Question

A further study finds that after 10 generations (≈ 200 years) a lot of inbreeding has taken place in the population. Two subpopulations (populations A and B), consisting of 30% and 70% of the general population, respectively, have formed. Within population A, prevalence of the recessive gene is 40%, whereas in population B it is 10%.

Suppose that in 25% of marriages both people are from population A, in 65% both are from population B, and in 10% there is one partner from population A and one from population B.

Suppose that a baby is born with a birth defect, but the baby’s ancestry is unknown. What is the posterior probability that the baby will have

1. both parents from population A?

2. both parents from population B?

3. mixed ancestry (i.e. one parent from population A and one from population B)?

Answer 1

Given:

Probability of Population A = 0.30

Probability of Population A, prevalence of the recessive gene = 0.40

Probability of Marriages where both persons are from Population A = 0.25

Probability of Population B = 0.70

Probability of Population B, prevalence of the recessive gene = 0.10

Probability of Marriages where both persons are from Population B = 0.65

Probability of Marriages where one person is from Population A and one person is from Population B = 0.10

1. Probability (Both Parents from Population A) = Probability of Population A * Probability of Marriages where both persons are from Population A

Probability (Both Parents from Population A) = 0.30 * 0.25 = 0.075 = 7.5 %

2. Probability (Both Parents from Population B) = Probability of Population B * Probability of Marriages where both persons are from Population B

Probability (Both Parents from Population B) = 0.70 * 0.65 = 0.455 = 45.5%

3. Probability (Mixed Ancestry) = Probability of Population A * Probability of Population B * Probability of Marriages where one person is from Population A and one person is from Population B

Probability (Mixed Ancestry) = 0.30 * 0.70 * 0.10 = 0.021 = 2.1%