## Allele Frequency Definition

The allele frequency is the number of individual alleles of a certain type, divided by the total number of alleles of all types in a population. In more simple terms, the allele frequency is the rate that a particular genetic variation is present within a population. The allele frequency is different from the *phenotypic ratio* in that it accounts for all alleles, even if they are recessive and are “hidden” within carrier organisms.

## How to Calculate Allele Frequency

To find the number of alleles in a given population, you must look at all the phenotypes present. The phenotypes that represent the allele are often masked by dominant and recessive alleles working in conjunction. To analyze the allele frequency in a population, scientists use the Hardy-Weinberg (HW) equation. The Hardy-Weinberg equation is written as follows:

**1 = p ^{2} + 2pq + q^{2}**

P and q each represent the allele frequency of different alleles. The term p^{2} represents the frequency of the homozygous dominant genotype. The other term, q^{2}, represents the frequency of the homozygous recessive genotype.

While it would be impossible to count all of the hidden alleles, it is easy to count the number of recessive phenotypes in a population. Recessive phenotypes are caused by two recessive alleles. Therefore, q^{2} can be easily observed by dividing the total number of recessive phenotypes by the total number of individuals. Let’s look at an example of how we can use this information to calculate the allele frequency of any given allele.

## Allele Frequency Example

In a simplified scenario, p and q are the only alleles in the population, and the population is not developing any mutations. If this is the case, the sum of the allele frequencies of p and q must equal 1 because with only two alleles the combined frequency must equal 100%.

### Finding q

In this example, consider a hypothetical population of rabbits. A certain recessive allele within rabbits causes the rabbits to be white, while all of the other rabbits are black. Only a rabbit with two recessive alleles for a particular gene will be white. When we observe the population, we find that there are 16 white rabbits and 84 black rabbits.

Since we already know what q^{2} is simply by observing the population, we can take the square root of q^{2} to find q. In this case, the white rabbits contain two recessive alleles. The white rabbits account for 16 of the 100 total rabbits. In a percentage, this is exactly 16%, or 0.16. This number is equivalent to q^{2}. Taking the square root, we find that the allele frequency of q (white) is 0.4, or 40%.

### Finding p

Once we know q, we can simply subtract q from 1 to find the frequency of p. This works only in a simplified scenario, where p and q are the only alleles. In this case, p will be equal to 60% of the alleles, or 0.6.

## Common Mistakes to Avoid

### Trying to Find p First

One mistake that students commonly make is trying to calculate p by observing the population, then taking the square root. This does not work in typical recessive/dominant allele relationships, simply because a dominant allele can hide a recessive allele. For instance, if we were to calculate the square root of .84 (proportion of black rabbits), we would get nearly 92%. This overestimates the p allele frequency because of the fact that heterozygous phenotypes are actually hiding a recessive allele and should not be counted towards p.

### Relating Allele Frequency to Fitness

A common misconception of allele frequency is that it is directly related to the evolutionary fitness of a particular allele. Just because an allele is frequent or infrequent has no bearing on the fitness of that allele. For example, many recessive traits that are deleterious “hide” in a population. This can mean that while it appears to exist at really low levels, it is in fact just hiding in the hybrids of the population.

Other times, a new beneficial mutation will have a very low allele frequency. A new allele must establish itself in a population by outcompeting other alleles. To do this is must be continuously replicated across many generations. In this way, many beneficial alleles are still highly underrepresented in the population because the population has not had time to evolve.

## Quiz

## References

- Darwin, C., & Wallace, A. (1980). On the Tendency of Species to Form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection. In P. H. Barrett (Ed.),
The Collected Papers of Charles Darwin(Vol. 2, pp. 3-18). Chicago: The University of Chicago Press.- Feldhamer, G. A., Drickamer, L. C., Vessey, S. H., Merritt, J. F., & Krajewski, C. (2007).
Mammology: Adaptation, Diversity, Ecology(3rd ed.). Baltimore: The Johns Hopkins University Press.- Hartwell, L. H., Hood, L., Goldberg, M. L., Reynolds, A. E., & Silver, L. M. (2011).
Genetics: From Genes to Genomes.Boston: McGraw Hill.