Local Ancestry Calls and Posterior Dosage

What a Local Ancestry Call Represents

At a genomic locus, a diploid individual carries two chromosome copies, one inherited through each parental line. Local ancestry describes the ancestral source assigned to each copy in that genomic region. It is a locus-specific inference: the labels can differ across the genome, and they do not by themselves describe an individual’s overall ancestry or identify the origin of a particular allele.

The assignment is inferred from observed genetic data and a model, rather than read directly from the genome. The model typically compares patterns of alleles along chromosome segments with allele-frequency information from reference populations. It may also use a phasing result, which assigns alleles to the two chromosome copies. A local ancestry output therefore needs to be read as an estimate conditional on the data, reference panel, and modeling choices used to create it.

The copy count is not the same as the genotype dosage for an allele. A genotype dosage concerns copies of a specified allele at a variant; local ancestry dosage concerns chromosome copies assigned to a specified ancestral source. For example, a local ancestry dosage of 1.4 for source \(k\) means an estimated posterior average of 1.4 chromosome copies from that source at the locus. It does not mean that a person has a literal fraction of a chromosome, nor does it state the ancestry of a particular allele.

Hard Calls and Posterior Dosages

Suppose the available observations for individual \(i\), including marker data and phasing information, are denoted by \(O_i\). Let \(R\) denote the reference-panel information and \(M\) the ancestry-inference model. A haplotype-level posterior probability is \(q_{i\ell hk}=P(Z_{i\ell h}=k\mid O_i,R,M)\). For each chromosome copy, these probabilities are nonnegative and sum to one across the \(K\) ancestry sources.

A haplotype-level hard call chooses an ancestry label with the largest posterior probability. A common alternative is to report a joint posterior over the two chromosome-copy labels, \(\pi_{i\ell}(a,b)=P(Z_{i\ell 1}=a,Z_{i\ell 2}=b\mid O_i,R,M)\). A joint hard call selects the pair with the largest joint probability. These two procedures need not give the same pair: selecting the most likely label separately for each copy uses marginal probabilities, whereas selecting the most likely pair uses the joint distribution.

For source \(k\), the posterior dosage is the expected local ancestry copy count:

Equivalently, using a joint posterior over chromosome-copy labels, \(\widehat{A}_{i\ell k}=\sum_{a=1}^{K}\sum_{b=1}^{K}\pi_{i\ell}(a,b)\{I(a=k)+I(b=k)\}\). The dosage lies between 0 and 2. Across all sources, the dosages sum to 2, because the individual has two chromosome copies and each copy must have one of the modeled ancestry labels.

A dosage preserves uncertainty that a hard call discards. A hard call can be useful for a compact display or for assigning a single label to a segment, but it hides how close the alternatives were. A dosage of 1.0 could arise from near certainty that the copy count is one, or from substantial probability on both zero and two copies. The number alone does not give the full posterior distribution, so it is useful to retain the underlying probabilities when available.

Why a Dosage Is a Posterior Mean

A posterior dosage is not an arbitrary fractional coding. It is the conditional expectation of a discrete copy count. One justification is that the posterior mean is the point estimate that minimizes expected squared error under the specified posterior distribution. If a candidate estimate is \(d\), the posterior expected squared error is \(L(d)=E[(A_{i\ell k}-d)^2\mid O_i,R,M]\). Expanding the square gives:

Differentiating with respect to \(d\) gives \(L'(d)=-2E(A_{i\ell k}\mid O_i,R,M)+2d\). Setting this derivative to zero yields \(d=E(A_{i\ell k}\mid O_i,R,M)\). Since \(L''(d)=2>0\), this value minimizes expected squared error. This property explains the use of posterior means as dosages; it does not make the underlying posterior model correct or guarantee that its probabilities are well calibrated.

Reference Panels, Phasing, and Uncertainty

Reference panels help define what the modeled ancestry sources look like genetically. Their composition and quality can therefore affect the inferred labels and posterior probabilities. If a relevant source is absent, poorly represented, or not well distinguished from another source in the panel, the model may assign a chromosome to the closest available category. A confident-looking call is not necessarily protected from this kind of model misspecification.

