Question

The following variances were calculated for two traits in a herd of hogs. $$\begin{array}{lccc}\text { Trait } & V_{P} & V_{C} & V_{A} \\\\\text { Back fat } & 30.6 & 12.2 & 8.44 \\\\\text { Body length } & 52.4 & 26.4 & 11.70\end{array}$$ (a) Calculate broad-sense \(\left(H^{2}\right)\) and narrow-sense \(\left(h^{2}\right)\) herita bilities for each trait in this herd. (b) Which of the two traits will respond best to selection by a breeder? Why?

Short answer

Answer: The Back fat trait will respond best to selection by a breeder because it has higher values for both broad-sense heritability (H^2 = 0.601) and narrow-sense heritability (h^2 = 0.276) than the Body length trait (H^2 = 0.496, h^2 = 0.223). This suggests that a larger proportion of the phenotypic variance for Back fat is due to genetic factors, making it more responsive to selection than the Body length trait.

Step-by-step solution

Calculate the genetic variance V_G for each trait

For the calculation of genetic variance (V_G), we can use the following formula: $$V_G = V_P - V_C$$ For Back fat: $$V_{G_{BF}} = 30.6 - 12.2 = 18.4$$ For Body length: $$V_{G_{BL}} = 52.4 - 26.4 = 26$$

Calculate the broad-sense heritability (H^2) for each trait

Using the formula for broad-sense heritability (H^2), we can now calculate H^2 for each trait: $$H^2 = \frac{V_G}{V_P}$$ For Back fat: $$H^{2}_{BF} = \frac{18.4}{30.6} = 0.601$$ For Body length: $$H^{2}_{BL} = \frac{26}{52.4} = 0.496$$

Calculate the narrow-sense heritability (h^2) for each trait

Using the formula for narrow-sense heritability (h^2), we can now calculate h^2 for each trait: $$h^2 = \frac{V_A}{V_P}$$ For Back fat: $$h^{2}_{BF} = \frac{8.44}{30.6} = 0.276$$ For Body length: $$h^{2}_{BL} = \frac{11.70}{52.4} = 0.223$$

Determine which trait will respond best to selection by a breeder

Comparison of the broad-sense and narrow-sense heritabilities for both traits: - Back fat: H^2 = 0.601, h^2 = 0.276 - Body length: H^2 = 0.496, h^2 = 0.223 The Back fat trait has higher values for both broad-sense heritability (H^2) and narrow-sense heritability (h^2) than the Body length trait. This indicates that a larger proportion of the phenotypic variance for Back fat is due to genetic factors. Consequently, selection by a breeder will have a greater effect on the Back fat trait, making it more responsive to selection than the Body length trait.

Key concepts

Genetic Variance

Genetic variance is a measure of the diversity within a population's genes. In other words, it quantifies the variation in heritable traits that can be passed on from parents to offspring. Consider a trait like the color of a flower; the variation in colors among a population of flowers can be attributed to the genetic variance. In the context of the example with the herd of hogs, genetic variance for each trait was computed as the difference between the phenotypic variance (\(V_P\)) and the environmental variance (\(V_C\)). Phenotypic variance encompasses both genetic and non-genetic factors, while environmental variance accounts for non-genetic influences, such as diet or climate.

Using the formula \(V_G = V_P - V_C\), we saw that back fat has a genetic variance of 18.4 and body length a variance of 26. These values are critical as they serve as the basis for calculating heritability and predicting how well traits might respond to selective breeding.

Broad-Sense Heritability

Broad-sense heritability (\(H^2\)) is a statistic used to describe the proportion of phenotypic variance in a population that can be attributed to genetic variance. It's a general measure, including all genetic contributions such as additive genetic variance, dominance variance, and epistatic variance (the interaction between genes). The formula to calculate \(H^2\) is \(H^2 = \frac{V_G}{V_P}\).

In the hog example, broad-sense heritability was calculated for both back fat (\(H^{2}_{BF} = 0.601\)) and body length (\(H^{2}_{BL} = 0.496\)). These values indicated that a majority of the variation in these traits is genetically determined, which is key when considering the potential efficacy of selective breeding programs as it offers a scope of improvement based on genetic factors.

Narrow-Sense Heritability

Narrow-sense heritability (\(h^2\)), a key concept in the field of genetics, refers to the fraction of phenotypic variance that is attributable to additive genetic variance, the kind passed on from parents to offspring. Additive genetics is the sum of the average effects of individual alleles and is particularly important for predicting the response to selection in breeding. The formula for \(h^2\) is \(h^2 = \frac{V_A}{V_P}\), where \(V_A\) represents the additive genetic variance.

For the hogs in the exercise, we found the narrow-sense heritability is 0.276 for back fat and 0.223 for body length. These calculations inform breeders about what proportion of the trait variance is due to additive genetic factors and therefore predict the likelihood of a trait being passed on to the next generation if selected for in breeding.

Phenotypic Variance

Phenotypic variance (\(V_P\)) captures the overall variability of a trait within a population. It includes genetic factors (\(V_G\)), environmental factors (\(V_E\)), and often, the interaction between these factors (\(V_{GE}\)). Simply put, it's the observable diversity in a trait, like the range of heights found within a group of individuals. Phenotypic variance is the sum of genetic variance and environmental variance, and possibly their interactions. In our numerical example, we had phenotypic variances of 30.6 for back fat thickness and 52.4 for body length in the herd of hogs. These values serve as denominators in the heritability calculations, demonstrating the importance of the overall variability when understanding the genetic makeup of traits.

Selection in Breeding

Selection in breeding is a foundational concept in genetics and agriculture. It's the process by which certain traits are chosen to be passed on to the next generation, potentially enhancing the desirable characteristics in a population. Breeders look at traits with higher heritability values because they are more reliably passed on to the offspring and are less influenced by environmental factors. In the exercise, the back fat trait in hogs had higher broad-sense and narrow-sense heritability values, suggesting it would respond better to selective breeding than body length. This means that breeders aiming to reduce back fat thickness could achieve more significant results by selectively breeding individuals with the desired trait, enhancing the overall lean quality of the herd. The principle of selection in breeding enables the strategic shaping of genetic populations over time.