables geneticists to calculate the probability of obtaining specific phenotypes by considering each gene separately and then applying the multiplication rule of probability.

In this problem, two independently assorting genes control two different traits in a nematode. The first gene (UNC) determines coordinated movement, whereas the second gene (DPY) determines normal body length. Since the two genes are located on different chromosomes, they follow independent assortment, making probability calculations straightforward.

Correct Answer

Correct Answer: 18.75% (3/16)

Detailed Explanation

The parental cross is:

UUDD × uudd

The female contributes only UD gametes, whereas the male contributes only ud gametes.

Therefore, every F₁ offspring has the genotype:

UuDd

Since both dominant alleles are present, all F₁ individuals show coordinated movement and normal body length.

When the F₁ individuals are self-fertilized, the cross becomes:

UuDd × UuDd

Because the two genes are located on different chromosomes, they assort independently during meiosis.

Step 1: Probability of Uncoordinated Movement

Uncoordinated movement is produced only by the homozygous recessive genotype:

uu

For the cross:

Uu × Uu

The genotypic ratio is:

1 UU : 2 Uu : 1 uu

Therefore,

P(uu) = 1/4

Step 2: Probability of Normal Body Length

Normal body length is expressed by either:

DD or Dd

For the cross:

Dd × Dd

The phenotypic ratio is:

3 Normal : 1 Dwarf

Therefore,

P(D−) = 3/4

Step 3: Apply the Multiplication Rule

Since the genes assort independently, multiply the probabilities of the two required phenotypes.

P(uu and D−) = P(uu) × P(D−)

= (1/4) × (3/4)

= 3/16

= 0.1875

Converting into percentage:

0.1875 × 100 = 18.75%

Step-by-Step Calculation

Parental Cross

UUDD × uudd

F₁ = UuDd

F₁ Self Cross

UuDd × UuDd

Probability for Each Trait

Combined Probability

(1/4) × (3/4) = 3/16

= 18.75%

Calculation Summary

Why Is the Multiplication Rule Used?

The UNC and DPY genes are located on different chromosomes. Therefore, they obey Mendel’s Law of Independent Assortment, which states that the segregation of one gene pair does not influence the segregation of another gene pair. As a result, the probability of obtaining both desired phenotypes simultaneously is calculated by multiplying their individual probabilities.

Expected F₂ Phenotypic Ratio

Biological Significance

Dihybrid crosses demonstrate how independent assortment generates new genetic combinations in sexually reproducing organisms. This process increases genetic diversity within populations and forms the basis of modern breeding programmes, evolutionary genetics, and inheritance studies. Probability calculations derived from Mendelian principles are widely applied in plant breeding, animal breeding, medical genetics, and genetic counseling.

Final Answer

Probability of uncoordinated movement (uu) = 1/4

Probability of normal body length (D−) = 3/4

Combined probability = (1/4) × (3/4) = 3/16

= 0.1875

= 18.75%

Correct Answer: 18.75% (3/16)