Hardy-Weinberg Equilibrium

Figure 1: Frequencies of genotypes AA, Aa and aa
p + q must equal 1.

What is Hardy-Weinberg Equilibrium?

Hardy-Weinberg equilibrium is a theorem that states that the allele and genotype frequencies will remain
constant from generation to generation in the absence of other evolutionary influences (for example: mutation or selection). In order for Hardy-Weinberg Equilibrium equation to apply some basic assumptions about the population are made.

Assumptions:

• Organisms are diploid
• Only sexual reproduction occurs
• Generations do not overlap
• Mating occurs at random
• The Population is infinitely large
• Allele frequencies are equal, regardless of sex
• There is no migration, gene flow, admixture, mutation or selection

As you can see, these conditions rarely apply in most wild populations. Rather, it describes the behaviour of an ideal population. Nevertheless, it can be used to gather information about genotype frequencies within populations. The formula to calculate Hardy-Weinberg Equilibrium for two alleles is:

p²+ 2pq + q² = 1

In this case, p² is the frequency of the dominant homozygmous genotype (AA) , 2pq is the frequency of the heterozygous genotype frequency (Aa) and q² is the frequency of the recessive homozygous genotype (aa). The relationship is demonstrated in Figure 1.

Question

Cystic Fibrosis (CF) is an inherited disorder which occurs when individuals are born with two recessive alleles (aa) (For more information of Cystic Fibrosis click here.)

The frequency of CF (aa) in European populations is estimated at 1/2500

Using the equation above and the assumption that p + q = 1, calculate the number of carriers (Aa) in Europe.