BiologyGeneticsA-Level
CambridgeOCREdexcelWJECAbiturAPAQABaccalauréat Général

Allele Frequency

Sum of allele frequencies is 1.

Understand the formulaSee the free derivationOpen the full walkthrough
Open Full WalkthroughTry Calculator

This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.

Core idea

Overview

This fundamental equation represents the total frequency of two alleles for a single gene locus within a population. It establishes that the sum of the proportions of the dominant allele (p) and the recessive allele (q) must always equal 1, representing 100 percent of the gene pool.

When to use: Apply this formula when analyzing a population with exactly two alleles for a specific trait. It is used as the first step in Hardy-Weinberg calculations to determine allele distribution before calculating genotype frequencies.

Why it matters: This relationship allows biologists to track evolutionary changes; if the sum of p and q shifts over generations, it indicates that forces like natural selection or genetic drift are acting on the population. It provides a mathematical baseline for the study of population genetics.

Symbols

Variables

p = Dom. Allele Freq, q = Rec. Allele Freq

Dom. Allele Freq
Variable
Rec. Allele Freq
Variable

Walkthrough

Derivation

Understanding Allele Frequency

Allele frequency is the proportion of a particular allele among all alleles of that gene in a population.

  • Two-allele model is used for the gene (dominant/recessive).
  • Organisms are diploid.
1

Define Symbols:

Commonly, p is used for the dominant allele and q for the recessive allele.

2

Use the Total Frequency Rule:

If there are only two alleles, their frequencies must add to 1 (100%).

Result

Source: Edexcel A-Level Biology B — Evolution and Ecology

Free formulas

Rearrangements

Solve for

Make p the subject

Rearrange the allele frequency equation to solve for the dominant allele frequency, .

Difficulty: 2/5

Solve for

Allele Frequency

Start from the Hardy-Weinberg allele frequency equation, . To make (recessive allele frequency) the subject, subtract (dominant allele frequency) from both sides.

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 downward-sloping straight line that crosses the y-axis at 1 and the x-axis at 1, showing a constant rate of change where an increase in q results in an equal decrease in p. For a biology student, this means that as the recessive allele frequency increases, the dominant allele frequency must decrease to maintain a total population frequency of 1. The most important feature is that the sum of p and q is always constant, meaning any change in one variable is perfectly balanced by the other.

Graph type: linear

Why it behaves this way

Intuition

Envision a complete collection of all alleles for a specific gene within a population, where 'p' quantifies the fraction of dominant alleles and 'q' quantifies the fraction of recessive alleles, with both fractions

Frequency of the dominant allele in a population
Represents the proportion of all alleles for a given gene that are the dominant form. A higher 'p' means the dominant allele is more common.
Frequency of the recessive allele in a population
Represents the proportion of all alleles for a given gene that are the recessive form. A higher 'q' means the recessive allele is more common.
1
Represents the total proportion (100%) of all alleles for a specific gene locus in the population
Acts as a normalization constant, ensuring that all possible allele frequencies for that gene are accounted for.

Free study cues

Insight

Canonical usage

Allele frequencies are dimensionless proportions, typically expressed as decimals between 0 and 1, or as percentages between 0% and 100%. The equation ensures their sum is consistently 1 (or 100%).

Common confusion

A common mistake is inconsistently mixing decimal and percentage representations within a single calculation. For instance, using p = 0.7 and q = 30% would lead to an incorrect sum.

Dimension note

Allele frequencies (p and q) are inherently dimensionless quantities, as they represent proportions or probabilities of alleles within a gene pool. Their sum must equal 1 (or 100%)

Unit systems

None - Represents the frequency of one allele (e.g., the dominant allele) in a population. It is a proportion and can be expressed as a decimal (0 to 1) or a percentage (0% to 100%).
None - Represents the frequency of the other allele (e.g., the recessive allele) in a population. It is a proportion and can be expressed as a decimal (0 to 1) or a percentage (0% to 100%).

One free problem

Practice Problem

In a population of fruit flies, the frequency of the dominant allele for normal wing shape (p) is determined to be 0.70. Calculate the frequency of the recessive vestigial wing allele (q).

Dom. Allele Freq0.7

Solve for:

Hint: Subtract the known frequency of the dominant allele from the total population frequency of 1.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

When finding recessive allele frequency from dominant allele data, Allele Frequency is used to calculate Dom. Allele Freq from Rec. Allele Freq. The result matters because it helps compare biological conditions and decide what the measurement implies about the organism, cell, or ecosystem.

Study smarter

Tips

  • Ensure p and q are expressed as decimals between 0 and 1.
  • The value of q can often be found by taking the square root of the frequency of the homozygous recessive phenotype (q²).
  • Always verify that p + q = 1 before moving on to complex genotype calculations.

Avoid these traps

Common Mistakes

  • Mixing p and q labels.
  • Using 70 instead of 0.7.
  • Applying to systems with more than two alleles (this only works for two-allele systems).
  • Forgetting that this is a definition, not a calculation to verify.

Common questions

Frequently Asked Questions

Allele frequency is the proportion of a particular allele among all alleles of that gene in a population.

Apply this formula when analyzing a population with exactly two alleles for a specific trait. It is used as the first step in Hardy-Weinberg calculations to determine allele distribution before calculating genotype frequencies.

This relationship allows biologists to track evolutionary changes; if the sum of p and q shifts over generations, it indicates that forces like natural selection or genetic drift are acting on the population. It provides a mathematical baseline for the study of population genetics.

Mixing p and q labels. Using 70 instead of 0.7. Applying to systems with more than two alleles (this only works for two-allele systems). Forgetting that this is a definition, not a calculation to verify.

When finding recessive allele frequency from dominant allele data, Allele Frequency is used to calculate Dom. Allele Freq from Rec. Allele Freq. The result matters because it helps compare biological conditions and decide what the measurement implies about the organism, cell, or ecosystem.

Ensure p and q are expressed as decimals between 0 and 1. The value of q can often be found by taking the square root of the frequency of the homozygous recessive phenotype (q²). Always verify that p + q = 1 before moving on to complex genotype calculations.

References

Sources

  1. Wikipedia: Hardy-Weinberg principle
  2. Campbell Biology
  3. Essentials of Genetics by Klug, Cummings, Spencer, Palladino
  4. Campbell Biology (11th Edition)
  5. Wikipedia: Allele frequency
  6. Campbell Biology by Lisa A. Urry, Michael L. Cain, Steven A. Wasserman, Peter V. Minorsky, and Rebecca B. Orr
  7. Principles of Population Genetics by Daniel L. Hartl and Andrew G. Clark
  8. Hardy-Weinberg principle (Wikipedia article)