The Hardy–Weinberg Equation Predicts Genotype Frequencies from Allele Frequencies
Definition
The Hardy–Weinberg principle
The Hardy–Weinberg principle is a mathematical model that predicts how allele and genotype frequencies remain constant in a population—unless evolutionary forces act upon it.
The Hardy–Weinberg equation predicts how alleles and genotypes are distributed in a population that is not evolving.
It uses two equations together: p + q = 1 and p² + 2pq + q² = 1.
What Each Term Means
p
Frequency of the dominant allele.
q
Frequency of the recessive allele.
p²
Frequency of homozygous dominant individuals.
2pq
Frequency of heterozygous individuals, the carriers.
q²
Frequency of homozygous recessive individuals.
How to Calculate Allele Frequencies
Find the frequency of homozygous recessive individuals, which equals q².
Take the square root of q² to find q, the recessive allele frequency.
Use p + q = 1 to find p, the dominant allele frequency.
Substitute p and q into p² + 2pq + q² = 1 to find the genotype frequencies.
Example
Suppose 4% of a population show a recessive condition, so q² = 0.04.
Then q = 0.2, and p = 1 − 0.2 = 0.8.
Carrier frequency 2pq = 2 × 0.8 × 0.2 = 0.32, so about 32% are carriers.
What the Equation Is Used For
Estimating carrier frequencies
It predicts how many people carry a recessive disease allele without showing the condition.
Detecting evolution
If observed frequencies deviate from the prediction, a force like selection, drift, or gene flow is acting.
Conservation
It tracks genetic diversity in endangered populations.
Active recall
Write the two Hardy–Weinberg equations.
What do p², 2pq, and q² each represent?
If q² = 0.09, what are q, p, and the carrier frequency?
What does a deviation from Hardy–Weinberg predictions tell you?
