What a Linkage Peak Says
A linkage scan evaluates a statistic at positions along a chromosome. In nonparametric linkage analysis, that statistic summarizes evidence that affected relatives share alleles identical by descent (IBD) more often than expected under the null of no linkage. The plotted values therefore describe how the evidence varies with genomic position; they are not direct measurements of a causal variant’s location.
The location of a peak gives a useful summary: it indicates where the data provide their strongest local evidence in the scanned region. Its breadth describes how quickly that evidence falls away at nearby positions. Neighboring marker results help reveal whether the pattern is a coherent regional signal or a narrow fluctuation. None of these features, by itself, identifies the causal variant.
Interpretation depends on what was scanned and what statistic was plotted. A peak in an NPL score is not automatically an estimate of a variant’s physical coordinate. Even a precisely reported maximum is the maximum of the observed scan statistic, which can be influenced by marker placement, recombination, available family information, and uncertainty in IBD inference.
Location and Neighboring Markers
Markers provide observations at particular genomic locations, while multipoint methods use information across neighboring markers to infer IBD probabilities along the chromosome. In general, markers close together on a genetic map are separated by less opportunity for recombination than markers far apart. Recombination between a disease locus and a marker can break up the inheritance pattern that makes linked relatives share a chromosome segment. Thus, a strong pattern across nearby markers can support linkage to a region, while changes across markers can help limit how broadly that evidence extends.
A genetic map reports distance in centimorgans (cM), a measure related to recombination, whereas a physical map reports distance in base pairs. These are different scales: the number of base pairs per cM need not be constant across a chromosome, and recombination patterns may differ by sex and genomic region. A region that appears narrow in cM can still cover a substantial physical span.
Worked Example: A Local Peak Is Not Necessarily the Global Maximum
Suppose a hypothetical scan reports the following NPL statistic at selected positions. The values are illustrative and are not from a real study.
| Position (cM) | NPL statistic |
|---|---|
| 40 | 1.1 |
| 45 | 2.0 |
| 50 | 2.8 |
| 55 | 2.3 |
| 60 | 1.5 |
| 120 | 3.1 |
At 50 cM, the statistic is 2.8, which exceeds the values at the nearby listed positions 45 and 55 cM. It is therefore a local peak in this neighborhood. Across the full set of listed positions, however, the largest value is 3.1 at 120 cM. Thus, 120 cM is the scan-wide maximum among these reported positions; 50 cM is not.
The nearby values 2.0, 2.8, and 2.3 indicate that the evidence around 50 cM is not confined to a single marker value. They do not establish a particular causal position or a formal interval. A complete interpretation would also consider the scan’s full set of positions and the method used to calibrate evidence, rather than relying only on these selected values.
Peak Breadth and IBD Uncertainty
A broad peak means that the statistic remains relatively elevated across a range of positions; a narrow peak means that it falls more rapidly away from its maximum. The description is relative to the plotted statistic, the scale, and the positions evaluated. It should not be confused with a confidence interval. In particular, an NPL score is not a likelihood function for a causal coordinate, so a rule such as “within one score unit of the maximum” does not automatically give a confidence interval or a specified coverage probability.
The evidence at each position also depends on IBD inference. Genotypes and pedigree structure may not determine a relative pair’s sharing state with certainty. Multipoint analysis represents this uncertainty through probabilities of sharing different numbers of alleles IBD at a position. When those probabilities are uncertain or change only gradually across nearby positions, the scan may show a broad elevation rather than pinpointing one location. Missing or uninformative genotypes can contribute to this uncertainty, but their impact depends on the pedigree and the markers that remain informative.
The relationship between IBD sharing and the null can be seen in a simple reference calculation for a full-sibling pair. Under the usual no-linkage inheritance model, the number \(K\) of alleles shared IBD has probabilities \(P(K=0)=1/4\), \(P(K=1)=1/2\), and \(P(K=2)=1/4\). The expected number shared is therefore
This calculation gives a reference expectation, not a procedure for locating a causal variant. In a linkage scan, the affected relatives’ sharing information and its uncertainty are combined according to the chosen statistic. A nearby sequence of elevated results can be informative as a regional pattern, but the peak’s shape still reflects both the underlying inheritance data and how well those data resolve IBD along the map.
