Look Who it Was Random video

How to solve Hardy-Weinberg problems

2,854 views · Published 4 January 2016 · 11:00 · Indexed 20 September 2026

Channel: Nikolay's Genetics Lessons · 2016 · Education

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Godfrey Hardy and Wilhelm Weinberg went on to develop a simple equation that can be used to discover the probable genotype frequencies in a population and to track their changes from one generation to another.  This has become known as the Hardy-Weinberg equilibrium equation.  In this equation (p² + 2pq + q² = 1), p is defined as the frequency of the dominant allele and q as the frequency of the recessive allele for a trait controlled by a pair of alleles (A and a).   In other words, p equals all of the alleles in individuals who are homozygous dominant (AA) and half of the alleles in people who are heterozygous (Aa) for this trait in a population.  In mathematical terms, this is

p = AA + ½Aa

Likewise, q equals all of the alleles in individuals who are homozygous recessive (aa) and the other half of the alleles in people who are heterozygous (Aa).

q = aa + ½Aa

Because there are only two alleles in this case, the frequency of one plus the frequency of the other must equal 100%, which is to say

p + q = 1

Since this is logically true, then the following must also be correct:

p = 1 - q

There were only a few short steps from this knowledge for Hardy and Weinberg to realize that the chances of all possible combinations of alleles occurring randomly is

(p + q)² = 1

or more simply

p² + 2pq + q² = 1

In this equation, p² is the predicted frequency of homozygous dominant (AA) people in a population, 2pq is the predicted frequency of heterozygous (Aa) people, and q² is the predicted frequency of homozygous recessive (aa) ones. 

From observations of phenotypes, it is usually only possible to know the frequency of homozygous recessive people, or q² in the equation, since they will not have the dominant trait.  Those who express the trait in their phenotype could be either homozygous dominant (p²) or heterozygous (2pq).  The Hardy-Weinberg equation allows us to predict which ones they are.  Since p = 1 - q and q is known, it is possible to calculate p as well.  Knowing p and q, it is a simple matter to plug these values into the Hardy-Weinberg equation (p² + 2pq + q² = 1).   This then provides the predicted frequencies of all three genotypes for the selected trait within the population.

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