# Allele Frequency: Definition, Calculation & Example

Instructor: Joseph Said
This lesson will discuss what an allele is and how its frequency is calculated in a population. The Hardy-Weinberg principle will also be explained mathematically in this lesson with practical examples.

## Alleles and the Population

In order to discuss alleles, we need to know the terms gene, genotype, and phenotype. A gene is a piece of DNA which is expressed ultimately as a protein. It is heritable, meaning it can be inherited from parents and passed on to future generations. Each gene usually shows some sort of variation, or slightly different sequences in a gene that codes for a specific trait. An allele represents variations of a gene, and different combinations of alleles for the same gene produce different outcomes. The different combinations of alleles are known as genotypes, and the observable traits that result from these varying combinations of alleles are known as phenotypes.

For example, suppose a single gene exists which determines eye color, and different genotypes of the same gene produce different variations of eye color. The phenotype would be the actual eye color which is produced by a specific genotype. So genotype A produces phenotype brown and genotype B produces phenotype blue.

In nature, some alleles are beneficial and others are not. Or an allele may become less beneficial to a population over time. Beneficial alleles tend to stay in populations, as individuals with those alleles are more likely to mate and pass them on. Organisms that carry alleles which cause a disadvantage to their survival are less likely to reproduce. Alleles in populations are constantly shifting and changing, as evolution is driven by the selection of gene variations that are more beneficial to a population's survival.

## Shifting Alleles and Evolution

As an example, let's use a population of brown rabbits which live in a forested area. Allele A, which produces brown fur, is beneficial as these rabbits easily blend into their forest environment. Within this population is an allele B which produces white fur. White fur is less advantageous because it does not camouflage the rabbits as well as brown fur, and these rabbits are less likely to survive to adulthood and reproduce. As a result, the rabbit population consists largely of brown rabbits with a few carrying the white fur allele but not expressing it.

Now let's say the climate changes, and the forest turns into a snow covered environment due to an ice age. Now, rabbits that have white fur blend in perfectly to the snow and rabbits with brown fur are more likely to stand out to predators. Allele B has become more beneficial and allele A, which produces the brown colored fur, is less so. Due to changes in the environment, the frequency for allele B will likely rise as the frequency for allele A drops. These changes in allele frequency are the direct result of changing environments and adaptations by the population to that new environment.

## Calculating Allele Frequencies

There are thousands of alleles for thousands of genes within populations. A larger population generally will maintain allele frequencies, advantageous or not, for longer periods of time due to their size. Imagine that a large population is represented by a four-lane highway and a small population is represented by a narrow dirt road. If half of the alleles in the small population 'fall off' the narrow road, there is an easier chance that one specific allele will be completely lost and go extinct. On our four-lane highway, one or two individuals might fall off the road, but the chance that one allele will disappear or change dramatically in frequency this way is lessened. However, while two differing alleles are occupying the same road, one will almost always out-compete the other for expression in the population over a long period of time.

But how do we calculate which allele will begin to decrease based on the current environmental state? We can use the Hardy-Weinberg model, which states alleles p and q, expressed in a population as the genotypes pp, pq, and qq, together represent 100% of the population. Remember, we double alleles because each individual receives a copy of each chromosome from both of their parents and therefore carries two alleles for each trait.

## Hardy-Weinberg Frequencies

We can express the alleles in the population using the following formula:

p² + 2pq + q² = 1

This formula above is based on a Punnett square which shows the expected genotypes given two individuals with both a p and q allele.

Using these frequencies, we can estimate at which generation an allele will become fixed (stay in the population) or when it will be lost (go extinct).

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