Genotype $\times$ Environment (G $\times$ E) Interaction in Animal Breeding:

• Definition: In the absence of G $\times$ E interaction, differences between genotypes are parallel across environments, meaning the best performing genotype in one management/climate environment remains the best in all other environments. Thus, Statement (I) is correct.
• Importance in sire evaluation: G $\times$ E interaction causes changes in scale and ranking of sires when tested across different regions or agro-climatic zones (e.g. temperate vs tropical heat stress). Ignoring G $\times$ E can result in poor progeny performance; hence it is extremely important for multi-location bull evaluation. Thus, Statement (II) is incorrect.
  
  Option analysis:
  Statement (I) is correct but Statement (II) is incorrect, matching Option 3 (Key 3).

Principles of Repeatability ($r$) in animal breeding:

• Prediction of future performance: Repeatability sets an upper limit to heritability and is used to compute a cow's Most Probable Producing Ability (MPPA) for future lactations based on past records: $\text{MPPA} = \mu + \frac{nr}{1 + (n-1)r}(\bar{P} - \mu)$. Thus, Statement (I) is correct.
• Advantage of repeated records: If repeatability ($r$) is high (e.g. $0.8$), one record already tells most of what can be known, and additional records provide little extra information. When repeatability is low (e.g. $0.2$), temporary environmental variance is large, so taking repeated measurements significantly averages out temporary errors, giving a much larger gain in precision and accuracy. Thus, Statement (II) is correct.
  
  Option analysis:
  Both Statement (I) and Statement (II) are correct, matching Option 1 (Key 1).