Hardy-Weinberg Equation

Question

Ellis-van Creveld syndrome is a rare homozygous recessive disorder that affects bone growth. Individuals with this disorder are characterized by dwarfism, polydactyly, heart defects, and other symptoms. The recessive allele that causes it is extremely common in the Amish community of Lancaster County, Pennsylvania, and in the indigenous population of Western Australia. For example, the birth rate of this disorder in Lancaster County is 1 in every 5000 births ( compared to 1 in every 150,000 births worldwide).

 

a) Approximately what percent of the Amish population are heterozygous carriers of the allele for Ellis-van Creveld syndrome? 

b) What percentage is homozygous dominant?

Answer 1

The Hardy-Weinberg equation states that a population will have the following allele distribution:

 

f(AA) = p²
f(Aa) = 2pq
f(aa) = q²

 

where AA is homozygous dominant, Aa is heterozygous, and aa is homozygous recessive; p is frequency of A allele and q is frequency of a allele.

 

We know from the data that f(aa) = 1/5000.

Therefore, q = √(1/5000) = 1.41%.

Then, p = 1 - q = 0.9859.

 

a) f(Aa) = 2pq = 2*0.0141*0.9859 = 0.0279 = 2.79%.

 

b) f(AA) = p² = 0.9859^2 = 0.9719 = 97.19%