• Offspring-Parent Regression and Heritability:
• When offspring values ($Y$) are regressed on the mean of the two parents (mid-parent value, $\bar{P}$):

• Because environmental correlation and dominance variance between parents and offspring are negligible, the linear regression slope ($b_{O\bar{P}}$) directly equals the narrow-sense heritability ($h_N^2$).
• Conclusion: If the regression coefficient is 0.32, narrow-sense heritability is 0.32. (Correct answer: Option 2)

• Assertion (A) is True: The "which-won-where" polygon view of the GGE (Genotype + Genotype $\times$ Environment) biplot is exceptionally well-suited for mega-environment analysis because it visually partitions multi-environment trial data into environmental sectors, directly identifying which specific genotype achieved superior performance at the vertices of each sector.
• Reason (R) is True: Unlike the AMMI1 model (which fits Genotype main effects and GE interaction on separate axes and accounts for only a portion of interaction variation), GGE biplots capture all relevant multi-environment trial variation ($G + GE$) directly through singular value decomposition of environment-centered data, allowing clearer geometric visualization of mega-environments.
• Relationship: Because GGE captures total $G + GE$ variance simultaneously in a single biplot framework, its vertex polygon construction directly provides superior identification of winning genotypes across mega-environments, making Reason (R) the correct explanation of Assertion (A).
• Conclusion: Both (A) and (R) are correct and (R) is the correct explanation of (A) (Option 1).

Correct option: (1) Both (A) and (R) are correct and (R) is the correct explanation of (A).

• Marker-Assisted Selection Efficiency:
• Recombination frequency ($r$) between marker locus ($M$) and target resistance gene ($G$) = $0.05$.
• In an $F_1$ coupling phase ($M\ G / m\ g$), the non-recombinant gametes are $M\ G$ and $m\ g$, each produced with frequency $\frac{1 - r}{2} = 0.475$.
• When selecting marker-positive individuals, the probability of selecting an individual carrying the linked target gene without recombination error is $1 - 2r = 1 - 2(0.05) = 0.90$ (or selection accuracy $90\%$). (Correct answer: Option 1)