Gene Frequency | Equation, Derivation and Rearrangements

Core idea

Overview

Allele frequency measures the relative proportion of a specific genetic variant at a locus within a population's gene pool. It is calculated by dividing the total number of occurrences of that allele by the total number of alleles across all individuals in the diploid population.

When to use: This formula is applied when analyzing the genetic structure of a diploid population to observe how specific traits are distributed. It is a prerequisite for Hardy-Weinberg calculations and is used to detect changes in genetic diversity over generations.

Why it matters: Tracking allele frequencies allows biologists to monitor evolution in real-time, identifying factors like natural selection or genetic drift. This data is also vital in conservation biology to assess the genetic health and viability of endangered species.

Symbols

Variables

p = Allele Frequency, A = Copies of Allele, N = Number of Individuals

p

Allele Frequency

Variable

A

Copies of Allele

Variable

N

Number of Individuals

Variable

Walkthrough

Derivation

Understanding Gene Frequency

Gene frequency (often used as allele frequency) is how common an allele is in a population’s gene pool.

Population is diploid.
The total number of individuals N is known.

1

Count Copies of the Allele:

Homozygotes contribute 2 copies; heterozygotes contribute 1 copy.

x = number of copies of the allele

2

Divide by Total Alleles:

There are 2N total allele copies for a gene in a diploid population of size N.

Frequency = \frac{x}{2 N}

Result

Frequency = \frac{x}{2 N}

Source: AQA A-Level Biology — Populations and Evolution

Free formulas

Rearrangements

Solve for $A$

Make A the subject

A = 2 N p

Start from Gene Frequency. Assign A to 'copies of allele', multiply by 2N to clear the denominator, and rearrange to isolate A.

Difficulty: 2/5

Solve for $N$

Make N the subject

N = \frac{A}{2 p}

Start from Gene Frequency. To make N the subject, clear 2N, then divide by 2p.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin, representing a direct one-to-one correspondence where p equals the allele frequency. For a biology student, this linear relationship means that as the proportion of a specific allele in the gene pool increases, the calculated frequency rises at a constant rate. The most important feature is that the slope remains constant, meaning that doubling the value of A relative to the population size N results in a proportional doubling of the allele frequency.

Graph type: linear

Why it behaves this way

Intuition

Imagine a large container holding all the alleles for a particular gene from every individual in a population; the gene frequency 'p' is the proportion of a specific type of allele in that container, representing the relevant quantity in the system.

p

The frequency or proportion of a specific allele within a population's gene pool.

A higher 'p' indicates that the allele is more common and thus more likely to be inherited by offspring in the next generation.

copies of allele

The total count of a particular allele across all individuals in the population.

This number directly quantifies the presence of a specific genetic variant within the population's entire set of alleles for that gene.

N

The total number of diploid individuals in the population being studied.

Represents the size of the population from which the alleles are sampled, influencing the total number of alleles available.

2N

The total number of alleles for a given gene in a diploid population of N individuals.

Since each diploid individual carries two alleles for a specific gene, multiplying the number of individuals by two gives the total allele count in the gene pool.

Free study cues

Insight

Canonical usage

Allele frequency is a dimensionless ratio representing the proportion of a specific allele within a population's gene pool.

Common confusion

A common mistake is to confuse allele frequency (a proportion) with genotype frequency, or to incorrectly apply the 2N denominator to haploid organisms or non-diploid genetic systems without adjustment.

Dimension note

The allele frequency (p) is a dimensionless quantity, as it is a ratio of the number of specific alleles to the total number of alleles in the population.

Unit systems

copies of alleledimensionless count - Represents the total number of specific alleles observed in the population.

2Ndimensionless count - Represents the total number of alleles in a diploid population, where N is the number of individuals.

One free problem

Practice Problem

In a population of 500 flowering plants, researchers found 300 copies of the white-petal allele. Calculate the frequency of this allele in the population.

Copies of Allele300

Number of Individuals500

Solve for: $p$

Hint: Divide the copies of the allele by twice the number of individuals.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

When estimating allele frequency from sample genotypes, Gene Frequency is used to calculate Allele Frequency from Copies of Allele and Number of Individuals. The result matters because it helps compare populations or ecosystems and decide whether the system is growing, stable, or under stress.

Study smarter

Tips

Remember that N represents individuals, so the total gene pool is 2N.
The sum of all allele frequencies for a single locus must always equal 1.0.
Check if the population is diploid before applying the 2N multiplier.

Avoid these traps

Common Mistakes

Forgetting the 2N denominator.
Using individuals instead of alleles.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

Gene frequency (often used as allele frequency) is how common an allele is in a population’s gene pool.

This formula is applied when analyzing the genetic structure of a diploid population to observe how specific traits are distributed. It is a prerequisite for Hardy-Weinberg calculations and is used to detect changes in genetic diversity over generations.

Tracking allele frequencies allows biologists to monitor evolution in real-time, identifying factors like natural selection or genetic drift. This data is also vital in conservation biology to assess the genetic health and viability of endangered species.

Forgetting the 2N denominator. Using individuals instead of alleles.

When estimating allele frequency from sample genotypes, Gene Frequency is used to calculate Allele Frequency from Copies of Allele and Number of Individuals. The result matters because it helps compare populations or ecosystems and decide whether the system is growing, stable, or under stress.

Remember that N represents individuals, so the total gene pool is 2N. The sum of all allele frequencies for a single locus must always equal 1.0. Check if the population is diploid before applying the 2N multiplier.

References

Sources

Campbell Biology
Wikipedia: Allele frequency
Griffiths, A. J. F., Wessler, S. R., Carroll, S. B., & Doebley, J. (2015). An Introduction to Genetic Analysis (11th ed.). W. H. Freeman.
IUPAC Gold Book: Allele frequency
Hartl, D. L., & Clark, A. G. (2007). Principles of Population Genetics (4th ed.). Sinauer Associates.
AQA A-Level Biology — Populations and Evolution