Haplotypes And Phase Ambiguity

Why Chromosome-Level Arrangement Matters

A genotype call at a variant site records which alleles an individual carries there. Across several sites, however, separate genotype calls do not necessarily say which alleles occur together on the same chromosome. That missing chromosome-level arrangement is called phase. Phase matters in genotype imputation because the matching patterns across chromosomes are haplotypes: a list of alleles carried together on one chromosome.

The discussion here assumes an individual has two copies of each autosomal region, the allele calls at the sites under consideration are known, and the sites have a specified order along the chromosome. For simplicity, examples use biallelic sites. A genotype such as \(A/G\) means one copy of allele \(A\) and one copy of allele \(G\), but by itself it does not identify which of the two homologous chromosomes carries either allele. Sex chromosomes, polyploid organisms, and uncertain or missing genotype calls require additional conventions.

The order of sites in a haplotype follows their order along the chromosome. In the notation \(AC\mid GT\), for example, one chromosome carries \(A\) at the first site and \(C\) at the second, while the other carries \(G\) and \(T\), respectively. The bar separates the two chromosome copies. Their labels are arbitrary: exchanging the two sides, \(GT\mid AC\), describes the same phase configuration. Unless there is additional information, the notation does not say which chromosome was inherited from which parent.

Two Sites: The Basic Phase Ambiguity

Consider two biallelic sites. At the first site, the alleles are \(A\) and \(G\); at the second, they are \(C\) and \(T\). Suppose the genotype is heterozygous at both sites: \(A/G\) at the first and \(C/T\) at the second. The genotype calls tell us which two alleles occur at each site, but not how the alleles are paired across the chromosome copies.

The first arrangement pairs the alleles that appear first in the site-by-site genotype notation, while the second pairs each of those alleles with the other allele at the second site. These arrangements are sometimes described as alternative phases; names such as “coupling” and “repulsion” may also be used when the alleles are coded as reference and alternate. The essential point is the actual allele sequence on each chromosome, not the label assigned to the arrangement.

Counting Configurations Across Several Sites

For a diploid individual with known biallelic genotypes at an ordered set of sites, only heterozygous sites create phase choices. At a homozygous site, both chromosome copies carry the same allele, so there is no choice about which copy carries which allele. At each heterozygous site, either allele can be assigned to a chosen first chromosome; the other allele must then be on the second chromosome.

Suppose there are \(h\) heterozygous sites. Before accounting for arbitrary chromosome labels, there are \(2^h\) ways to assign the two alleles at those sites to a first chromosome. But every arrangement is counted twice: once with the two haplotypes in one order and once with their order exchanged. Therefore, when \(h\geq 1\), the number of distinct phase configurations is \(2^h/2\). When there are no heterozygous sites, there is just one configuration.

This count assumes the genotype is known at each site and that there are exactly two chromosome copies. It counts configurations consistent with the calls; it does not say that the configurations are equally likely in a population or equally supported by other evidence.

A Short Justification for the Count

The count follows by construction. At each heterozygous site, select which of its two alleles goes on the first chromosome; the other allele is forced onto the second. These independent binary choices produce \(2^h\) ordered pairs of haplotypes. Swapping the chromosome labels maps each ordered pair to another description of the same physical arrangement. For \(h\geq1\), that swap has no fixed configuration, because the haplotypes differ at every heterozygous site. Thus the \(2^h\) ordered pairs form groups of two descriptions per physical configuration, giving \(2^h/2=2^{h-1}\). If \(h=0\), the two haplotypes are identical, so swapping them changes nothing and there is only one arrangement.

Reading and Checking Phased Data

A useful check is to translate a proposed pair of haplotypes back into per-site genotypes. At each position, collect the allele on the first haplotype and the allele on the second. The resulting unordered pair must match the observed genotype. If a proposed phase gives \(A/A\) at a site where the recorded genotype is \(A/G\), it is inconsistent with the calls and should not be treated as an alternative phase.

The reverse translation is not always unique. The two-site example demonstrates that unphased genotypes can map to more than one pair of haplotypes. A phased data file may represent the two chromosome alleles separately, whereas an unphased genotype file typically represents the allele count or unordered pair at each site. File conventions vary, so the meaning of separators and allele codes must be checked rather than assumed.

Phase ambiguity is also different from missingness. With phase ambiguity, the alleles at each site can be known exactly while their arrangement across chromosome copies is unresolved. With a missing genotype, the allele or alleles at one or more sites are not known. A region can have both problems at once, but they are not interchangeable. More sites with known genotypes may increase the number of compatible phase configurations; missing calls make the set of constraints less complete still.

Why Phase Matters, and Where This Account Stops

Haplotypes provide the chromosome-level patterns that genotype imputation uses to compare an individual’s observed sequence with patterns in reference data. A set of allele counts across sites may be compatible with multiple haplotype pairs, and those pairs need not match the same reference patterns. Recognizing this ambiguity explains why genotype data alone may not establish the chromosome-level sequence needed for imputation.

This tutorial defines the ambiguity, not a procedure for resolving it. Phase may be informed by direct observations spanning multiple sites, family transmission information, or statistical patterns in a population. Those sources have different assumptions and uncertainty; the existence of a plausible haplotype pair is not, by itself, proof that it is the true arrangement. Statistical phasing procedures address how to estimate phase and are a separate subject.

A common mistake is to read two heterozygous calls as if the allele order in the genotype notation identifies the chromosome pair. For example, seeing \(A/G\) at one site and \(C/T\) at another does not establish \(AC\mid GT\); \(AT\mid GC\) is also consistent. The correction is to separate what each site’s genotype tells us from what phase would additionally tell us: genotype gives the alleles at each position, while phase specifies which alleles occur together on each chromosome.