Philip L. answered • 09/05/22
Gene therapy/genetics/biology tutor for students/professionals
Question: Imagine that fondness for mathematics has a genetic basis. Here we'll suppose that math fondness is recessive, but also highly beneficial. About 10% of the population are of math-genotype aa with about an additional 30% carriers.
i. If it is known that your father is not a carrier, what is the probability that your mother has the gene?
ii. Suppose you have two siblings.
A. What is the probability that you have the gene given that one of your other siblings has the gene?
B. What is the probability that you have the gene given that your brother, Maple, has the gene?
Answer
This answer assumes a working understanding of the terms allele, locus, genotype, phenotype, recessive, dominant, homozygous and heterozygous, that would have been described earlier in the course.
The problem is discussing a trait called “math fondness” that is recessive in the population. To exhibit math fondness, you would have to be homozygous for the recessive math fondness gene, a (genotype aa). Other possible genotypes would include homozygosity for the non-math fondness gene, A (an AA genotype), or heterozygosity at the math fondness locus, Aa, which would result in a non-math fondness phenotype because the non-math fondness gene, A, is dominant when paired with the recessive a math fondness allele, a. The question goes on to tell us that 10% of the population has an aa genotype and that about 30% of the population are carriers (Aa).
The first question reads: “If it is known that your father is not a carrier, what is the probability that your mother has the gene.” In the absence of any other information, the first half of the question is irrelevant. The chance that any one person in the population is a carrier depends on the frequency with which the alleles are found in the population, and is independent of the genotype of family members. The question says that “about 30% of the population are carriers.” That is the answer. It seems like some information is missing. For example, if the question included the information that one of your siblings was a carrier, and then went on to say that your father was not a carrier, then the answer would be that the probability that your mother has the gene is 100%. You had to get it from one of your parents.
ii. The second question has two parts.
a. The last question reads: What is the probability that you have the gene given that one of your siblings has the gene?
b. What is the probability that you have the gene given that your brother, Maple, has the gene?
For question a., here is the missing information confirming our answer to the question above. The information that your sibling has the gene should have been provided at the beginning of the question. We now know that the mother must be a carrier. The gene can either be on an autosome (any chromosome that is not a sex chromosome) or it could be on a sex chromosome…specifically the X chromosome, but not the Y chromosome because your mother does not have a Y chromosome. In either case (autosome or X chromosome), the answer is that you have a 50% chance of having the gene. If we assume that the math fondness locus is on an autosome, then there is a 50% chance that the a gene was included in the gamete that led to your creation and there was a 50% chance that your mother’s other gene, the A gene, was included in the gamete that led to your creation. So, there is a 50% chance that you have the gene. The math is the same for X chromosome in this case because your mother has two X chromosome and she gives only one to each of her children, whether they are male or female. If the father had been the carrier of the a gene and it was located on the X chromosome, then the chances of inheriting the gene would have been 100% if you were a girl (the father always contributes an X chromosome to a female child) and it would have been 0% if you were a boy (the father always contributes a Y chromosome, not an X chromosome) to a male child. If the father had been the carrier of the a gene and it was located on the Y chromosome, then the chances of inheriting the gene would have been 0% if you were a girl (you would have inherited your father’s X chromosome instead of the Y chromosome); but it would have been 100% if you were male because you must have inherited your father’s Y chromosome and the a gene along with it.
