Hardy-Weinberg Calculator — Calculate Allele and Genotype Frequencies

Hardy-Weinberg Equation and Genotype Frequencies

How to Use the Hardy-Weinberg Calculator

1. Open the Hardy-Weinberg calculator.
2. Option 1 — From allele frequencies: Enter the frequency of the dominant allele (p) or recessive allele (q). Since p + q = 1, entering one calculates the other. The tool then computes p², 2pq, and q².
3. Option 2 — From genotype counts: Enter the observed number of AA, Aa, and aa individuals in a sample population. The calculator determines allele frequencies and tests whether the observed genotype frequencies match Hardy-Weinberg expectations (chi-squared test).
4. Option 3 — Find carrier frequency: Enter the frequency of a recessive condition (q²) to find q and then 2pq (carrier frequency).

The Hardy-Weinberg Equations

The principle is expressed in two equations:

Allele frequencies: p + q = 1

Genotype frequencies: p² + 2pq + q² = 1

Where p = frequency of the dominant allele (A) and q = frequency of the recessive allele (a).

The second equation is derived by squaring the first: (p + q)² = p² + 2pq + q² = 1. This is exactly what you would expect if individuals mate randomly — the probability of two alleles combining is the product of their individual frequencies.

The Five Assumptions of Hardy-Weinberg

Worked Example: Cystic Fibrosis Carrier Frequency

Cystic fibrosis (CF) is an autosomal recessive condition. In the UK, approximately 1 in 2,500 children born is affected.

1. Affected individuals are homozygous recessive: q² = 1/2500 = 0.0004
2. Recessive allele frequency: q = √0.0004 = 0.02 (2%)
3. Dominant allele frequency: p = 1 − q = 1 − 0.02 = 0.98
4. Carrier frequency: 2pq = 2 × 0.98 × 0.02 = 0.0392 ≈ 1 in 25

So approximately 1 in 25 UK individuals are carriers of the CF allele — far more than the 1 in 2,500 who are affected. This illustrates why recessive alleles can be maintained at relatively high frequency in a population even when the homozygous recessive phenotype is harmful.

Testing for Hardy-Weinberg Equilibrium

To test whether a population is in Hardy-Weinberg equilibrium:

1. Count observed genotypes (O): number of AA, Aa, aa individuals
2. Calculate allele frequencies from observed data: p = (2×AA + Aa) / (2×total); q = 1 − p
3. Calculate expected genotype numbers (E): total × p², total × 2pq, total × q²
4. Perform chi-squared test: χ² = Σ(O − E)² / E
5. With 1 degree of freedom (for 2 alleles), critical value at p=0.05 is χ² = 3.841
6. If χ² > 3.841, reject null hypothesis — population is NOT in Hardy-Weinberg equilibrium

A significant deviation from equilibrium indicates that one or more of the five assumptions is violated — evolution is occurring at this locus.

Why Hardy-Weinberg Matters in Evolution

The Hardy-Weinberg principle is the null hypothesis of population genetics. It describes what would happen if evolution were NOT occurring. By comparing observed genotype frequencies to Hardy-Weinberg predictions:

• Identify which evolutionary forces are at work
• Estimate selection coefficients from deviations
• Detect inbreeding (excess homozygotes) or outbreeding (excess heterozygotes)
• Identify loci under selection in genome-wide association studies (GWAS)

Applications in Medicine and Conservation

Genetic disease screening

Hardy-Weinberg is used to estimate carrier frequencies of recessive genetic conditions from the known incidence of affected individuals (q² known → calculate 2pq). This informs genetic counselling and population screening programmes.

Forensic genetics

DNA profiling uses multiple loci. The probability of a random match is calculated using Hardy-Weinberg: frequency of a specific genotype = p² or 2pq at each locus. The product across loci gives the overall match probability (assuming independence — tested using Hardy-Weinberg).

Conservation genetics

Small isolated populations (endangered species) deviate from Hardy-Weinberg equilibrium due to genetic drift. Monitoring deviations guides conservation decisions — when to introduce genetic diversity from other populations to counteract inbreeding depression.

Common Questions

What does it mean if a population is in Hardy-Weinberg equilibrium?

A population in Hardy-Weinberg equilibrium at a given locus is not evolving at that locus — allele frequencies are stable across generations. This does not mean the population is not evolving at other loci. Real populations are rarely in perfect equilibrium for any locus, but many loci approximate equilibrium closely enough that deviations are meaningful signals of evolutionary forces.

Can q² be greater than q?

Yes — but only when q > 1, which is impossible since allele frequencies must be between 0 and 1. For valid allele frequencies (0 ≤ q ≤ 1), q² ≤ q always. This means homozygous recessives are always at lower frequency than the recessive allele itself — a recessive allele is often hidden in carriers (Aa) and not expressed, allowing it to persist even if harmful when homozygous.

How do you calculate allele frequency from a sample?

From a sample of N individuals: count the alleles (2N total). p = (2 × count of AA + count of Aa) / 2N. q = (2 × count of aa + count of Aa) / 2N. Alternatively, q = 1 − p. Enter these counts in the calculator and it performs this calculation automatically.