Hardy-Weinberg Calculator
Calculate allele ($p, q$) and genotype frequencies ($p², 2pq, q²$) for population genetics.
Configuration
Genotype Distribution
Genotype Frequencies
Understanding Genetic Equilibrium
The Hardy-Weinberg principle provides a mathematical baseline for comparing evolving populations. By establishing what genetic frequencies should look like in a static population, biologists can identify evolutionary forces at play when real-world data deviates from the model.
In simple terms, if a population is not evolving, the amount of dominant and recessive alleles remains constant generation after generation. This state of constancy is known as Genetic Equilibrium.
The Variables
- pDominant Allele FrequencyThe percentage of the total gene pool that is dominant (A).
- qRecessive Allele FrequencyThe percentage of the total gene pool that is recessive (a).
The 5 Constraints
Evolution is occurring if any of these are violated:
- No Mutation
- Random Mating
- No Gene Flow (Migration)
- Very Large Population
- No Natural Selection
Solver Strategy
In 99% of textbook problems, you are given the count of individuals with the Recessive Phenotype (aa).
Real World Application: Carrier Screening
The most powerful application of the Hardy-Weinberg equation is calculating the Carrier Frequency ($2pq$) for recessive genetic disorders like Cystic Fibrosis or Phenylketonuria (PKU).
For example, if we know that 1 in 2,500 babies is born with Cystic Fibrosis ($q^2 = 1/2500 = 0.0004$), we can easily calculate that the carrier frequency is approximately 1 in 25 people ($2pq \approx 0.039$). This information is vital for genetic counselors and public health planning.
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Frequently Asked Questions
What is the Hardy-Weinberg equation?
The Hardy-Weinberg equation is a mathematical model used in population genetics to calculate allele and genotype frequencies. It is expressed as: p² + 2pq + q² = 1 (Genotype Frequencies) and p + q = 1 (Allele Frequencies).
What do p and q represent?
p represents the frequency of the dominant allele in the population, while q represents the frequency of the recessive allele. Together, they sum to 1 (100% of the gene pool).
What are the 5 assumptions of Hardy-Weinberg equilibrium?
For a population to remain in H-W equilibrium (no evolution), five conditions must be met: 1) No Mutation, 2) Random Mating, 3) No Gene Flow (Migration), 4) Infinite Population Size (No Genetic Drift), and 5) No Natural Selection.
How do I calculate genotype frequencies from q²?
If you know the frequency of the recessive phenotype ($q^2$), take the square root to find $q$. Then subtract $q$ from 1 to find $p$ ($p = 1 - q$). Finally, calculate the homozygous dominant frequency ($p^2$) and heterozygous frequency ($2pq$).
Why is 2pq used for heterozygotes?
The term 2pq accounts for the fact that a heterozygote can be formed in two ways: inheriting a dominant allele from the father and recessive from the mother ($pq$), or vice versa ($qp$). Since $pq = qp$, we sum them to get 2pq.
Can allele frequencies change over time?
Yes. In real populations, the 5 assumptions are rarely met perfectly. Factors like natural selection, genetic drift, and mutation constantly shift allele frequencies, driving evolution.
What is the Carrier Frequency?
The Carrier Frequency refers to the percentage of heterozygous individuals ($2pq$) who carry a recessive allele (like a disease gene) but do not express the phenotype. This calculator automatically outputs this value as "Heterozygous (Aa)".
How does this apply to X-linked traits?
For X-linked traits in males (who have only one X chromosome), the genotype frequency equals the allele frequency ($p$ or $q$). For females ($XX$), the standard H-W equation ($p^2 + 2pq + q^2$) still applies.