The following variances were calculated for two traits in a herd of hogs.

Which of the two traits will respond best to selection by a breeder? Why?

Verified step by step guidance

1. Step 1: Understand the key variances given in the table: \(V_P\) (phenotypic variance), \(V_G\) (genetic variance), and \(V_A\) (additive genetic variance) for each trait. These variances help us understand the genetic contribution to the traits and their potential response to selection.
2. Step 2: Recall that the response to selection depends primarily on the narrow-sense heritability (\(h^2\)), which is the proportion of phenotypic variance due to additive genetic variance. It is calculated as: \[h^2 = \frac{V_A}{V_P}\]
3. Step 3: Calculate the narrow-sense heritability for each trait using the formula above. This will give you a measure of how much of the trait's variation is heritable and can be passed on to the next generation.
4. Step 4: Compare the heritability values for back fat and body length. The trait with the higher \(h^2\) value will respond better to selection because a greater proportion of its variation is due to additive genetic factors.
5. Step 5: Conclude which trait will respond best to selection based on the higher heritability value, and explain that this is because selection acts on additive genetic variance, which directly influences the trait's improvement in the population.

Key Concepts

Phenotypic Variance (VP)

Phenotypic variance (VP) represents the total variation observed in a trait within a population. It includes both genetic variance and environmental variance, reflecting all factors that contribute to differences in the trait among individuals.

Additive Genetic Variance (VA)

Additive genetic variance (VA) is the portion of genetic variance that contributes to the resemblance between parents and offspring. It represents the cumulative effect of individual alleles and is crucial for predicting the response to selection in breeding programs.

Heritability and Response to Selection

Heritability in the narrow sense (h²) is the ratio of additive genetic variance to phenotypic variance (VA/VP). It indicates the proportion of trait variation due to additive genetics and predicts how effectively a trait will respond to selection by breeders.