Learn Hardy-Weinberg

The cheat sheet to understanding Hardy-Weinberg.

You'll see these two equations on the AP Biology formula sheet: $p + q = 1$ $p^{2} + 2 p q + q^{2} = 1.$

Let's learn how to use them. Hardy-Weinberg looks daunting at first, but it's not hard to get the hang of!

Recall dominant and recessive alleles. Punnett Squares are used to predict individual genotypes, but the Hardy-Weinberg equations are used to predict genotypes in an entire population.

For a given trait, there are three possible genotypes: homozygous dominant (AA), heterozygous (Aa), and homozygous recessive (aa).

The collective alleles of all members in a population put together is called the population's gene pool. Within this gene pool, there is a proportion of each genotype. For example, there might be $100$ AA giraffes in a population of $1000$ giraffes, making the AA genotype frequency $10 %$ , or $0.1$ .

Within a gene pool, there is an allele frequency for both the dominant and recessive allele. For example, if a certain population consists of $100$ tigers, there are $100 \times 2 = 200$ alleles. Out of these alleles, there might be $120$ dominant alleles and $80$ recessive alleles. The dominant allele frequency would then be $120 / 200 = 0.6$ while the recessive allele frequency would be $80 / 200 = 0.4$ . Note that $120 + 80 = 200$ and $0.6 + 0.4 = 1$ since every allele--for the purposes of Hardy-Weinberg--is either dominant or recessive (complications like multiple alleles don't factor into Hardy-Weinberg).

The dominant allele frequency is called $p$ . The recessive allele frequency is called $q$ . Because all alleles are either dominant or recessive for the purposes of Hardy-Weinberg, $p + q = 1$ .

Using algebra, we know that you can square both sides of an equation. Therefore, $(p + q)^{2} = 1^{2}$ , so $p^{2} + 2 p q + q^{2} = 1$ .

$p^{2}$ is the frequency of the homozygous dominant genotype. $2 p q$ is the frequency of the heterozygous genotype. $q^{2}$ is the frequency of the homozygous recessive genotype. Adding the dominant and recessive frequencies, $p^{2} + q^{2}$ is the frequency of homozygous genotypes in general.

Using algebra, you can convert between allele frequencies and genotype frequencies. For example, if the dominant allele frequency (A) is $0.6$ (recall that this value is $p$ ), then the homozygous dominant genotype frequency (AA) is $p^{2} = {0.6}^{2} = 0.36$ . Using more steps, you could find other genotype frequencies. The recessive allele frequency is $1 - q = 1 - 0.6 = 0.4$ , so the heterozygous genotype frequency is $2 p q = 2 (0.6) (0.4) = 0.48$ while the homozygous recessive genotype frequency is $q^{2} = {0.4}^{2} = 0.16$ .

Hardy-Weinberg questions will often ask you to find one frequency given another frequency. Using the Hardy-Weinberg equations $p + q = 1$ and $p^{2} + 2 p q + q^{2} = 1$ with some algebra, you can do so.

Most real-world populations actually living on Earth are not in Hardy-Weinberg equilibrium. This is because Hardy-Weinberg equilibrium requires five conditions to be satisfied all at once, which rarely happens in reality. Rather, Hardy-Weinberg is primarily theoretical tool to understand the genetic distribution of unchanging populations.

The conditions for Hardy-Weinberg equilibrium are as follows:

Large population. If a population is small, random chance can have a disproportionately large effect on the overall gene pool of a population.** If you flip a coin twice and it comes up heads both times, for example, you cannot conclude that it can only ever come up heads all the time.
Random mating. Alleles do not combine randomly, affecting the overall gene pool of a population.
No mutations. If an allele is modified, the gene pool is affected.
No migration. If individuals enter or exit the population, their alleles will not interact with other alleles as predicted.
No natural selection. If an organism's phenotype affects their chance of survival, the overall gene pool of a population will change.

Five conditions is a lot to remember, so don't memorize them directly. Remember one condition for each of your five fingers instead! This idea comes from Paul Andersen, who explains the mnemonic beautifully in the Ted-Ed video below.

That's it!

Grab your calculator and head over to the practice page for unlimited practice problems. The values are randomly computer-generated, so you'll never get the same problem twice.