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Q8:
Two heterozygous parents are crossed. If the two loci are linked what would be the distribution of phenotypic features in (F_{1}) generation for a dibybrid cross?

Solution :

Step 1: Establishing Genetic Configuration

Given that the parents are heterozygous for two linked loci (Dihybrid), we define the alleles as $A, a$ and $B, b$. The term "linked" implies that the loci are situated on the same chromosome. The phenotypic distribution depends on the phase of linkage:

  • Cis-arrangement (Coupling): Dominant alleles ($AB$) are on one chromosome, and recessive alleles ($ab$) are on the homologous chromosome. Genotype: $\frac{AB}{ab}$.
  • Trans-arrangement (Repulsion): Dominant and recessive alleles are cross-linked. Genotype: $\frac{Ab}{aB}$.

Step 2: Analytical Implications of Linkage

Per the Law of Linkage (Morgan, 1910), linked genes do not follow Mendel’s Law of Independent Assortment. Instead, they tend to be inherited together unless separated by crossing over (recombination).

Inheritance Pattern Expected Ratio (Independent Assortment) Result with Complete Linkage
Phenotypic Ratio $9:3:3:1$ $3:1$ (Cis) or $2:1:1$ (Trans)

Step 3: Calculating Phenotypic Distribution (Assuming Complete Linkage)

If genes are completely linked and in cis-configuration ($\frac{AB}{ab} \times \frac{AB}{ab}$):

  1. Gametes produced by each parent: $AB$ and $ab$ (in equal proportions).
  2. Punnett Square setup:
    AB ab AB ab AABB AaBb AaBb aabb
  3. Phenotypic frequency: 3 (Dominant-Dominant) : 1 (Recessive-Recessive).

Step 4: Incorporating Recombination (Incomplete Linkage)

In biological reality, linkage is rarely 100%. If crossing over occurs, the distance between loci determines the frequency of recombinant phenotypes. If $p$ is the frequency of recombination, the offspring frequency is defined as:

  • Parental combinations: $\frac{1-p}{2}$ for each type.
  • Recombinant combinations: $\frac{p}{2}$ for each type.

[By the Principle of Recombination Frequency]: As the distance between loci increases, the ratio shifts from $3:1$ toward the Mendelian $9:3:3:1$ ratio.

Final Solution: If linkage is complete, the phenotypic ratio is 3:1. If linkage is incomplete, the phenotypic distribution will deviate from the Mendelian 9:3:3:1 ratio, with parental phenotypes appearing with higher frequency than recombinant phenotypes.


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