Question

Index is ______ of an individual's breeding value
A. Best linear prediction
B. Best linear unbiased prediction
C. Best prediction
D. Best linear biased prediction
Choose the correct answer from the options given below

• A. A and B only
• B. A only
• C. C and D only
• D. D only

Hint:

Selection Index Theory: Hazel's Selection Index = BEST LINEAR PREDICTION (BLP) of breeding value ($I = \mathbf{b'X}$). Henderson's Mixed Model = BLUP.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Selection index theory (Hazel, 1943): the classical selection index ($I = \mathbf{b'X}$) is the Best Linear Prediction (BLP) of an individual's aggregate genetic economic breeding value when population parameters are known.
Key Formula or Approach:
\[ I = \sum b_i X_i = \mathbf{b'X} = \mathbf{P}^{-1}\mathbf{G}\mathbf{a} \quad [\text{Best Linear Predictor (BLP) of Aggregate Breeding Value } H] \]

Step 2: Detailed Explanation:
In selection index theory (Hazel 1943, Henderson 1963):
1. When population means and genetic/phenotypic variances are assumed to be known parameters, the classical Selection Index ($I$) is mathematically defined as the Best Linear Prediction (BLP) (A only) of the individual's net genetic merit true breeding value, maximizing the correlation between the index and the aggregate genotype ($r_{IH}$).
2. When population fixed effects (herd-year-season) must be estimated simultaneously with breeding values from field data, the methodology is extended to Best Linear Unbiased Prediction (BLUP).
Thus, the classical Selection Index is the Best Linear Prediction (A only).

Step 3: Final Answer:
Hence, Index is the Best linear prediction (A only), corresponding to option (B).