Hurler syndrome is an autosomal recessive disease caused by a deficiency of the enzyme alpha-L-iduronidase. Affected individuals are mentally retarded, and they have skeletal abnormalities and short stature. The population incidence is about 1 in 90,000.

a.  Calculate the allelic and genotypic frequencies for the disease assuming Hardy-Weinberg equilibrium. Show your work and express your answer to three significant figures.

Answer:

b.  What would be the increased risk of Hurler syndrome among the offspring of first-cousin matings? Show your work and express your final answer to three significant figures.

 

Question: A.

Representation:

·        Genotype for individuals with Hurler = hh = recessive homozygous condition.

·        Normal individuals, will have genotypes:

·        HH = Homozygous dominant

·        Hh = Heterozygous dominant

Genotype:

·        Total population = 90,000

·        Since 1 out of 90,000 individuals in the population have Hurler disease, genotype frequency of aa = q2

·        Genotype frequency for aa = q2 = 1/ 90000 = 0.0009

Allele frequency for q = 0.03

As per Hardy-Weinberg equilibrium p+q = 1

Thus, p = 1- 0.03 = 0.97

Genotype frequency for AA = p2= (0.97)²= 0.9409

Answer:

Allele frequency of disease = 0.03

Genotype frequency of disease = 0.97

Question: B.

·        For first cousin, coefficient of relationship or proportion of diseased genes shared = 1/8.

·        The diseased gene in the offspring = ½

·        Thus, coefficient of inbreeding for first cousin mating = 1/16

·        The allele frequency in this case = q= 0.03.

·        Risk of disease = q x 1/16 = 0.03/ 16 = 0.001875