AQA A-Level Biology: Populations and the Hardy-Weinberg Principle

Genetics at the level of a whole population is about the frequencies of alleles rather than the genotype of one individual. This guide introduces the idea of a gene pool and allele frequency, then explains the Hardy-Weinberg principle, a mathematical model that predicts how those frequencies behave when nothing is disturbing them. Knowing the conditions the model assumes is as important as knowing the equation itself.

Populations, gene pools and allele frequency

A population is a group of organisms of the same species living in the same place at the same time that can interbreed to produce fertile offspring.

Within a population, the gene pool is all the alleles of all the genes present at a given time. The allele frequency is the proportion of a particular allele within that gene pool, given as a decimal or a percentage. Studying how these frequencies change, or stay the same, is how we describe genetics at the level of a population rather than an individual.

The Hardy-Weinberg principle

The Hardy-Weinberg principle states that the allele frequencies in a population will not change from one generation to the next, provided a set of conditions is met. It is a mathematical model: a baseline that shows what happens when no evolutionary force is acting, so that any change from it points to a force that is.

The principle only holds if all of the following are true.

• The population is large.
• There is no immigration or emigration, so no alleles are added or removed.
• There are no mutations, so no new alleles are created.
• There is no selection for or against any allele.
• Mating is random.

In reality one or more of these conditions is usually broken, which is precisely why allele frequencies do change and populations evolve.

The Hardy-Weinberg equation

The principle is expressed as two linked equations, which let you calculate allele and genotype frequencies from limited information.

The first deals with allele frequencies:

p + q = 1

• p is the frequency of one allele (usually the dominant one).
• q is the frequency of the other allele (usually the recessive one).
• their frequencies must add up to 1, because there are only two alleles.

The second deals with genotype frequencies:

p² + 2pq + q² = 1

• p² is the frequency of the homozygous dominant genotype.
• 2pq is the frequency of the heterozygous genotype.
• q² is the frequency of the homozygous recessive genotype.

The two equations are used together. The usual starting point is that the frequency of the recessive phenotype in a population equals q², because only homozygous recessive individuals show it. From q² you can find q, then p, and from there the frequencies of every genotype. (If the alleles are codominant rather than dominant and recessive, either allele can be assigned to p or q.)

How this fits together

The Hardy-Weinberg principle is deliberately a model of a population that is not changing. Its real value is as a comparison: when allele frequencies do shift over generations, one of its conditions has been broken, and that shift is evolution. What drives those shifts, and how they can eventually produce new species, is the subject of the natural selection and evolution guide.