3.7.2 - Populations and allele frequencies

Populations and allele frequency

Before you can say how common an allele is, you must define the group and count allele copies, not individuals.

Species exist as one or more populations. “All organisms in a pond” is not one population, because it describes more than one species. “All members of a species worldwide” may include populations that rarely exchange alleles.

Counting allele copies

A diploid individual has two copies of an autosomal gene, so for 200 individuals the denominator is 400 allele copies, not 200.

When genotypes are known, count alleles directly. Suppose 200 beetles comprise 98 AA, 84 Aa and 18 aa. Heterozygotes contribute one of each allele:

• A: $2(98)+84=280$ copies, so $p=280/400=0.70$
• a: $2(18)+84=120$ copies, so $q=120/400=0.30$

The frequencies sum to 1 because this gene has two alleles. Direct counting does not require Hardy–Weinberg equilibrium, the idealised state you meet in the next section.

Counting individuals instead

Genotype frequencies count individuals: $98/200=0.49$ are AA, $84/200=0.42$ are Aa and $18/200=0.09$ are aa. If A is completely dominant, AA and Aa look alike, so the dominant phenotype frequency is $(98+84)/200=0.91$.

The Hardy–Weinberg principle

Why doesn't a dominant allele spread until everyone has it? Because dominance changes phenotypes, not allele counts.

A recessive allele hidden in a heterozygote is still passed on in half of that individual's gametes, so it stays in the gene pool.

The five conditions

Each condition, also called an assumption, rules out one way alleles could be gained, lost or combined unevenly at this gene:

A population that meets these conditions is at Hardy–Weinberg equilibrium: its allele frequencies stay constant, and its genotype frequencies match the predictions in the next section.

Real populations rarely meet all five exactly: these are idealisations. The model is still a useful baseline, and it estimates genotypes you can't see.

Allele frequency or genotype frequency?

Non-random mating can change genotype frequencies without changing allele frequencies. If individuals mate mainly with others of the same genotype, AA × AA and aa × aa pairs produce only homozygotes. Heterozygotes become rarer, yet no allele copies are gained or lost.

So “allele frequencies unchanged” is a different claim from “genotype frequencies fit the random-mating prediction”.

The Hardy–Weinberg equations

Two short equations turn allele frequencies into genotype predictions; a gamete grid shows why they work.

For a gene with two alleles, A and a, let $p$ be the frequency of A (usually the dominant allele) and $q$ the frequency of a (usually the recessive allele). Each allele copy is one or the other, so $p+q=1$.

Where the terms come from

Under random mating, gametes pair by chance, so multiply their frequencies:

A heterozygote can form from two mutually exclusive parental combinations: A from the first parent with a from the second, or a from the first with A from the second. Each has probability $pq$, so their sum is $2pq$. The grid covers all offspring, so its cells add up to 1.

Try $p=0.6$ and $q=0.4$: AA is 0.36, Aa is 0.48 and aa is 0.16, which sum to 1.

All the alleles in AA and half of those in Aa are A, so the offspring's A frequency is $0.36+(0.48/2)=0.60$. That recovers $p$, the same as their parents. This is why the model predicts no change between generations.

From genotypes to phenotypes

With complete dominance, only aa has the recessive phenotype, so at equilibrium the recessive phenotype frequency equals $q^2$. The dominant phenotype includes both AA and Aa, so its frequency is $p^2+2pq=1-q^2$, not $p^2$.

With codominance, all three phenotypes can reveal genotypes, so count alleles directly.