Explain allele frequencies and gene pools, and use the Hardy-Weinberg principle to detect change

What this dot point is asking

You need to define gene pool and allele frequency, state the Hardy-Weinberg conditions, and use the Hardy-Weinberg equations to calculate allele and genotype frequencies. This dot point treats evolution quantitatively.

Gene pools and allele frequencies

A gene pool is the total collection of all alleles for all genes in a population. The allele frequency is the proportion of a particular allele among all the copies of that gene in the population.

Evolution can be defined at this level as a change in allele frequencies in a gene pool over generations. The mechanisms that change them are natural selection, genetic drift, gene flow and mutation. This definition is powerful because it makes evolution measurable: rather than describing whole organisms changing, we track the proportions of alleles, which lets the Hardy-Weinberg model give precise, testable predictions.

To calculate an allele frequency directly, count the copies of that allele and divide by the total number of allele copies in the population. For a gene with two alleles in a diploid population of $N$ individuals there are $2N$ allele copies in total. For example, if a population of $100$ individuals contains $130$ copies of allele A and $70$ copies of allele a, then the frequency of A is $130 / 200 = 0.65$ and the frequency of a is $70 / 200 = 0.35$, which together sum to $1$ as required.

The Hardy-Weinberg principle

The Hardy-Weinberg principle describes a theoretical population in which allele frequencies stay constant from generation to generation - a population that is not evolving. It acts as a null model: if a real population matches it, no evolution is occurring; if it deviates, evolution is.

It uses two equations, where $p$ and $q$ are the frequencies of two alleles of a gene:

Here $p^2$ is the frequency of the homozygous dominant genotype, $2pq$ the heterozygous genotype, and $q^2$ the homozygous recessive genotype.

The conditions for equilibrium

Allele frequencies stay constant only if all the following hold:

• a large population (so drift is negligible)
• no mutation
• no gene flow (no migration)
• random mating
• no natural selection

If any condition is broken, allele frequencies can change - that is, evolution can occur.

Reading the equations carefully

The most common stumbling block is mapping the right quantity to the right symbol. Work in this order: the observed recessive phenotype gives $q^2$ (because only homozygous recessive individuals show it), so take the square root to get the recessive allele frequency $q$. Then $p = 1 - q$ gives the dominant allele frequency. Only then can you find the genotype frequencies: $p^2$ for homozygous dominant, $2pq$ for heterozygous carriers, and $q^2$ for homozygous recessive. A useful sanity check is that the three genotype frequencies must always add to $1$, and the two allele frequencies must always add to $1$. If they do not, an arithmetic slip has crept in.

Why deviation signals evolution

The real value of the Hardy-Weinberg model is as a null hypothesis. It tells you what the genotype frequencies should be if none of the evolutionary forces are acting. If a real population's observed genotype frequencies match the predicted $p^2 : 2pq : q^2$ ratio, then within the limits of measurement no evolution is detected. If they differ - for example, far fewer homozygous recessives than predicted - then at least one condition is being broken, and you can reason about which force is responsible. Heavy selection against the recessive phenotype would lower $q$ over generations; a small population would let drift shift frequencies randomly; immigration would introduce gene flow. This is how a static equation becomes a tool for detecting and quantifying evolutionary change.