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

Also, can the offspring from a minimum height individual and an intermediate or moderate height individual be taller than the tall parent? Answer: It is possible for two individuals of moderate height to produce offspring that are taller than themselves, but not shorter. However, when a minimum height individual and a moderate height individual have offspring, none of the children will be taller than the tall parent.

Step-by-step solution

Determine possible genotype combinations

With four loci, each having either an additive or partially additive allele, a person can have a number of different genotype combinations. We will list all the possible genotypes in terms of height units contributed by each allele: - Additive (A): 2 units - Partially additive (P): 1 unit We have a total of \(2^4=16\) possible genotype combinations for the four loci. Next, compute the total number of height units contributed to an individual for all genotype combinations.

Calculate offspring height possibilities

We will add the height units contributed by each allele for every possible genotype combination and create a table showing the total height units for every combination: Here is the table of possibilities: 1. AAAA: 8 units 2. AAA P: 7 units 3. AA P P: 6 units 4. AA PP PP: 5 units 5. A P A P: 6 units 6. A P P P: 5 units 7. APP PP: 4 units 8. P P A P: 6 units 9. P P P P: 5 units 10. P P PP PP: 4 units 11. P A P A: 6 units 12. P A PPP: 5 units 13. PP PA: 6 units 14. PPAAP: 5 units 15. PPP AP: 4 units 16. PPP PPP: 3 units Now we can analyze these tables to answer the two questions in the exercise.

Analyze offspring possibilities of moderately tall parents

(a) To answer whether two individuals of moderate height can produce taller or shorter offspring, let's see which genotype combinations produce moderate height: Possible combinations which produce moderate height (5 or 6 height units) are 3, 5, 8, 11, and 13. Let's take the combination of 3 (AA PP) and 11 (PAPA) as an example for two moderate height individuals. When they have offspring, they can produce: 1. AA PA: 7 units (combination 2) 2. AAP A: 6 units (combination 3) 3. AAP P: 5 units (combination 4) 4. PA PA: 6 units (combination 11) In this case, it is possible for two moderate height individuals to produce offspring taller than themselves, but not shorter.

Analyze offspring from minimum height and moderate height individuals

(b) Now let's examine if an individual with the minimum height specified by these genes (combination 16: PPP PPP) marries an individual of intermediate or moderate height (combination 3: AA PP), and determine whether any of their children can be taller than the tall parent: 1. AAP PPP: 5 units (combination 12) 2. PA PP PPP: 4 units (combination 15) 3. PP A PPP: 4 units (combination 10) 4. PPP PP PPP: 3 units (combination 16) As visible from the combinations above, none of their children will be taller than the tall parent (combination 3: AA PP). This is because the individual with the minimum height carries only partially additive alleles, which always results in offspring with heights equal to or less than their parents' height.

Key concepts

Additive Alleles

When it comes to understanding traits such as height in humans, the concept of additive alleles plays a crucial role. These alleles have a straightforward effect on phenotypes; each additive allele contributes a set amount to the trait. For example, in height genetics, if an allele is considered to be additive, it might contribute two units to an individual’s total height. In contrast, a partially additive allele contributes just one unit.

Imagine having two parents, each with a combination of additive and partially additive alleles. Additive alleles follow the simple principle that their effects stack up. So, if a child inherits two additive alleles for height from their parents at a certain genetic locus, the child’s height will increase by a total of four units (two from each allele). This is a critical notion because it simplifies the way we predict the offspring's traits based on the parental genotype.

• Additive effect: straightforward contribution to the phenotype
• Contribution example: two units per additive allele for height
• Hereditary impact: cumulative effect on offspring traits

In summary, additive alleles provide a predictable building block for quantitative traits, allowing for a more straightforward analysis of genetic outcomes.

Genotype Combinations

Another interesting aspect of quantitative genetics is the study of genotype combinations. Considering the example of human height controlled by four loci, each with the potential for additive or partially additive alleles, there are quite a few possibilities. Specifically, there are a total of 16 different genotype combinations, ranging from all additive alleles contributing the maximum height units to all partially additive alleles contributing the minimum.

The concept of genotype combinations is pivotal since it determines the variety of phenotypes that can occur in a population. For a given trait like height, these combinations represent the genetic diversity and explain why individuals within the same family can have varying heights. Here's how to visualize this diversity:

• Each locus can have an additive or partially additive allele.
• The total number of genotype combinations is calculated as 2 to the power of the number of loci (in this case, 2⁴ or 16).
• A table can be used to summarize the height units contributed by each genotype.

By understanding these combinations, we can predict the height variation among offspring based on the specific alleles inherited from the parents.

Genetic Contribution to Height

Lastly, let's delve into the genetic contribution to height. Height is a classic example of a trait influenced by multiple genetic factors as well as environmental factors. In the context of the given exercise scenario, we are looking at a simplified model that considers only the genetic contribution, which is significant.

The presence of additive and partially additive alleles across multiple loci means that there is a wide range of height outcomes. It becomes clear that if one parent has the shortest possible combination of alleles and the other one of moderate height, the offspring will not surpass the parent of moderate height. This example illustrates how the genetic makeup of an individual can set limits on certain traits, including height.

• Height is influenced by multiple genetic and environmental factors.
• Inheritance patterns can set limits on trait outcomes.
• Predicting height involves considering both parents' genotype combinations.

Understanding the genetic contribution is fundamental in foreseeing the potential height of offspring and in studying the inheritance patterns of quantitative traits like height in populations.