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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

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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

01

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.
02

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.
03

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

In this chapter, we focused on a mode of inheritance referred to as quantitative genetics, as well as many of the statistical parameters utilized to study quantitative traits. Along the way, we found opportunities to consider the methods and reasoning by which geneticists acquired much of their understanding of quantitative genetics. From the explanations given in the chapter, what answers would you propose to the following fundamental questions: (a) How do we know that threshold traits are actually polygenic even though they may have as few as two discrete phenotypic classes? (b) How can we ascertain the number of polygenes involved in the inheritance of a quantitative trait?

An inbred strain of plants has a mean height of \(24 \mathrm{cm} .\) A second strain of the same species from a different geographical region also has a mean height of \(24 \mathrm{cm} .\) When plants from the two strains are crossed together, the \(\mathrm{F}_{1}\) plants are the same height as the parent plants. However, the \(\mathrm{F}_{2}\) generation shows a wide range of heights; the majority are like the \(P_{1}\) and \(F_{1}\) plants, but approximately 4 of 1000 are only \(12 \mathrm{cm}\) high and about 4 of 1000 are \(36 \mathrm{cm}\) high. (a) What mode of inheritance is occurring here? (b) How many gene pairs are involved? (c) How much does each gene contribute to plant height? (d) Indicate one possible set of genotypes for the original \(P_{1}\) parents and the \(\mathrm{F}_{1}\) plants that could account for these results. (e) Indicate three possible genotypes that could account for \(\mathrm{F}_{2}\) plants that are \(18 \mathrm{cm}\) high and three that account for \(\mathrm{F}_{2}\) plants that are \(33 \mathrm{cm}\) high.

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?

Erma and Harvey were a compatible barnyard pair, but a curious sight. Harvey's tail was only \(6 \mathrm{cm}\) long, while Erma's was \(30 \mathrm{cm} .\) Their \(\mathrm{F}_{1}\) piglet offspring all grew tails that were \(18 \mathrm{cm}\) When inbred, an \(\mathrm{F}_{2}\) generation resulted in many piglets (Erma and Harvey's grandpigs), whose tails ranged in \(4-\mathrm{cm}\) intervals from 6 to \(30 \mathrm{cm}(6,10,14,18,22,26, \text { and } 30) .\) Most had \(18-\mathrm{cm}\) tails, while \(1 / 64\) had \(6-\mathrm{cm}\) tails and \(1 / 64\) had \(30-\mathrm{cm}\) tails. (a) Explain how these tail lengths were inherited by describing the mode of inheritance, indicating how many gene pairs were at work, and designating the genotypes of Harvey, Erma, and their 18 -cm-tail offspring. (b) If one of the \(18-\mathrm{cm} \mathrm{F}_{1}\) pigs is mated with one of the \(6-\mathrm{cm}\) \(\mathrm{F}_{2}\) pigs, what phenotypic ratio will be predicted if many offspring resulted? Diagram the cross.

If one is attempting to determine the influence of genes or the environment on phenotypic variation, inbred strains with individuals of a relatively homogeneous or constant genetic background are often used. Variation observed between different inbred strains reared in a constant or homogeneous environment would likely be caused by genetic factors. What would be the source of variation observed among members of the same inbred strain reared under varying environmental conditions?

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