Question

If one male from each sire’s progeny and one female from each dam’s progeny is chosen, the variance of family size will be

• A. 1
• B. positive
• C. negative
• D. zero

Hint:

Equalizing family sizes so that every parent contributes the same number of offspring reduces the variance of family size to zero, which helps slow down the rate of genetic drift.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In quantitative genetics and selection theory, family size refers to the number of offspring from a parent or family that are selected to become parents of the next generation.
The variance of family size describes how much this number varies among different families in the population.

Step 2: Detailed Explanation:
Let us analyze the selection scenario described in the question:
The breeder selects exactly one male from the progeny of each sire, and exactly one female from the progeny of each dam.
This means that from every single sire family, exactly one offspring is selected to contribute to the next generation.
Similarly, from every single dam family, exactly one offspring is selected.
Under this system, the family size (\(k\)) is constant for every family in the population:
\[ k_i = 1 \text{ for all families } i \]
In statistics, the variance of a constant set of numbers is always zero because there is no variation around the mean value:
\[ \text{Variance} = \frac{\sum (k_i - \bar{k})^2}{N} \]
Since \(k_i = 1\) for every family, the mean family size (\(\bar{k}\)) is also
Thus, the deviation from the mean (\(k_i - \bar{k}\)) is zero for every family, resulting in a variance of zero.
This structured selection method is used in breeding programs to maximize the effective population size (\(N_e\)) and minimize the rate of inbreeding, as it ensures that every parent contributes equally to the next generation.

Step 3: Final Answer:
Therefore, the variance of the family size under this selection scheme will be zero.