Question

A hypothetical study investigated the vitamin A content and the cholesterol content of eggs from a large population of chickens. The following variances (V) were calculated. (a) Calculate the narrow-sense heritability \(\left(h^{2}\right)\) for both traits. (b) Which trait, if either, is likely to respond to selection?

Short answer

Answer: The trait of vitamin A content is more likely to respond to selection due to its higher narrow-sense heritability. The narrow-sense heritability for vitamin A content is 0.3173, while that for cholesterol content is 0.21.

Step-by-step solution

Write down the given variances

The variances are given as: For vitamin A content: Additive genetic variance, \(V_{A}(\text{vitamin A}) = 0.33\) Total phenotypic variance, \(V_{P}(\text{vitamin A}) = 1.04\) For cholesterol content: Additive genetic variance, \(V_{A}(\text{cholesterol}) = 0.21\) Total phenotypic variance, \(V_{P}(\text{cholesterol}) = 1.00\)

Calculate the narrow-sense heritability for vitamin A content

Using the formula \(h^{2}=\frac{V_{A}}{V_{P}}\), we can find the narrow-sense heritability for vitamin A content: \(h^{2}(\text{vitamin A}) = \frac{V_{A}(\text{vitamin A})}{V_{P}(\text{vitamin A})} = \frac{0.33}{1.04} = 0.3173\)

Calculate the narrow-sense heritability for cholesterol content

Using the same formula, we can find the narrow-sense heritability for cholesterol content: \(h^{2}(\text{cholesterol}) = \frac{V_{A}(\text{cholesterol})}{V_{P}(\text{cholesterol})} = \frac{0.21}{1.00} = 0.21\)

Determine which trait is likely to respond to selection

Comparing the narrow-sense heritabilities calculated in Step 2 and Step 3: \(h^{2}(\text{vitamin A}) > h^{2}(\text{cholesterol})\) Since the narrow-sense heritability for vitamin A content is greater than that for cholesterol content, the trait of vitamin A content is more likely to respond to selection.

Key concepts

Additive Genetic Variance

When we look at the genetic contributions to a trait within a population, we often refer to something called additive genetic variance, or simply, V_A. This term is important in understanding how traits are inherited and how they might change over time due to selective breeding or natural selection.

Additive genetic variance is the portion of the total variation seen within a trait that can be attributed to the additive effects of alleles (different versions of a gene). These are the genetic effects that can be summed up across multiple genes to influence the overall phenotype—the observable characteristics of an organism. In other words, if you inherit specific alleles from your parents that influence a trait in a way that can simply be added together, that influence is considered part of V_A.

Imagine, for instance, that we're looking at the height of a plant population. Some alleles contribute a few centimeters to the plant's height independently of other alleles. When these small contributions from individual alleles are added together, they give us the additive genetic variance of that trait. This is critical because it is the additive genetic variance that primarily determines the potential response to selection, whether by nature or by human intervention.

Phenotypic Variance

Now, it's vital to know that the traits we can measure and observe—the phenotype—do not rely solely on genetics. Phenotypic variance, denoted as V_P, includes all variation in a trait, which contains genetic variation but also encompasses environmental influences and the interaction between genes and the environment.

Consider a scenario where two identical seeds from a plant are planted in very different environments—one in fertile soil with plenty of sunlight and the other in poor soil with inadequate light. Despite their identical genetic makeup, one plant might grow tall and robust while the other remains stunted. This difference in growth is a direct result of environmental effects, which, along with genetic factors, contribute to the phenotypic variance.

Total phenotypic variance is, therefore, an amalgamation of different types of variance, including V_A, and can be expressed in a quantitative manner. Understanding V_P is crucial, as it sets the stage for predicting how a population might evolve or improve in response to selection, as it represents the total observable differences among individuals for a trait.

Response to Selection

The concept of response to selection is based on the expectation of how much a trait will change in a population as a result of selection, either natural or artificial. This can be particularly interesting when breeders want to enhance certain traits in a population, such as the yield of a crop or the milk production in livestock.

The formula to estimate the response to selection (R) is given by R = h² x S, where h² is the narrow-sense heritability of the trait and S is the selection differential, which is the difference between the mean phenotype of the selected parents and the mean phenotype of the original population.

When the narrow-sense heritability of a trait is higher, as we saw for the vitamin A content in our exercise, the trait is more likely to respond favorably to selection. A higher h² value indicates a strong genetic influence, meaning that selected individuals will pass on the desirable traits to their offspring more consistently. On the other hand, if h² is low, changes due to selection will be slower and less predictable, as the trait is more influenced by environmental factors. This understanding allows breeders and scientists to predict and manage genetic improvement in populations over time.