Use allele and genotype frequencies, and the Hardy-Weinberg model, to describe how a gene pool stays constant or changes over time (Ohio's Learning Standards for Science, Biology, B.E.2).

What this topic is asking

Ohio standard B.E.2 asks students to understand variation of organisms within a species due to population genetics and gene frequency, and the standards reserve using statistical mathematics to predict changes in a gene pool for high school biology. The Ohio Biology EOC turns this into items where you work with allele and genotype frequencies and use the Hardy-Weinberg model as a baseline. The crosscutting idea is stability and change and the practice is using mathematics: the model describes a population that stays constant, so any departure from it signals evolution. This builds on the allele vocabulary from chromosomes, genes, and alleles.

Gene pools and allele frequencies

A population is a group of the same species living in one area and interbreeding. Its gene pool is the total collection of alleles for every gene carried by all its members. Population genetics studies how the frequencies of those alleles change.

An allele frequency is the proportion of a particular allele among all copies of that gene in the population. If a gene has just two alleles, a dominant one and a recessive one, their frequencies are written $p$ and $q$, and because every copy is one or the other:

Evolution, at the population level, is simply a change in allele frequencies over time. If $p$ and $q$ stay the same generation after generation, the population is not evolving; if they shift, it is.

The Hardy-Weinberg model

The Hardy-Weinberg principle describes the special case of a population whose allele frequencies stay constant, called Hardy-Weinberg equilibrium. It connects allele frequencies ($p$ and $q$) to genotype frequencies using the expansion of $(p + q)^2$:

Reading each term:

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

Because a recessive phenotype shows only in homozygous recessive individuals, $q^2$ is often the one quantity you can measure directly (count the recessive individuals), and from it you can work back to $q$, then $p$, then the other genotype frequencies.

The five conditions

Hardy-Weinberg equilibrium holds only if a population meets five conditions. Each one, if broken, is a mechanism of evolution (it changes allele frequencies):

• No mutation. Mutation adds or removes alleles.
• No gene flow (no migration). Individuals entering or leaving carry alleles in or out.
• A very large population. Small populations drift by chance (genetic drift).
• Random mating. Non-random (selective) mating shifts genotype proportions.
• No natural selection. Selection favors some alleles over others.

A real population almost never meets all five, so its allele frequencies change over time. The model's value is as a null baseline: it tells you what to expect with no evolution, so any difference points to one of these five mechanisms.

Using the model

The model lets you predict genotype frequencies from a known allele frequency, or recover allele frequencies from a measured genotype frequency.

Try this

Q1. Define evolution in terms of a gene pool. [1]

• Cue. A change in the allele (gene) frequencies of a population over time.

Q2. In a population, $p = 0.8$ and $q = 0.2$. Calculate the frequency of heterozygous individuals using the Hardy-Weinberg model. [1]

• Cue. $2pq = 2 \times 0.8 \times 0.2 = 0.32$ (32%).