Haplotype Blocks and Their Boundaries

Why Summarize Local LD as Blocks?

Across a genomic region, linkage disequilibrium (LD) can vary from one pair of variants to another. A run of variants with substantial pairwise LD may be summarized as a haplotype block, while a change in the pattern may suggest a boundary. This is a useful way to describe local structure, but it is a summary of estimated LD, not a directly observed wall in the genome.

The boundary depends on which variants were measured, the population sampled, the LD measure and uncertainty procedure, and the rule used to call a block. Two analyses of the same region can therefore produce different block partitions without either being arithmetically wrong. A block is not necessarily a region with no recombination, nor does it mean that every sampled chromosome carries the same haplotype.

From Pairwise LD to Candidate Boundaries

For biallelic variants, one common measure is \(D'\), a normalized version of the two-locus disequilibrium coefficient \(D\). Its estimated value and confidence interval can be used to classify pairwise evidence. A widely used Gabriel-style rule distinguishes strong LD from evidence compatible with historical recombination; comparisons meeting neither definition are inconclusive. The following cutoffs describe that particular operational rule, not universal biological constants.

The two conditions for strong LD are both needed: a high upper endpoint alone does not establish that the lower plausible values are high, and a high lower endpoint alone does not meet the rule’s upper-endpoint requirement. Likewise, an inconclusive pair is not evidence that recombination did occur. It means the interval did not qualify for either of the two classifications.

A pairwise matrix makes the pattern visible. Rows and columns represent variants in genomic order; each cell summarizes the pair’s estimated LD or its classification. Candidate boundaries are suggested when comparisons within an interval tend to be strong while comparisons spanning a particular gap tend to show evidence of recombination. Pairwise comparisons share variants, so they are not independent observations. Counting them is part of the specified block rule, not a claim that each count supplies independent evidence.

What a Boundary Rule Can—and Cannot—Establish

The aggregation rule is useful because it makes the decision reproducible: it specifies which pairwise evidence counts and how much of it is required. The logic is straightforward. If an interval is to be summarized as a block of strong LD, most of its relevant pairs must satisfy the strong-LD criterion; a substantial fraction classified as recombination evidence argues against treating the whole interval as one block.

For example, if an interval has \(m\) informative comparisons, \(s\) classified as strong LD, and \(r\) classified as recombination evidence, its proportions are \(s/m\) and \(r/m\). Under the rule above, the interval qualifies only if \(s/m \geq 0.95\) and \(r/m < 0.05\). These requirements explain why a single weak-looking pair does not automatically create a boundary: its classification, the total number of comparisons, and the other pairs all matter.

The conclusion remains conditional on the measurement and analysis. A confidence interval for \(D'\) may be wide because the sample is small, haplotype frequencies are uncertain, or some alleles are rare. Also, \(D'\) can be high even when the allelic correlation is not especially strong, particularly when allele-frequency constraints limit its possible value. A block call should therefore be read as an operational summary of the stated pairwise evidence, not as a universal measure of how interchangeable variants are.

Sampling and Thresholds Change the Inferred Partition

A block procedure does not remove sampling uncertainty. In smaller samples, pairwise LD estimates and their confidence intervals may be imprecise. A pair that would be classified as evidence of recombination in a larger sample may instead be inconclusive in a smaller one. Conversely, estimates can vary across samples even when the underlying population structure is unchanged. In diploid samples, the number of observed individuals is not automatically the number of independently known haplotypes: phase may be uncertain, and relatedness or other sampling features can also matter.

The numerical cutoffs matter as well. Raising the lower confidence-limit requirement for strong LD makes that classification harder to attain; changing the recombination cutoff changes how many pairs count as evidence against a block. A different block procedure may use a different statistic or criterion altogether. Therefore, report the method and thresholds when describing inferred boundaries, and avoid presenting them as uniquely correct coordinates.

Reading Block Results Carefully

Block summaries can help describe how local LD is organized and compare patterns across regions or populations, provided the analysis choices are made explicit. They can also be sensitive to variant selection: adding or removing a measured variant changes which pairs enter the assessment. A boundary is therefore tied to the sampled variants and the analyzed population, as well as to the block rule.

A common mistake is to treat the block diagram as a map of fixed biological segments: “These variants are in one block, so recombination never happens inside it; the next variant marks the exact recombination site.” That conclusion is not justified. A block is inferred from population-level pairwise patterns and a chosen threshold. Those patterns can reflect historical recombination together with sampling, allele frequencies, and other features of population history. A more careful interpretation is: “Under this method and in this sample, pairwise LD supports summarizing these variants as one block; comparisons across the proposed boundary show a different pattern.”