What is the Hardy-Weinberg equation?

The Hardy-Weinberg equation was developed in the early 20th century. This equation describes the way that allele frequencies change (or do not change) over generations. It is generally used to examine one trait with two alleles, one dominant (represented by p in the equation) and one recessive (represented by q). It is also common to represent the dominant allele with a capital letter (e.g., "A") and the recessive allele with the same letter in lower case (e.g., "a"). To test this equation, we examine the gene pool, which consists of all the alleles that are present in  the population. Evolution is occurring when the frequencies of these alleles change from one generation to the next. Because there are only two possible alleles, their frequencies must add up to a total of 1.

p + q = 1 (equation 1).

This means that if you know the frequency of the dominant allele, you can calculate the recessive (and the reverse is also true). This must always be true, whether evolution is happening or not. The test of the equation is in how well it is able to predict the genotype frequencies in the population. If we are dealing with a population that is diploid and a gene with only two alleles, then there are three possible genotype frequencies, homozygous dominant (an individual with two copies of the dominant allele,, which can be abbreviated as "AA"), heterozygous (one dominant and one recessive, represented as "Aa"), and homozygous recessive (two recessive alleles, represented as "aa"). The standard way to present the Hardy-Weinberg equation is to start with equation 1 and square it, because there are two alleles in diploid individuals

(p + q)² = 1 (equation 2)

This can then be expanded to

p² + 2pq + q² = 1 (equation 3)

In this equation, each of the items corresponds to a genotype, with p² representing the homozygous dominant frequency, 2pq representing the heterozygotes, and q² representing the homozygous recessive frequency. These are the values you expect to see for the genotypes if the Hardy-Weinberg equation is accurately describing your population. The equation describes a situation where evolution should not be occurring, meaning that the allele frequencies will remain unchanged from one generation to the next. This requires several assumptions:

1. There is no factor that allows some individuals to be more successful than others
2. The population size is large and there are no large-scale random events affecting it
3. There is no net mutation in the population
4. There is no net movement of individuals into or out of the population
5. Mating is random

These assumptions do not have to be perfectly met, but the closer they are, the better the equation will apply. Even in situations where the assumptions do apply, there will tend to be some variation over time, because some randomness cannot be avoided. The figure below shows how two particular alleles are changing over time when the Hardy-Weinberg assumptions are met. Note that the alleles are tied together - when one allele goes up, the other goes down in response.

These assumptions need to apply to the particular trait being studied, not every trait in the organism. This means that some traits might be evolving while others are not. It is also generally applied to traits that are autosomal, although this is not required. This app will only focus on autosomal traits to minimize the complications. See other sections on this website for specifics on how to calculate the values and how the app tests your understanding...