How Do You Calculate Genetic Diversity Using Hardy–Weinberg?

Use Hardy–Weinberg to estimate allele and genotype frequencies, not to calculate genetic diversity as a single number. In AQA A Level Biology, genetic diversity means the number of different alleles in a population. Hardy–Weinberg tells you how common two alleles and their genotypes are, provided its assumptions apply.

The equations

For a gene with two alleles, let $p$ be the frequency of one allele and $q$ the frequency of the other:

$$p+q=1$$

The predicted genotype frequencies are:

$$p^2+2pq+q^2=1$$

Here, $p^2$ and $q^2$ are the frequencies of the two homozygous genotypes (two copies of the same allele). $2pq$ is the frequency of the heterozygous genotype (one copy of each allele). A frequency is a proportion of the population, so it lies between $0$ and $1$.

Worked example

Suppose a recessive phenotype occurs in $16\%$ of a population. Assuming Hardy–Weinberg equilibrium and that this phenotype is shown only by people with two recessive alleles:

$$q^2=0.16,q=\sqrt{0.16}=0.4$$

Then $p=1-0.4=0.6$, and the predicted heterozygote frequency is:

$$2pq=2(0.6)(0.4)=0.48$$

So the estimated allele frequencies are $0.6$ and $0.4$, and $48\%$ of the population is predicted to be heterozygous. You have estimated frequencies, not found a numerical value for overall genetic diversity.

What the result means

A higher heterozygote frequency can suggest more variation at one gene because more individuals carry two different alleles. However, it is not the AQA definition of genetic diversity and does not show the number of alleles across the population. To compare populations, scientists may examine allele frequencies at many genes or compare DNA base sequences. In an exam, report each frequency, convert it to a percentage only if required, and state that Hardy–Weinberg is a model based on assumptions.

The common exam mistake is treating $16\%$ as $q$. A recessive phenotype gives you $q^2$, so take its square root first. Also, do not use the equations as a reliable prediction without considering the model’s assumptions, including a large population, random mating, and no selection, mutation or migration.