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?

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.

(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.

(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.