## Hardy-Weinberg Principle

The Hardy-Weinberg equation is a means by which the frequency of two alternate alleles can be predicted within a population

For two alleles of a given genetic characteristic, three genotypes are possible (assuming Mendelian inheritance): AA, Aa and aa

• Dominant allele is A, with a frequency of p
• Recessive allele is a, with a frequency of q

The Hardy-Weinberg Equation

•  The total frequency of both alleles will be 100% – in other words:  p + q = 1

•  Because genotypes consist of two alleles, this equation must be squared:  ( p + q ) 2  =  1

•  This gives the expanded Hardy-Weinberg equation:  p2 + 2pq + q2 =  1   (whereby p2 = AA ; 2pq = Aa ; q2 = aa

Graphical Representation of the Hardy-Weinberg Principle

Hardy-Weinberg Conditions

For the Hardy-Weinberg equation to be accurate, certain population conditions are assumed:

• The population is large with random mating
• There is no mutation or gene flow
• There is no natural selection or allele-specific mortality

Worked Example

Suppose we had a population of 500 people, in which 9% were albino (albinism is a recessive characteristic)

• How many individuals in this population are heterozygous?

Using the equations:    p + q =  1    and
p2 + 2pq + q2 =  1

• If q2 = 0.09   ⇒   q = 0.3  (√ 0.09)
• If q = 0.3   ⇒   p = 0.7  (p + 0.3 = 1)
• If p = 0.7   ⇒   p2 = 0.49   (0.72)
• 2pq = 0.42   ⇒   (0.49 + 2pq + 0.09 = 1)

Substituting these numbers for frequencies and applying them to the original population shows that:

• 49% of people are homozygous dominant (AA), which is 245 individuals (0.49 × 500)
• 9% of people are homozygous recessive (aa), which is 45 individuals (0.09 × 500)
• 42% of people are heterozygous (Aa), which is 210 individuals (0.42 × 500)

Practice Question

In cats, the trait for black fur (B) is dominant to white fur (b).
In a population of 250 cats, there are 40 cats with white fur.
What is the relative frequencies of the two alleles (B and b) within the population?
How many of the cats with black fur are heterozygous for this characteristic?
Remember:        p + q = 1      AND      p2 + 2pq + q2 = 1