Hardy-Weinberg analysis tool • 2026 edition
\( p + q = 1 \)
\( p^2 + 2pq + q^2 = 1 \)
Where:
These equations describe genetic equilibrium in populations.
Example: If p = 0.7, then q = 0.3
Genotype frequencies: AA = 0.49, Aa = 0.42, aa = 0.09
Allele frequency is the relative frequency of an allele at a particular gene locus in a population. It's calculated as the number of copies of the allele divided by the total number of alleles in the population.
Allele frequencies: \( p + q = 1 \)
Genotype frequencies: \( p^2 + 2pq + q^2 = 1 \)
The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. The conditions required are:
When these conditions are met, \( p + q = 1 \) and \( p^2 + 2pq + q^2 = 1 \).
Allele frequencies are calculated as:
Genotype frequencies are calculated as:
These calculations help determine if a population is evolving.
Deviations from Hardy-Weinberg equilibrium indicate evolutionary forces:
Which of the following is NOT a condition required for Hardy-Weinberg equilibrium?
The answer is C) Natural selection. Hardy-Weinberg equilibrium requires the absence of natural selection. All other conditions (random mating, large population, no mutations) must be met for equilibrium. Natural selection causes changes in allele frequencies, violating the equilibrium.
The Hardy-Weinberg principle describes an idealized population where no evolutionary forces act. Natural selection is an evolutionary force that changes allele frequencies by favoring certain genotypes. When selection is present, allele frequencies change over time, violating the equilibrium. The five conditions must all be met simultaneously for Hardy-Weinberg equilibrium to hold.
Hardy-Weinberg Equilibrium: Stable allele frequencies over generations
Evolutionary Force: Factor that changes allele frequencies
Natural Selection: Differential survival and reproduction
• Equilibrium requires absence of evolutionary forces
• Selection changes allele frequencies
• Five conditions must all be met
• Remember: Evolutionary forces disrupt equilibrium
• H-W equilibrium = no evolution occurring
• Confusing conditions that maintain vs disrupt equilibrium
• Thinking selection helps maintain equilibrium
In a population of 500 individuals, 180 are homozygous dominant (AA), 240 are heterozygous (Aa), and 80 are homozygous recessive (aa). Calculate the allele frequencies and verify Hardy-Weinberg equilibrium.
First, calculate total number of alleles: 500 × 2 = 1000
Number of A alleles: (180 × 2) + 240 = 600
Number of a alleles: (80 × 2) + 240 = 400
Frequency of A: p = 600/1000 = 0.6
Frequency of a: q = 400/1000 = 0.4
Expected frequencies: AA = p² = 0.36, Aa = 2pq = 0.48, aa = q² = 0.16
Expected counts: AA = 180, Aa = 240, aa = 80
The observed and expected match perfectly, confirming equilibrium.
This example demonstrates how to calculate allele frequencies from genotype counts. The key insight is that each individual carries two alleles, so the total number of alleles is twice the population size. We count A alleles as 2 per AA individual plus 1 per Aa individual. The verification confirms that the population is in Hardy-Weinberg equilibrium since observed and expected values match.
Allele Frequency: Proportion of an allele in a population
Genotype Frequency: Proportion of a genotype in a population
Equilibrium: Stable frequencies over generations
• Count alleles, not individuals
• Total alleles = 2 × population size
• Expected = calculated from Hardy-Weinberg equations
• Use p + q = 1 to verify calculations
• Check that p² + 2pq + q² = 1
• Forgetting to count alleles (not individuals)
• Miscalculating heterozygote contributions
Q: Why is Hardy-Weinberg equilibrium important in population genetics?
A: Hardy-Weinberg equilibrium provides a null hypothesis for population genetics. It establishes what allele and genotype frequencies would be in the absence of evolutionary forces. When observed frequencies deviate from expected Hardy-Weinberg frequencies, it indicates that evolutionary processes are acting on the population.
Mathematically, if p and q are allele frequencies, then under equilibrium:
This framework allows researchers to detect selection, genetic drift, migration, or mutation in natural populations.
Q: How do you test if a population is in Hardy-Weinberg equilibrium?
A: The Chi-square goodness-of-fit test compares observed and expected genotype frequencies:
χ² = Σ[(Observed - Expected)² / Expected]
Steps:
If χ² > critical value, reject the null hypothesis of equilibrium, indicating evolutionary forces are acting on the population.