Hardy-Weinberg Equilibrium Calculator

The Hardy-Weinberg Equilibrium Calculator is a core population genetics tool that analyzes the mathematical relationship between allele frequencies and genotype frequencies in sexually reproducing diploid organisms.

Formulated independently in 1908 by English mathematician G. H. Hardy and German physician Wilhelm Weinberg, the principle demonstrated that Mendelian inheritance does not inherently cause dominant alleles to spread or recessive alleles to vanish. Instead, genotype frequencies naturally settle into stable binomial equilibrium ($p^2 + 2pq + q^2 = 1$) after a single generation of random mating.

In medical genetics and evolutionary biology, the theorem serves two indispensable purposes: (1) calculating asymptomatic carrier rates for rare genetic diseases from observed disease incidence, and (2) serving as a null hypothesis to detect evolutionary forces acting on wild and domesticated populations.

1. Recessive Disease Prevalence Modeling: When given an incidence rate ($q^2$), the calculator takes the square root to determine recessive allele frequency: $q = \sqrt{q^2}$. The dominant allele frequency is then found by subtraction: $p = 1 - q$.

2. Carrier Frequency Computation: The heterozygous carrier frequency ($2pq$) is computed directly. Because $p$ is close to 1 for rare diseases, carriers ($2pq$) vastly outnumber affected individuals ($q^2$) by a ratio of $2p/q$.

3. Allele Counting for Sample Data: When provided with observed genotype counts ($N_{AA}, N_{Aa}, N_{aa}$), allele frequencies are calculated directly: $p = (2N_{AA} + N_{Aa}) / 2N$ and $q = (2N_{aa} + N_{Aa}) / 2N$.

4. Expected Genotype Counts: Expected genotype counts under equilibrium are computed: $E_{AA} = p^2 \times N$, $E_{Aa} = 2pq \times N$, and $E_{aa} = q^2 \times N$.

5. Chi-Square Goodness-of-Fit Test: The deviation between observed and expected counts is evaluated: $\chi^2 = \sum \frac{(O - E)^2}{E}$ with $df = 1$. If $\chi^2 \le 3.841$ ($p > 0.05$), the population conforms to equilibrium. If $\chi^2 > 3.841$ ($p \le 0.05$), equilibrium is rejected.

6. Fixation Index (Inbreeding Coefficient F): Evaluates the departure of observed heterozygosity from expected: $F = 1 - \frac{H_{obs}}{H_{exp}}$.

Dominant Allele Frequency (p): The proportion of normal/dominant alleles in the gene pool.

Recessive Allele Frequency (q): The proportion of mutant/recessive alleles in the gene pool.

Homozygous Dominant Frequency (p²): Expected percentage of individuals possessing two normal alleles (AA).

Carrier Frequency (2pq): Expected percentage of healthy, asymptomatic individuals carrying one mutant recessive allele (Aa).

Homozygous Recessive Frequency (q²): Expected percentage of individuals clinically affected by the autosomal recessive trait (aa).

Chi-Square Statistic (χ²) and P-Value: Quantifies whether discrepancies between observed and expected counts are due to random sampling noise or true evolutionary pressures.

Inbreeding Coefficient (F): Measures non-random mating; positive values denote inbreeding/structure, while negative values denote outbreeding/heterozygote advantage.

• Non-Random Mating: Assortative mating (phenotypic preference) or inbreeding (mating between relatives) increases homozygosity without altering allele frequencies.
• Natural Selection: Differential survival or reproductive success changes allele frequencies over generations (e.g., lethal recessive alleles or sickle cell heterozygote advantage).
• Genetic Drift: In small populations, random sampling of gametes causes stochastic fluctuations in allele frequencies, leading to accidental fixation or allele loss.
• Gene Flow (Migration): Influx of migrants from populations with differing allele frequencies shifts the local gene pool equilibrium.
• Mutation Pressure: The spontaneous conversion of allele A to a (or back-mutation) introduces new genetic variation at low baseline rates ($10^{-5}$ to $10^{-6}$ per locus per generation).

• Genetic Counseling: Estimating the probability that a prospective parent is an asymptomatic carrier of an autosomal recessive disease.
• Conservation Biology: Assessing loss of genetic diversity and inbreeding depression in endangered species populations.
• Forensic Genetics: Calculating match probabilities for multi-locus STR DNA profiles across ethnic databases.
• Genome-Wide Association Studies (GWAS): Quality control screening to detect genotyping errors, PCR allele dropout, or copy number variations when SNP markers fail HWE.

• Assumes a single autosomal bi-allelic locus in diploid organisms; X-linked or mitochondrial genes require sex-specific or haploid modifications.
• Assumes discrete non-overlapping generations and equal allele frequencies between sexes.
• Chi-Square goodness-of-fit test requires expected counts of at least 5 in every cell for robust asymptotic validity; small samples require Fisher’s exact test.