# How to Calculate Allelic Frequencies

By John Brennan
dna image by Allyson Ricketts from Fotolia.com

Genes are segments of DNA that code for proteins, which are specialized molecules that perform a wide variety of tasks in cells. If a gene has more than one variant, each variant is called an allele. Diploid organisms like humans, which have two copies of each gene, can inherit two different alleles, one from each parent. If the two inherited alleles are the same, they are homozygous; if the alleles are different, they are heterozygous. The fraction of the total number of alleles for a given gene represents the allele frequency for a specific allele.

Determine how many alleles are present in the population for a given gene. If you're conducting your own experiment, you'll need to take a sample of the population and identify the variants of the gene present in that sample. This is a complex procedure, and beyond the scope of this article.

If you're working this problem on a test for a genetics class, the population size and number of gene variants should appear in the question.

Determine whether the gene is X-linked. In humans and other mammals, a normal male only inherits one copy of a gene on the X chromosome. If you're working on a genetics quiz, test or homework problem, the question will generally indicate whether the gene for a trait is X-linked. If it is not X-linked, it is autosomal, which means that it is not on the sex chromosomes.

Choose a letter or symbol to represent each of the alleles for a given gene in your calculations. Since each individual has two copies of a gene (unless it is X-linked), each individual will have two alleles.

For example, let's imagine we have a population of rabbits in which a single gene determines whether the rabbits have hairy or smooth ears. This gene has two alleles: one for hairy ears, and one for smooth ears. In this case, we could choose the letter H to represent this gene; a capital H would represent the hairy-ear allele, and a lowercase h would represent the smooth-ear allele.

In this example, an individual rabbit could inherit an HH gene, an Hh gene, or an hh gene.

Write down all possible allele combinations for the gene. In the previous example, the rabbits could have the combinations HH, Hh or hh. Thus, there are three possible combinations of alleles for a single rabbit. If a rabbit has two copies of the same allele (e.g., HH), it is homozygous for that gene. If it has two different alleles (e.g., Hh), it is heterozygous.

Determine how many individuals in the population are homozygous for an allele, and how many are heterozygous. In our rabbit example, let's say we have 100 rabbits: 50 of them have HH, 30 have Hh, and 20 have hh.

Assuming we want to find the frequency of the allele H, we'd note that 50 rabbits are homozygous for this allele (HH), and 30 are heterozygous (Hh).

Divide the number of homozygotes by the total number of individuals in the population.

Divide the number of heterozygotes by 2, and then divide the result by the total number of individuals in the population. Finally, add both results to calculate the allele frequency.

In our rabbit example, we had 50 rabbits with HH and 30 rabbits with Hh, out of 100 total rabbits. First, we divide 50 by 100, and get 0.5. Next, we divide 30 by 2, and divide the result---which is 15---by 100, which gives us 0.15. Last, we add 0.5 and 0.15 to get 0.65.

This is the allele frequency for H; it tells us what fraction of the alleles in the rabbit population are H, as opposed to h.