Question

If there is complete dominance, the additive variance is maximal when the frequency of recessive allele is

• A. 0.25
• B. 0.50
• C. 0.75
• D. 1.00

Hint:

Genetic Variance Maxima: Additive variance under complete dominance peaks at intermediate gene frequency ($p = q = 0.50$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Quantitative genetics under complete dominance: additive genetic variance ($V_A = 2pqlpha^2$) reaches its theoretical peak at intermediate gene frequencies ($p = q = 0.50$).
Key Formula or Approach:
\[ V_A = 2pq \left[ a + d(q - p) \right]^2 \xrightarrow{d = a \text{ (Complete Dominance)}} V_A = 8a^2 p q^3 \implies \text{Maximized at intermediate frequency } q = 0.50 \]

Step 2: Detailed Explanation:
In quantitative genetics (Falconer and Mackay):
- Additive genetic variance ($V_A$) is the primary component of phenotypic variance that determines resemblance between relatives and response to selection.
- In a single locus with two alleles ($A_1, A_2$) with frequencies $p$ and $q$ ($p + q = 1$):
When allele frequencies are intermediate at $p = q = 0.50$, heterozygosity ($2pq$) and genetic variance are maximized under standard complete dominance models.

Step 3: Final Answer:
Therefore, additive variance is maximal when recessive allele frequency is 0.50, matching option (B).