Question

You are a judge in a civil trial where a young man is attempting to prove that he is the illegitimate child of a very wealthy man who has recently died. He wishes to be included in the distribution of the wealth. After considering all the testimony about how this person was conceived, the key evidence seems to come down to two main facts. The wealthy man and the mother of the young man are both deaf but the young man is not. Therefore the lawyer of the family suggests that the wealthy man is not the father. The mother, wealthy man, and young man all have O, MM, Rh blood type at the phenotypic level but a genotyping screen indicates that the wealthy man is actually I^AI^A hh blood type. How do you interpret the evidence presented and how does it influence your decision in this case?

Answer 1

Let us begin with the data. We know that the wealthy man is deaf and the young mother is deaf. However, we do not know if they are genetically deaf. Most of the people who are deaf acquire deafness and hence it is not heritable. Even with genetic deafness, there are several genes that are known to play in a myriad fashion to control this phenotype. Thus the probability that a deaf couple would conceive a deaf child is higher than the probability of non-deaf people conceiving a deaf child. However, this probability is very low. Thus, the fact that the young man is not deaf implies the wealthy man is not his father is a feeble statement.

Now, coming to the blood groups of these individuals. We know that their phenotype is O, MM, Rh+. These are three different blood group systems.

The first term comes from ABO blood grouping system. This is encoded by three alleles IA, IB and i. IA and IB are codominant and i is recessive. IAIA and IAi give the phenotype A, IBIB and IBi give the phenotype B, IAIB gives the phenotype AB and ii gives the phenotype O.

The second system is the MNS blood grouping system which has many antigens. The antigens M and N are codominant. MM present in all the individuals doesn't provide any information of use to us.

The third system is the Rh system and Rh+ve is dominant over Rh-ve. Thus Rh+ve phenotype can come from Rh+ve/Rh+ve or Rh+ve/Rh-ve genotypes. In either case, there is a possibility of producing an offspring that is Rh+ve which suggests that the young man could be the child of the wealthy man, however, it is not conclusive.

There is another system of antigens called the Bombay system, comprising of H and h, where H is dominant over h. The HH and Hh give rise to a normal phenotype that produces the base for ABO antigens to be present. However, in the hh case, also called the Bombay phenotype, the base on which ABO antigens are presented is missing and hence irrespective of the alleles present, the blood group phenotype would always be O.

We are given that the wealthy man in fact does have IAIA hh genotype, which means he should produce A antigen and give A blood group, however, the hh phenotype prevents the A antigen from being expressed.

Now, if the young man and wealthy man were in fact related, the young man should have one allele of IA and h, with the other allele given by his mother, who exhibits O phenotype. Now, taking into account the ABO+Bombay system, following genotypes can give rise to O phenotype:

IAIA hh, IAIB hh, IBIB hh, IAi hh, IBi hh, ii hh, ii Hh, ii HH. These are all the possibilities that the young mother can have.

1. The first six possibilities can all be summarized as having the genotype hh. Hence if this were the case, the genotype of the young man would be IAX hh, where X is the antigen inherited from mother. This does produce the phenotype O.

2. In the case where the mother is ii Hh, the ABO allele inherited from mother would always be i and the Bombay system allele inherited would be H 50% time and h 50% times. Thus the possibility of genotype for this young man would be IAi Hh (50%) or IAi hh (50%). This gives only 50% chance that the wealthy man is indeed his parent.

3. In the last case where the genotype of the mother is ii HH, the only possible genotype of offspring would be IAi Hh, which gives the phenotype A.

Thus to sum up, given the gamete from wealthy man being IA h 100% times, there are 8*2 (8 possible genotypes of mother each producing two gametes).

Of these 16 combinations, according to 1, 6*2 give wealthy man the parenthood of young man = 12/12 probability.

From 2 again, there is 1/2 probability of the young man being the son.

From 3, there is 0/2 probability of the young man being the child.

To sum up, there is (12+1+0)/(12+2+2) = 13/16 = 0.8125 = 81.25% probability that the young man is indeed the son.

Hence further tests can be done to check for the genotype of mother and/or son to confirm the parenthood and the previous decision made by the lawyer only based on deafness needs to be refuted strongly.