Evolution Frequency Calculator Formula

This calculator works out the frequency of an allele (a version of a gene) in a population from genotype counts or genotype frequencies. You enter the number of individuals with each genotype (or their frequencies), and you get the allele frequency for the allele you choose, plus the complementary allele frequency. The core formula is the standard Hardy–Weinberg allele frequency calculation: p = (2 × count of homozygous dominant + count of heterozygous) / (2 × total individuals).

Formula

The allele frequency formula comes from the Hardy–Weinberg principle. For a diploid organism (two copies of each gene), the frequency of allele A is:

p = (2 × n_AA + n_Aa) / (2 × N)

where:

• n_AA = number of individuals homozygous for A (genotype AA)
• n_Aa = number of heterozygous individuals (genotype Aa)
• N = total number of individuals (n_AA + n_Aa + n_aa)
• p = frequency of allele A (a number between 0 and 1)

The frequency of the other allele, a, is simply q = 1 – p, or equivalently q = (2 × n_aa + n_Aa) / (2 × N).

Worked Example

Using the default values from the calculator: 30 AA, 50 Aa, and 20 aa individuals.

1. Total individuals N = 30 + 50 + 20 = 100
2. Total alleles = 2 × 100 = 200
3. Number of A alleles = 2 × 30 (from AA) + 50 (from Aa) = 60 + 50 = 110
4. Frequency of A: p = 110 / 200 = 0.55
5. Frequency of a: q = (2 × 20 + 50) / 200 = 90 / 200 = 0.45

The calculator shows p = 0.55 and q = 0.45, matching the hand calculation.

When to Use This Calculator

Use this calculator whenever you have genotype counts (or frequencies) and need the allele frequencies for a population genetics problem. Typical situations include:

• Teaching or homework problems on Hardy–Weinberg equilibrium
• Estimating allele frequencies from observed genotypes in a sample
• Checking whether a population is in Hardy–Weinberg equilibrium (by comparing observed and expected genotype frequencies)
• Calculating carrier frequencies for autosomal recessive conditions (if you know the frequency of affected individuals, q², you can find q and then p)

This calculator works for any diploid species, from humans to plants to animals. It assumes you know the genotype for each individual or at least the counts of each genotype.

How to Read the Result

The result is a fraction between 0 and 1. For example, p = 0.55 means that 55% of all alleles in the gene pool are A. If you prefer percentages, multiply by 100. The sum of p and q always equals 1 (or 100%).

In a population of 100 individuals, p = 0.55 means there are 110 A alleles out of 200 total alleles. That is the same as saying the frequency of A is 0.55.

If you are using this for a Hardy–Weinberg equilibrium test, you would then compare the observed genotype frequencies (0.30 AA, 0.50 Aa, 0.20 aa) with the expected frequencies (p² = 0.3025, 2pq = 0.495, q² = 0.2025). The close match suggests the population is near equilibrium, but a formal chi-square test is needed to confirm.

Common Mistakes and Pitfalls

• Forgetting to multiply homozygotes by 2: Each AA individual contributes two A alleles, not one. A common error is to use n_AA + n_Aa instead of 2n_AA + n_Aa.
• Using genotype frequencies instead of counts: If you have frequencies (e.g., 0.30, 0.50, 0.20), you can use them directly as long as they sum to 1. The formula becomes p = (2 × freq(AA) + freq(Aa)) / 2. Do not mix counts and frequencies.
• Rounding too early: Round only at the final step. Rounding intermediate values can change the final allele frequency by a few percent.
• Confusing allele frequency with genotype frequency: The frequency of AA is not the same as the frequency of A. In the example, AA frequency is 0.30, but A frequency is 0.55.
• Assuming Hardy–Weinberg equilibrium: The allele frequency formula does not require equilibrium; it is a direct count from the sample. However, if you use q² to estimate q, you are assuming equilibrium.

Limitations of the Formula

This formula assumes a diploid organism, which covers most animals and plants, but not all (some organisms are haploid or polyploid). It also assumes you have correctly identified genotypes, which may require genetic testing. In reality, dominant and recessive alleles cannot always be distinguished by phenotype alone; you cannot tell AA from Aa by appearance if A is dominant.

The formula gives the allele frequency in your sample, not necessarily the entire population. Sampling error can make the estimate differ from the true population frequency. Larger samples give more precise estimates.

Finally, the Hardy–Weinberg equilibrium itself assumes random mating, no mutation, no migration, no natural selection, and infinite population size. Real populations rarely meet all these conditions, so allele frequencies may change over time.

How to Calculate from Phenotype Data

If you only know phenotypes (e.g., dominant vs. recessive), you cannot directly count heterozygotes. In that case, you can estimate allele frequencies only if you assume Hardy–Weinberg equilibrium:

1. Calculate the frequency of the recessive phenotype (q²). For example, if 16 out of 100 individuals show a recessive trait, q² = 0.16.
2. Take the square root to get q = 0.4.
3. Then p = 1 – q = 0.6.
4. The carrier frequency (heterozygotes) is 2pq = 2 × 0.6 × 0.4 = 0.48, or 48%.

This method is common in medical genetics for autosomal recessive disorders. For instance, if 1 in 2,500 newborns has cystic fibrosis (q² = 0.0004), then q = 0.02 and p = 0.98, giving a carrier frequency of about 1 in 25.

Frequently Asked Questions

What is the difference between allele frequency and genotype frequency?

Allele frequency is the proportion of a specific allele among all alleles of that gene in the population. Genotype frequency is the proportion of individuals with a specific genotype. For example, in the default example, the frequency of the AA genotype is 0.30, but the frequency of the A allele is 0.55.

Can I use this calculator for X-linked genes?

Not directly. For X-linked genes, males have only one copy of the gene, so the total allele count is different. You would need to adjust the denominator: count male alleles once and female alleles twice. This calculator assumes autosomal inheritance.

What does it mean if p + q does not equal 1?

It means you made an error in entering the genotype counts or frequencies. The sum of all genotype counts must equal the total number of individuals, and the sum of genotype frequencies must equal 1. If p + q ≠ 1, double-check your inputs.

How do I calculate allele frequency from a DNA sequence?

You would first identify the genotype at a specific SNP (single nucleotide polymorphism) for each individual. Then count how many copies of each allele you see. For example, if you sequence 50 diploid individuals and find 70 copies of allele A and 30 copies of allele a, then p = 70/100 = 0.7.

Is this the same as the Hardy–Weinberg equation?

No. The Hardy–Weinberg equation (p² + 2pq + q² = 1) describes expected genotype frequencies under equilibrium. The allele frequency formula is simpler and does not assume equilibrium. You use the allele frequency formula to calculate p and q, then you can use the Hardy–Weinberg equation to predict genotype frequencies.

What if I have more than two alleles?

For multiple alleles (e.g., ABO blood groups), you calculate each allele frequency separately. For allele A, you count all A alleles and divide by the total number of alleles. The sum of all allele frequencies will still be 1, but you need more than two categories.

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in a | Count of AA | individuals | 30 | 0
in b | Count of Aa | individuals | 50 | 0
in c | Count of aa | individuals | 20 | 0
out p | Frequency of A | - | (2*a + b) / (2*(a + b + c)) | 4
out q | Frequency of a | - | (2*c + b) / (2*(a + b + c)) | 4
out total | Total alleles | - | 2*(a + b + c) | 0