Panel size and genetic diversity matter as well. Sparse sampling can give noisy estimates of allele frequencies, while a panel that represents only a narrow subset of a source population may not capture its full variation. The labels themselves also require careful interpretation: they refer to the sources as represented and defined in the analysis, not to perfectly discrete biological populations. Dosage is conditional on those categories. Changing the set of categories can change the meaning, as well as the numerical value, of a dosage.

Phasing assigns alleles at nearby variants to chromosome copies. Local ancestry inference often uses patterns along these copies, so an incorrect phase or a phase switch can disrupt the patterns used for inference. A phase switch can make evidence appear to move from one chromosome copy to the other; depending on the surrounding data and model, it can alter haplotype-level calls or their confidence. Even when the total ancestry count at a particular locus is unchanged by swapping the two copies, the assignment of ancestry to each copy may differ. That distinction matters when interpreting chromosome-specific output.

The reported posterior probabilities usually condition on the observed data, reference information, and model assumptions. They are not automatically probabilities that account for every source of uncertainty, such as uncertainty about which populations belong in the panel, whether the phasing is correct, or whether the model’s ancestry categories are adequate. Consequently, posterior probabilities should be read as model-based uncertainty, not as a guarantee of accuracy.

Diagnostics and Common Pitfalls

Useful checks focus on whether the inference is adequately supported and whether its uncertainty is being represented honestly. At minimum, inspect the available probabilities or posterior distributions rather than relying only on hard-call labels. Low maximum posterior probabilities, diffuse probabilities across sources, or substantial posterior mass on multiple copy counts indicate ambiguity under the fitted model. A single dosage cannot diagnose all of these patterns.

• Check phase quality and consistency. Review available phasing quality information and look for patterns suggesting switch errors. Uncertainty in phase can be especially consequential where ancestry evidence is weak or changes rapidly along the region.
• Check panel suitability. Confirm that the intended ancestry sources are represented, that the reference labels match the analysis question, and that the panel is not an obviously narrow or inadequate representation.
• Compare reasonable analysis choices. Where feasible, assess whether calls or dosages change markedly under defensible panel or phasing choices. Large changes signal sensitivity that should be reported, not averaged away without justification.
• Assess calibration when truth or a suitable benchmark is available. In simulated or otherwise validated data, compare stated posterior confidence with observed accuracy. For example, calls assigned probabilities near 0.9 should be correct at roughly that rate across a sufficiently large, comparable set if those probabilities are well calibrated.

Common mistake: “The hard call says two copies of source A, so the ancestry at this locus is certain.” A hard call records the selected label, not the strength of evidence for it. The correction is to report the call together with posterior probabilities or another uncertainty summary, and to remember that the probabilities themselves depend on phasing, reference panels, and the model. A second mistake is to read a dosage of 1.4 as a directly observed fractional ancestry state. It is the expected copy count under the posterior, not an observed chromosome count.

Choosing What to Report

Hard calls and posterior dosages serve different purposes. A hard call is easy to tabulate and is useful when a downstream task explicitly requires a discrete label. It is most interpretable when the posterior is concentrated and the reference and phasing assumptions are credible. Its limitation is information loss: a call does not show whether the selected option was only slightly more probable than its alternatives.

A posterior dosage retains more of the probability information in a compact numerical summary and avoids an arbitrary threshold for converting probabilities into labels. It is useful to report alongside the hard call when both are needed. However, a dosage also compresses information: different posterior distributions can have the same mean, as a concentrated count of one and a mixture of counts zero and two can both have expected count one. When that distinction matters, report the posterior distribution or additional uncertainty summaries.

A clear report names the locus or region, the ancestry source categories, whether values are hard calls or posterior dosages, and the relevant reference-panel and phasing procedures. It should also state what uncertainty information is available and note material sensitivity to reasonable choices. Such reporting helps distinguish an observed result from the assumptions that give the result its interpretation.