Question

Height in humans depends on the additive action of genes. Assume that this trait is controlled by the four loci \(\mathrm{R}, \mathrm{S}, \mathrm{T}\) and \(\mathrm{U}\) and that environmental effects are negligible. Instead of additive versus nonadditive alleles, assume that additive and partially additive alleles exist. Additive alleles contribute two units, and partially additive alleles contribute one unit to height. (a) Can two individuals of moderate height produce offspring that are much taller or shorter than either parent? If so, how? (b) If an individual with the minimum height specified by these genes marries an individual of intermediate or moderate height, will any of their children be taller than the tall parent? Why or why not?

Short answer

Also, can children be taller than the tall parent if the parents themselves have minimum and intermediate/moderate height? Answer: Yes, two individuals of moderate height can produce offspring that are much taller or shorter than either parent. If an individual with the minimum height marries an individual of intermediate or moderate height, at least some of their children can indeed be taller than the tall parent.

Step-by-step solution

Identifying combinations with the least and the most height

In order to determine whether offspring can have very different height from their parents, let's first consider the minimum and maximum heights possible through the four loci. Minimum height: All four loci have two partially additive alleles. In this case, an individual's height would be \(4 \times 1 = 4\) units. Maximum height: All four loci have two fully additive alleles. In this case, an individual's height would be \(4 \times 2 = 8\) units.

Analyzing the potential offspring's height

(a) Let us consider two individuals of moderate height, say 6 units each. We can represent their genotypes as follows: Parent 1: R=AP, S=AA, T=PP, U=AA Parent 2: R=PA, S=PP, T=AP, U=AA Here, the height of each parent is calculated as (1+1)+(2+2)+(1+1)+(2+2) = 6 units. The possible combinations of their alleles in offspring would be: Offspring 1: R=AA, S=AA, T=PP, U=AA -> Height: (2+2)+(2+2)+(1+1)+(2+2) = 8 units Offspring 2: R=PP, S=PP, T=PP, U=AA -> Height: (1+1)+(1+1)+(1+1)+(2+2) = 4 units Therefore, yes, two individuals of moderate height can produce offspring that are much taller or shorter than either parent.

Marriage between individuals with minimum and intermediate/moderate height

(b) Now, let's consider a couple where one has minimum height (4 units) and one has intermediate height (6 units). Their genotypes can be represented as: Parent with minimum height: R=PP, S=PP, T=PP, U=PP Parent with intermediate/moderate height: R=AP, S=AA, T=PP, U=AA Here, the height of each parent is calculated as: (4x1)=4 units and (1+1)+(2+2)+(1+1)+(2+2) = 6 units. We will look at their offspring's possible maximum height based on their alleles: Offspring: R=AA, S=AA, T=PP, U=AA -> Height: (2+2)+(2+2)+(1+1)+(2+2) = 8 units In this case, the offspring does have a height that is taller than the tall parent (6 units). Therefore, if an individual with the minimum height specified by these genes marries an individual of intermediate or moderate height, at least some of their children can indeed be taller than the tall parent.

Key concepts

Additive Alleles

Additive alleles are essential for understanding how traits like height can vary within a population. These alleles contribute to a trait's quantitative expression by adding a certain value to its overall measure. In the context of height in humans, additive alleles contribute two units to the height trait. This means that the more additive alleles an individual has, the taller they can potentially be.

In this exercise, we explored a scenario with genetic loci labeled \(R, S, T, \text{and} U\). Each locus can have either additive alleles, which contribute two height units, or partially additive alleles, which add one unit. The key idea here is that each allele's contribution stacks up; if an individual inherits more additive alleles, their total trait value increases.

• Each additive allele contributes a fixed value (e.g., two units for height).
• Genetic variation arises from different combinations of these alleles across generations.

Thus, additive alleles provide a basis for predicting phenotypic outcomes, such as offspring potentially being taller or shorter than their parents.

Genotype

The term "genotype" refers to the genetic makeup of an individual, particularly the specific alleles they possess at pertinent loci. In our example with height, each parent's genotype consists of alleles from loci \(R, S, T, \text{and} U\), contributing to their overall height. Understanding the genotypic structure helps us predict potential variations in offspring.

For instance, two parents with genotypes indicating moderate height may produce offspring with varying genotypes, resulting from the random combination of parental alleles. Each offspring's genotype influences their phenotypic expression, like height. Here’s an overview of how genotype plays a role:

• The genotype is composed of alleles that determine the specific traits.
• Different combinations can yield diverse phenotypes, even in similar parental genotypes.
• In polygenic traits, the effect of all gene loci needs to be considered together.

Genotype serves as a framework to understand the inheritance pattern of traits and the continual variation apparent in polygenic characteristics.

Quantitative Traits

Quantitative traits are those traits that are influenced by multiple genes and exhibit a range of phenotypes, rather than the distinct categories often seen in single-gene (Mendelian) traits. Height in humans is a classic example of a quantitative trait, since it is determined by the collective effect of several loci, each contributing incrementally to the final phenotype.

In the exercise, height is controlled by four genetic loci \(R, S, T, \text{and} U\). Each locus contributes additively or partially additively to the overall trait. Unlike binary traits (e.g., pea plant flowers being purple or white), quantitative traits show a gradient, resulting in a wide distribution of phenotypes within a population.

• Quantitative traits have a continuous distribution of phenotypes.
• The more loci involved, the smoother the phenotypic gradient.
• Traits exhibit variation due to high genetic complexity and environmental interactions.

Quantitative traits highlight the complexity of genetic inheritance and how multiple genes contribute to traits like human height.