Genomic Variant Matrices: Loci, Genotypes, and Allele Dosage

What a Genomic Variant Matrix Records

A genomic variant matrix records genetic variation across measured samples. Its rows identify genomic loci, such as a particular position in the genome, and its columns identify samples. A matrix entry describes the genotype or an allele count for one sample at one locus. Reading the entry correctly depends on knowing which locus and alleles are being represented, and what encoding was used.

For clarity, let \(G_{ij}\) denote the entry for locus \(i\) and sample \(j\). The symbol \(G_{ij}\) does not, by itself, tell us whether the entry is a genotype label, an allele count, or an estimated dosage. That meaning comes from the data definition and the column’s coding convention. A matrix without this information is not fully interpretable.

A locus is usually identified using a reference genome assembly, a chromosome or contig, a position, and allele labels. For a biallelic locus, the two alleles are often called the reference allele and the alternate allele. These names identify the alleles relative to a chosen reference sequence; they do not mean that the reference allele is necessarily common, ancestral, or biologically normal.

Genotype Codes and Allele Dosage

For a diploid sample at a biallelic locus, there are two allele copies. If the reference allele is coded 0 and the alternate allele is coded 1, the possible genotypes can be written as \(0/0\), \(0/1\), and \(1/1\). The slash indicates an unphased genotype: the two alleles are known, but their assignment to the two chromosome copies is not specified. A vertical bar, as in \(0|1\), is commonly used when the two alleles are phased.

The same three genotypes are often represented by the number of alternate-allele copies: 0 for \(0/0\), 1 for \(0/1\), and 2 for \(1/1\). Under this convention, the numeric value is an alternate-allele dosage. The genotype strings are categories; the numbers 0, 1, and 2 are counts, even though they correspond one-to-one with the genotype categories at a diploid biallelic locus.

Genotype fields and dosage matrices are not interchangeable without checking their meaning. A string such as \(0/1\) identifies a genotype directly. A value of 1 in a dosage matrix usually means one copy of the specified allele, but the specified allele must be named. If a matrix instead uses the integers 0, 1, and 2 merely as labels for three genotype categories, those values should not be treated as measured allele counts unless the encoding documentation confirms the correspondence.

Matrix Layout and a Worked Read-Through

A matrix entry has meaning only in the context of its row and column labels. For example, a row might identify a variant by chromosome, position, reference allele, and alternate allele; the columns then contain values for individual samples. The row’s allele definition is essential: a dosage value of 1 is not interpretable as “one copy” until we know which allele is being counted.

Assuming each entry is diploid alternate-allele dosage, the first row means that Sample A has zero G copies, Sample B has one G copy, and Sample C has two G copies. In the second row, the values count T copies, not C copies. The same number can therefore refer to different alleles in different rows.

Dosage Can Be an Estimate

Some data sets contain dosage estimates rather than certain hard genotype calls. For example, an analysis may assign probabilities to the three possible diploid genotypes and report the expected number of alternate-allele copies. If the probabilities are \(p_0\), \(p_1\), and \(p_2\) for genotypes with zero, one, and two alternate copies, respectively, the expected dosage is the probability-weighted average of the possible copy counts.

Here the genotype probabilities must be nonnegative and sum to 1. The expected dosage can be fractional, even though the actual genotype of a diploid individual has an integer number of alternate-allele copies. A fractional dosage is therefore not a claim that a person has a fraction of an allele; it summarizes uncertainty about which discrete genotype is present.

Assumptions, Diagnostics, and Limits

The familiar 0–2 coding assumes a diploid sample and a biallelic locus, with a declared allele whose copies are being counted. These conditions often hold for autosomal variants in diploid samples, but they should not be presumed for every genomic region or organism. Ploidy can differ for sex chromosomes, organellar genomes, copy-number-altered regions, and some organisms. At a locus with ploidy \(q\), the count of a specified allele may range from 0 to \(q\), rather than always from 0 to 2.

At a multiallelic locus, more than two alleles are possible. A single number in the range 0–2 is insufficient to identify all possible genotypes or all allele counts unless the data definition specifies which allele is being counted and how the others are represented. Genotype strings, allele-specific count fields, or multiple dosage columns may be used instead.

Several checks help reveal coding or data problems before analysis:

• Confirm the reference and alternate allele labels and the genome position used to define each row.
• For hard calls under diploid biallelic alternate-dosage coding, check that nonmissing values are 0, 1, or 2. Values outside this set may indicate a different encoding, a different ploidy, or an error.
• Check whether a value is an integer hard call or a possibly fractional dosage estimate. Do not apply integer-only checks to expected dosages.
• Distinguish missing-value codes from zero. A missing call means the genotype or dosage is unavailable; zero means a measured or assigned count of zero copies of the specified allele.
• Verify that dosage refers to the same allele across rows and data sources. Allele labels and orientation must be aligned before values are compared or combined.

A genotype-category representation preserves the distinction among possible genotypes explicitly. An allele-dosage representation gives a numeric copy count and can retain uncertainty when it is estimated. A hard-call dosage is compact and easy to read, but may discard uncertainty; an expected dosage can retain that uncertainty but does not state one certain genotype. Neither form alone communicates all relevant information about locus quality, allele orientation, or missingness.

A frequent mistake is to read every 0, 1, or 2 as an alternate-allele dosage automatically. That interpretation is justified only when the data documentation says the values count copies of a named allele under an appropriate ploidy model. Another mistake is to treat a missing entry as 0; doing so changes “unknown” into “no copies” and can distort summaries. In genomic data, coding conventions are part of the measurement definition, not a cosmetic detail.