A recessive autosomal condition affects 6.4 in every 1000 births in a large population…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A recessive autosomal condition affects in every births in a large population. The population mates at random and is in Hardy-Weinberg equilibrium for this gene, with alleles (normal) and (condition). A town in this population has people.
- What is the frequency of the allele ?
- What is the frequency of carriers in the whole population?
- How many carriers are expected in the town?
- A healthy person is chosen at random. What is the probability that this person is a carrier?
- Two unrelated healthy people have a child. How many affected children are expected in every such births?
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Use and the genotype frequencies , and .
(a) , so and .
(b) Carriers: .
(c) carriers.
(d) Among healthy people (a fraction of the population), the carrier share is . This is a little more than because the affected people have been left out.
(e) Both parents must be carriers, with probability , and then the child is affected with probability . So the risk is , which is in births. A population with no knowledge of the parents would give in , so two healthy parents carry a lower risk than the population as a whole.
Check. Listing every pair of healthy genotypes ( or for each parent) with its frequency and adding the chance of an child gives the same in when exact fractions are used.
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