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

Calculate broad-sense (H²) and narrow-sense (h²) heritabilities for each trait in this herd.

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Identify the variances given for each trait: phenotypic variance (\(V_P\)), genetic variance (\(V_G\)), and additive genetic variance (\(V_A\)). These are provided in the table for back fat and body length.

Recall the formula for broad-sense heritability (\(H^2\)), which is the proportion of phenotypic variance due to total genetic variance: \(H^2 = \frac{V_G}{V_P}\)

Recall the formula for narrow-sense heritability (\(h^2\)), which is the proportion of phenotypic variance due to additive genetic variance: \(h^2 = \frac{V_A}{V_P}\)

For each trait (back fat and body length), substitute the values from the table into the formulas for \(H^2\) and \(h^2\) to set up the calculations.

Interpret the heritability values to understand the genetic contribution to the traits: higher values indicate a greater genetic influence on the phenotypic variation.

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Phenotypic Variance (V_P)

Phenotypic variance represents the total variation observed in a trait within a population. It includes genetic variance, environmental variance, and their interactions. Understanding V_P is essential because it forms the denominator in heritability calculations, reflecting all sources of trait variation.

Genetic Variance (V_G) and Additive Genetic Variance (V_A)

Genetic variance (V_G) is the portion of phenotypic variance due to genetic differences among individuals. Additive genetic variance (V_A) is the part of V_G attributable to the additive effects of alleles, which predictably pass from parents to offspring. V_A is crucial for narrow-sense heritability, while V_G is used for broad-sense heritability.

Broad-sense (H²) and Narrow-sense (h²) Heritability

Broad-sense heritability (H²) is the ratio of total genetic variance (V_G) to phenotypic variance (V_P), indicating the proportion of trait variation due to all genetic factors. Narrow-sense heritability (h²) is the ratio of additive genetic variance (V_A) to V_P, reflecting the proportion of variation that can be passed to offspring and is key for predicting response to selection.

The following variances were calculated for two traits in a herd of hogs.Calculate broad-sense (H²) and narrow-sense (h²) heritabilities for each trait in this herd.