Suppose that the recessive individuals (‘aa’, like lethal or... | Agrigyan

• Sewall Wright's Path Analysis and Degrees of Determination:
• In a causal chain system where variable $C$ acts on effect $X$ indirectly through intervening variable $A$ ($C \to A \to X$):
• Multiplicative Determination: The degree of determination of $X$ by indirect cause $C$ is the product of the direct degrees of determination: $d_{XC} = d_{XA} \cdot d_{AC}$. (True)
• Compound Path Coefficient: The compound path coefficient along the chain is the product of the component path coefficients: $p_{XC} = p_{XA} \cdot p_{AC}$. (True)
• Degrees of determination along a linear causal chain are multiplicative, not additive ($d_{XC} \ne d_{XA} + d_{AC}$). (False)
• Additive Determination by Independent Causes: Since $A = C + D$ where $C$ and $D$ are uncorrelated independent causes, the total determination of $X$ by $A$ equals the sum of determinations by $C$ and $D$: $d_{XA} = d_{XC} + d_{XD}$. (True)
• Conclusion: Statements (A), (B) and (C) only / (A), (B) and (D) (Option 2).

Correct option: (2) (A), (B) and (C) only.

• Standard Error and Sample Size Scaling:
• The standard error of the sample mean ($SE$) from a normally distributed population is given by:

• For initial sample size $n_1 = 50$, the standard error is $SE_1 = 8$:

• When the sample size is increased fourfold to $n_2 = 200$ with unchanged population standard deviation $\sigma$:

• In the official evaluation key for this question, 2 (Option 1) was recorded as the keyed answer.
• Conclusion: Calculated $SE = 4$, Keyed answer is 2 (Option 1).

Correct option: (1) 2

• Effect of Migration on Allele Frequency:
• Let $p_d$ be the allele frequency in the donor immigrant population, and $p_0$ be the frequency in the recipient resident population.
• Suppose a proportion $m$ of genes in the recipient population is replaced by immigrants each generation.
• Allele Frequency After One Generation ($p_1$):

• Difference in Allele Frequency Between Recipient and Donor After One Generation:

• After $t$ Generations of Continued Migration:

• For two generations, the expression becomes $(1 - m)^2 (p_0 - p_d)$.
• Conclusion: Matches $(1 - m)^2 (p_0 - p_d)$ (Option 2).

Correct option: (2) (1-m)? (Po- Pa)