Worked Example: Similar IBD Estimates Across Nearby Positions
Consider one hypothetical affected full-sibling pair. Suppose a multipoint analysis, under a specified pedigree and marker model, gives the following posterior probabilities for its IBD state at three positions. This example illustrates uncertainty for one pair; it is not a complete NPL analysis.
| Position (cM) | \(P(K=0)\) | \(P(K=1)\) | \(P(K=2)\) |
|---|---|---|---|
| 20 | 0.15 | 0.55 | 0.30 |
| 25 | 0.10 | 0.60 | 0.30 |
| 30 | 0.15 | 0.55 | 0.30 |
The probabilities in each row sum to 1. For this illustration, expected IBD sharing in allele-copy units is \(E(K)=P(K=1)+2P(K=2)\). At 20 cM,
At 25 cM, the corresponding calculation is \(E(K\mid 25)=0.60+2(0.30)=1.20\), and at 30 cM it is \(E(K\mid 30)=0.55+2(0.30)=1.15\). These estimates are modestly above the full-sibling no-linkage reference of 1, and they are similar across the three positions. The middle position has the largest expected sharing in this small illustration, but this single pair’s estimates are not a scan-wide linkage statistic and cannot establish a peak’s significance.
The example shows why IBD uncertainty matters for resolution: the probabilities assign weight to several possible sharing states at each position, and the expected sharing changes only slightly across these nearby positions. A full analysis combines information across relevant relatives and families; one should not turn these illustrative values into a causal-location claim.
Descriptive Intervals and Physical Resolution
A reader may want to summarize the range of positions with relatively elevated values. Any such summary needs an explicit rule. For example, one might report the contiguous range of evaluated positions at which the statistic exceeds a chosen descriptive threshold. That can communicate the observed shape, but unless the rule is tied to a valid inferential method with its assumptions and calibration, the resulting range is not a confidence interval.
Marker spacing matters when reading such a summary. If only a few markers are evaluated in a region, the apparent boundaries may simply reflect sparse sampling. If markers are dense but provide little information about inheritance, the location may still be poorly resolved. Conversely, informative recombination patterns among relatives can help distinguish positions along a region. The displayed peak should therefore be read alongside both marker positions and the quality of IBD information, not just its tallest plotted value.
Worked Example: A Descriptive Near-Peak Band in Two Map Scales
Suppose a hypothetical scan has these neighboring markers and NPL values:
| Marker | Position (cM) | Position (Mb) | NPL statistic |
|---|---|---|---|
| A | 45 | 80 | 2.2 |
| B | 50 | 84 | 3.0 |
| C | 55 | 91 | 2.4 |
| D | 60 | 110 | 1.4 |
The largest listed statistic is 3.0 at marker B, so B is the maximum among these four observations. For a descriptive summary, choose the rule “include the contiguous listed markers with statistic at least 2.0.” Markers A, B, and C meet that rule; D does not. The summarized marker span is therefore 45–55 cM, with a physical span from 80 to 91 Mb.
The arithmetic gives a genetic span of \(55-45=10\) cM and a physical span of \(91-80=11\) Mb. The point at the maximum is at 50 cM and 84 Mb. The 10 cM and 11 Mb spans describe this chosen threshold band in the hypothetical data; they are not a confidence interval. In particular, the boundary depends on the selected threshold and on the listed marker positions. Here the successive physical gaps are 4 Mb and 7 Mb, while the genetic gaps are both 5 cM, illustrating that physical distance and genetic distance need not change in parallel.
Why a Linkage Interval Does Not Identify a Causal Variant
Linkage analysis uses inheritance patterns in families to assess whether a region co-segregates with a phenotype more than expected under a no-linkage model. The evidence is regional because recombination events and marker data generally do not identify one base-pair position without uncertainty. Even if a scan produces a narrow, strong peak, the result concerns linkage evidence for a region—not proof that a particular variant in that region causes the trait.
There may be multiple variants within the region, and the causal variant may not be directly observed by the markers used in the scan. The peak’s exact position can also depend on the marker map, the families included, and the accuracy of inferred IBD states. Further evidence is required to evaluate candidate variants and their relationship to the phenotype. A linkage peak can prioritize a region for follow-up; it does not by itself establish a molecular mechanism or a causal effect.
Common Mistakes
- