Describing the genotype of some simply-inherited traits in an individual animal can be straightforward — horned cattle are always ‘pp’, and looking at an Andalusian chicken will tell you if it is ‘BB’ (black), ‘Bb’ (slate-blue) or ‘bb’ (white). We know the exact alleles carried, and in which proportions.

When it comes to describing the genotype of a population however, we refer to gene and genotypic frequencies instead.

Gene Frequency

A gene (or allelic) frequency is a measure of how common a particular allele is at a particular locus in a population. For example, how frequently ‘B’ and ‘b’ appears in an Andalusian flock.

An allele that doesn’t appear in a population at all has a gene frequency of 0 (0%).
An allele that is the sole allele at that locus in a population has a gene frequency of 1 (100%).
And an allele that makes up 50% of the genes at that locus has a gene frequency of 0.5 (50%).

Gene frequencies are denoted by lowercase letters. The frequency of the dominant allele at a locus is represented by p and that of the recessive one by q. If neither allele is dominant, p and q are assigned arbitarily. A third allele at that locus would have a gene frequency r.

The sum of all frequencies within a population always adds up to 1 (or 100%). From above, p + q = 1, or p + q + r = 1.

Let’s work an example with a flock of 100 Andalusian chickens, of which 42 are black (’BB’), 33 are slate-blue (’Bb’) and 25 are white (’bb’). There are 200 total alleles for feather colour in this population.

Each black chicken has two ‘B’ alleles, thus 42 × 2 = 84 ‘B’ alleles. Each slate-blue chicken has one ‘B’ each, thus 33 ‘B’ alleles. The sum total of ‘B’ alleles is 84 + 33, or 117.

Each white chicken has two ‘b’ alleles, or 25 × 2 = 50 ‘b’ alleles total. Each slate-blue chicken has one ‘b’ each, thus another 33 alleles to make 83 ‘b’ alleles total.

The sum of all alleles, ‘B’ and ‘b’, is 117 + 83, or 200 total.

The gene frequency of the ‘B’ allele is therefore p = 117 ÷ 200 = 0.585 (or 58.5%)
The gene frequency of the ‘b’ allele is therefore q = 83 ÷ 200 = 0.415 (or 41.5%)

And p + q = 1.

Genotypic Frequency

A genotypic frequency is a measure of how common a particular one-locus genotype is in a population. For example, how frequently the homozygous dominant, heterozygous dominant, and homozygous recessive genotypes occur.

Genotypic frequencies are denoted by uppercase letters. The frequency of the homozygous dominant genotype is represented by P, that of the heterozygous dominant genotype by H, and that of the homozygous recessive genotype by Q. Again, these designations are arbitrary if there is no clearly dominant genotype.

In our flock of 100 Andalusians above:
the ‘BB’ genotype has a genotypic frequency of P = 42 ÷ 100 = 0.42 (or 42%)
the ‘Bb’ genotype has a genotypic frequency of H = 33 ÷ 100 = 0.33 (or 33%)
the ‘bb’ genotype has a genotypic frequency of Q = 25 ÷ 100 = 0.25 (or 25%)

And P + H + Q = 1.

How do you express genotypes with more than two alleles at a locus? Let’s take a locus B, with the alleles ‘B’, ‘b’ and ‘b′’. The possible one-locus genotypes with possible genotypic frequency representatives could be:

where P + Q + R + H_(’Bb’) + H_{(’Bb′’)} + H_{(’bb′’)} = 1.

And that’s how gene and gene frequencies are calculated! Just remember that lowercase letters (eg p, q, r) denote gene frequencies and uppercase letters (eg P, Q, R, H) denote genotypic frequencies as we’ll be using these a bit.

Next week we’ll see the effect selection has on changing gene and genotypic frequencies.