Question

Height in humans depends on the additive action of genes. Assume that this trait is controlled by the four loci $R,S,T,$ and $U$ 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

If so, how? If an individual with the minimum height (all PP genotypes with 8 units of height) marries an individual of intermediate or moderate height, can any of their children be taller than the tall parent? Answer: Yes, two individuals of moderate height with all partially additive alleles (AP) can produce offspring that are significantly taller or shorter than either parent. Their offspring can inherit a different combination of alleles, potentially producing much taller offspring (by inheriting all additive alleles, total height contribution of 16 units) or much shorter offspring (by inheriting all partially additive alleles, total height contribution of 8 units). However, if an individual with the minimum height (all PP genotypes with 8 units of height) marries an individual of intermediate or moderate height, none of their children will be taller than the tall parent, as the maximum height contribution possible for their offspring would be 12 units.

Step-by-step solution

Understand the trait and alleles involved

The given trait we are analyzing (height) is controlled by four loci R, S, T, and U. Additive alleles contribute two height units, while partially additive alleles contribute one height unit to the overall height. Environmental effects are negligible in this case. #Step 2: Determine the height contribution for each genotype#

Determine the height contribution for each genotype

For each of the four loci, there are two possible alleles: additive (A) and partially additive (P). Using the given information, the possible genotypes and height contributions for each locus are: AA (4 units), AP or PA (3 units) and PP (2 units). #Step 3: Answering question (a)#

Determine if offspring can be much taller or shorter than moderate height parents

Yes, two individuals of moderate height can produce offspring that are significantly taller or shorter than either parent. This is because both parents can be heterozygous (AP) for all four loci, giving them moderate heights. However, their offspring can inherit a different combination of alleles, potentially producing much taller or shorter offspring. For example: - An offspring inheriting all additive alleles (all AA) will have a total height contribution of 16 units, which is significantly taller than both parents. - An offspring inheriting all partially additive alleles (all PP) will have a total height contribution of 8 units, which is significantly shorter than both parents. #Step 4: Answering question (b)#

Determine if any children can be taller than the tall parent

If an individual with the minimum height (all PP genotypes with 8 units of height) marries an individual of intermediate or moderate height, none of their children will be taller than the tall parent. This is because: - For each locus, the only possible genotype combination for the offspring is PP or AP (since the parent with the PP genotype will only provide a partially additive allele to each locus). - Even if the offspring inherits all the additive alleles from the taller parent (resulting in a genotype of all AP for each locus) and a partially additive allele from the shorter parent, the offspring will still only have a total height contribution of 12 units, which is not taller than the tall parent.

Key concepts

Genetic Variation

Genetic variation is the diversity in gene frequencies within a population. This diversity allows for a wide range of physical characteristics among individuals. In the context of polygenic inheritance, such as human height, genetic variation ensures that traits are not uniform across the population.

The alleles at each of the four loci (R, S, T, U) contribute differently to the trait, leading to potential variations. Genetic variation can come from multiple sources, including:

• Mutation: Changes in DNA that create new alleles.
• Recombination: Process during meiosis that shuffles alleles, increasing variation.
• Independent Assortment: Random distribution of alleles during gamete formation.

This variation is crucial as it provides the raw material for natural selection and adaptation.

Alleles

Alleles are different forms of the same gene that reside at a specific locus on a chromosome. In our exercise, alleles at loci R, S, T, and U come in two forms: additive and partially additive.

Additive alleles contribute two units to height, while partially additive alleles contribute one unit. The combination and interaction of these alleles determine an individual's height.

Understanding alleles helps in predicting offspring traits in polygenic inheritance. In height inheritance, this means that parents carrying different combinations of alleles can produce offspring with varying heights, depending on which alleles are inherited.

Genotype

A genotype is the genetic profile of an organism. It refers to the set of alleles that an individual possesses at a particular locus or loci. In our context, it is the combination of alleles at loci R, S, T, and U that accounts for a person's height.

The possible genotypes formed by the alleles could be:

• AA for both additive alleles (4 units),
• AP or PA, a mix of one additive and one partially additive allele (3 units), and
• PP for both partially additive alleles (2 units).

The genotype affects the phenotype, in this case, the observed height of the person. Polygenic inheritance exhibits complex genotypes producing a spectrum of phenotypes, rather than discrete categories.

Height Inheritance

Height inheritance is a classic example of polygenic inheritance, where the trait is regulated by many loci, not just one. In this scenario, the loci R, S, T, and U all contribute to the determination of height.

Each locus can carry alleles contributing differently (either additive or partially addictive) to the height outcome. The total height of an individual is the sum of the contributions from each allele at these loci.

Here is how it works:

• Offspring of moderate height parents can be much taller or much shorter, depending on inherited allele combinations.
• Even with certain limits, such as a parent carrying only partially additive alleles, offspring can achieve new height combinations.
• The interplay of alleles at multiple loci shows how genetic diversity enables a broad range of potential height expressions in offspring.

This highlights the complex but fascinating way genes work together to shape traits like height.