Question

4. In the human population there is a recessive allele, d, that results in both polydactylism and dwarfism. The Amish are a small religious denomination founded in Switzerland in 1693. The incidence of the allele "d" in the Amish population is higher as compared with the greater human population. Studies have revealed that the original Swiss Amish population consisted of 10,000 individuals; 8100 with DD genotype, 1800 with Dd genotype, and 100 with dd genotype. Assuming this population is in Hardy-Weinberg equilibrium, calculate all of the allele and genotypic frequencies for this gene in this population. (Show all your calculations below)

Answer 1

The Hardy-Weinberg principle states that in any population allele and genotype frequencies remain constant i.e. they are in equilibrium. In order for the equilibrium to continue the following conditions require to be met:

The population is very large

individuals in the population mate randomly

there is no migration into or out of the population

natural selection does not act on any specific genotypes

males and females have the same allele frequencies [vs. individuals are diploid and reproduce sexually]

no mutations occur.

The frequency of an allele is defined as the total number of copies of that allele in the population divided by the total number of copies of all alleles of the gene. We can calculate population allele frequencies from genotype numbers

Allele frequency = the total number of a particular allele in the population, and divide by the total number of total alleles. Since the population size is 10000, The total number of all alleles of the genes in population equals 20000, which is 2 times the number of individuals in the population (since the individuals are diploid). When calculating an allele frequency for a diploid species, remember that homozygous individuals have two copies of an allele, whereas heterozygotes have only one.

a)Frequency of d allele= {(100*2) + 1800 }/20000   

= 0.1

b)Frequency of D allele= {(8100*2) + 1800 }/20000   

= 0.9

According to Hardy-Weinberg equation for genotypes, we must use the formula D2+2Dd+d2= 1, Thus,

c)Frequency of dd genotype (d2)= 0.1*0.1

= 0.01

d)Frequency of Dd genotype (2Dd)= 2*0.1*0.9

=0.18

e)Frequency of DD genotype= 0.9*0.9

= 0.81