Selection Index Method (Hazel, 1943): Selection index is the most efficient and mathematically superior method for multi-trait phenotypic selection because it simultaneously evaluates multiple economic traits weighted by their economic values, genetic parameters (heritabilities), and phenotypic and genetic correlations:
$$I = b_1 X_1 + b_2 X_2 + \dots + b_n X_n$$
Comparison of Multi-Trait Selection Methods:
Selection Index: Maximizes the correlation ($r_{IH}$) between the index ($I$) and the true aggregate breeding value ($H$), yielding the maximum genetic progress per unit of time.
Independent Culling Levels: Animals must meet minimum thresholds for all traits independently; culls superior individuals that fall slightly short in one trait.
Tandem Selection: Selects for one trait at a time across cycles; least efficient due to negative genetic correlations and long time required.
Correct option: (4) Index based
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