Counting Alleles From Diploid Genotype Data

From Genotypes to Allele Copies

A genotype record describes the alleles observed in one individual, while an allele frequency describes the relative abundance of allele copies in a set of individuals. Converting between them is a counting task, but it requires a clear denominator: for complete diploid genotype calls, each individual contributes two allele copies. Missing or partial records change how many copies are actually observed.

The calculations below concern a single locus in a set of diploid individuals. Assume that each included individual has two allele copies at that locus, and that the genotype labels correctly identify the alleles and their reference or alternate status. The records may have been filtered using genotyping quality checks; the formulas do not themselves assess whether a call is accurate.

Biallelic Diploid Genotypes

For a biallelic locus, label the reference allele \(A\) and the alternate allele \(G\). The possible complete diploid genotypes are \(AA\), \(AG\), and \(GG\). Let their counts be \(n_{AA}\), \(n_{AG}\), and \(n_{GG}\). An \(AA\) individual contributes two copies of \(A\), an \(AG\) individual contributes one copy of each allele, and a \(GG\) individual contributes two copies of \(G\).

Here \(C_A\) and \(C_G\) are allele counts, and \(N\) is the number of complete diploid genotype calls. There are \(2N\) allele copies in total, so the reference- and alternate-allele frequency estimates are

Every observed copy is either \(A\) or \(G\). Consequently, \(C_A+C_G=2N\), and the frequency estimates sum to one: \(\hat{p}_A+\hat{p}_G=1\). This relationship is a useful arithmetic check, not an extra modeling assumption.

Why Heterozygotes Count Once for Each Allele

A direct derivation makes the counting rule clear. For each individual \(i\), define \(X_i\) as the number of alternate-allele copies in that individual’s genotype. Then \(X_i=0\) for \(AA\), \(X_i=1\) for \(AG\), and \(X_i=2\) for \(GG\). Summing \(X_i\) across all complete calls counts every alternate copy exactly once. The sum can also be grouped by genotype category: each of the \(n_{AG}\) heterozygotes contributes one, and each of the \(n_{GG}\) alternate homozygotes contributes two.

Dividing this total by the \(2N\) allele copies gives the alternate-allele frequency estimate. The reference count follows by the same argument: \(AA\) contributes two reference copies and \(AG\) contributes one. This also explains why counting each heterozygote as two alternate copies is wrong: a heterozygote contains only one copy of the alternate allele.

More Than Two Alleles

At a multiallelic locus, each genotype contributes its number of copies to each allele category. For a diploid locus with alleles \(A\), \(C\), and \(G\), the possible unordered genotypes are \(AA\), \(AC\), \(AG\), \(CC\), \(CG\), and \(GG\). Let \(g_{ij}\) denote the count of genotype \(ij\), with \(g_{ij}=g_{ji}\) because the two allele copies have no order for this single-locus count.

For any allele \(k\), a homozygote \(kk\) contributes two copies of \(k\), and every heterozygote containing \(k\) contributes one. Therefore, its count is twice the homozygote count plus the counts of all heterozygote categories containing it. With complete calls, the total number of allele copies is twice the number of individuals, and the frequency estimate for allele \(k\) is its count divided by that total.

Incomplete Genotype Records and the Denominator

A genotype may be complete, partially observed, or fully missing. A complete diploid call contributes two observed allele copies. A partial call, such as \(A/.\), identifies one allele and leaves the other unobserved. A fully missing call, such as \(./.\), contributes no observed allele copies. The denominator must match the records used in the numerator.

One consistent approach is to count every observed allele copy, including the known allele in a partial call. In that case, divide each allele count by the total number of observed copies, which may be less than twice the number of individuals. Another consistent approach is to restrict the calculation to complete diploid calls; then use only their allele counts and a denominator of twice their number. Do not include an allele observed in a partial call in the numerator while omitting that copy from the denominator.

A frequency calculated from called copies describes those copies. Whether the called copies represent the intended population is a separate question: in particular, incomplete records should not be silently treated as if their missing alleles had been observed. The counting step alone does not establish that missingness is unrelated to allele type or any other feature.

A Reliable Counting Workflow

A short sequence of checks prevents most errors, especially when a data set contains several allele categories or incomplete calls.

Common Pitfalls and Why the Counts Matter

• Using the number of individuals as the denominator. A complete diploid sample has two allele copies per individual, so its denominator is \(2N\), not \(N\).
• Counting a heterozygote twice for one allele. An \(AG\) genotype contributes one \(A\) and one \(G\), not two copies of either allele.
• Assuming every record contributes two observed copies. Partial and fully missing calls contribute fewer than two or no known copies; use the actual observed-copy total for an allele-copy calculation.
• Confusing genotype proportions with allele frequencies. The proportion of individuals with genotype \(GG\) is \(n_{GG}/N\). The alternate-allele frequency is \((n_{AG}+2n_{GG})/(2N)\). They are different quantities.
• Assuming equilibrium is needed for counting. The formulas add observed allele copies directly. They do not require genotype proportions to follow Hardy–Weinberg proportions.