Hardy Weinberg Equilibrium Calculator
Compute hardy weinberg equilibrium using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
p^2 + 2pq + q^2 = 1 ; p + q = 1
Where p = frequency of dominant allele (A), q = frequency of recessive allele (a), p^2 = frequency of AA genotype, 2pq = frequency of Aa genotype (carriers), q^2 = frequency of aa genotype. The sum of all genotype frequencies equals 1.
Worked Examples
Example 1: Cystic Fibrosis Carrier Frequency
Problem: Cystic fibrosis affects 1 in 2,500 Caucasians. What is the carrier frequency?
Solution: q squared = 1/2500 = 0.0004\nq = sqrt(0.0004) = 0.02\np = 1 - 0.02 = 0.98\nCarrier frequency (2pq) = 2 x 0.98 x 0.02 = 0.0392
Result: Carrier frequency = 3.92% (approximately 1 in 25 people)
Example 2: Testing HWE with Observed Data
Problem: In 500 individuals: 280 AA, 190 Aa, 30 aa. Is this in HWE?
Solution: p = (2x280 + 190) / 1000 = 0.75, q = 0.25\nExpected: AA = 0.5625 x 500 = 281.25, Aa = 0.375 x 500 = 187.5, aa = 0.0625 x 500 = 31.25\nChi-square = (280-281.25)^2/281.25 + (190-187.5)^2/187.5 + (30-31.25)^2/31.25\n= 0.0056 + 0.0333 + 0.05 = 0.0889
Result: Chi-square = 0.089 < 3.841 — Population IS in HWE
Frequently Asked Questions
What is the Hardy-Weinberg equilibrium equation?
The Hardy-Weinberg equation states that p squared + 2pq + q squared = 1, where p is the frequency of the dominant allele and q is the frequency of the recessive allele. Additionally, p + q = 1. The term p squared represents the frequency of homozygous dominant (AA) individuals, 2pq represents heterozygous (Aa) carriers, and q squared represents homozygous recessive (aa) individuals. This equation predicts genotype frequencies from allele frequencies in an ideal population at equilibrium, serving as a null model against which evolutionary change can be detected.
What are the five conditions for Hardy-Weinberg equilibrium?
For a population to remain in Hardy-Weinberg equilibrium, five conditions must be met: (1) No mutation, so alleles are not converted from one form to another. (2) Random mating, meaning individuals do not choose mates based on genotype. (3) No natural selection, so all genotypes have equal fitness. (4) Infinitely large population size, eliminating genetic drift. (5) No gene flow, meaning no migration into or out of the population. In reality, no natural population meets all conditions perfectly, but HWE serves as a useful baseline for detecting evolutionary forces.
How do you use Hardy-Weinberg to find carrier frequency?
To find carrier frequency, first determine q squared from the frequency of affected (homozygous recessive) individuals. Take the square root to get q, then calculate p = 1 - q. The carrier frequency is 2pq. For example, if a disease affects 1 in 10,000 people, then q squared = 0.0001, q = 0.01, p = 0.99, and carrier frequency = 2 x 0.99 x 0.01 = 0.0198, or about 1 in 50 people. This application is particularly important in medical genetics for estimating how many people carry a recessive disease allele without showing symptoms.
What causes a population to deviate from Hardy-Weinberg equilibrium?
Any violation of the five HWE assumptions can cause deviation. Natural selection changes allele frequencies by favoring certain phenotypes. Genetic drift causes random fluctuations in small populations. Mutation introduces new alleles. Gene flow (migration) adds or removes alleles. Non-random mating (assortative mating, inbreeding) alters genotype frequencies. Population bottlenecks and founder effects also cause deviations. The chi-square test can detect significant deviations from expected HWE proportions, helping identify which evolutionary forces may be acting.
What is chemical equilibrium and Le Chatelier's principle?
Chemical equilibrium occurs when forward and reverse reaction rates are equal. Le Chatelier's principle states that a system at equilibrium will shift to counteract any change. Adding reactant shifts equilibrium toward products. Increasing temperature favors the endothermic direction.
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