Question

In a population with a coefficient of inbreeding F, change of mean resulting from inbreeding is

• A. -2dpqF
• B. 2dpqF
• C. -pdqF
• D. -4dpqF

Hint:

The term \(-2dpqF\) shows that inbreeding depression is directly proportional to the dominance deviation (\(d\)) and the inbreeding coefficient (\(F\)). If there is no dominance (\(d = 0\)), there is no inbreeding depression.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Inbreeding increases homozygosity and decreases heterozygosity. This change in genotype frequencies affects the mean of quantitative traits, a phenomenon known as inbreeding depression.

Step 2: Key Formula or Approach:
For a single locus with two alleles (A and a) with frequencies \(p\) and \(q\), let the genotypic values be:
\(a\) for AA, \(d\) for Aa, and \(-a\) for aa.

Step 3: Detailed Explanation:
The mean of an outbred population (\(F = 0\)) is:
\[ M_0 = a(p - q) + 2dpq \]
In an inbred population with inbreeding coefficient \(F\), the genotype frequencies change to:
\(f(\text{AA}) = p^2 + pqF\)
\(f(\text{Aa}) = 2pq(1 - F)\)
\(f(\text{aa}) = q^2 + pqF\)
The mean of this inbred population (\(M_F\)) is:
\[ M_F = a(p - q) + 2dpq(1 - F) \]
Comparing \(M_F\) with \(M_0\):
\[ M_F = M_0 - 2dpqF \]
Thus, the change in the population mean due to inbreeding (\(\Delta M\)) is:
\[ \Delta M = M_F - M_0 = -2dpqF \]

Step 4: Final Answer
The change of mean resulting from inbreeding is \(-2dpqF\).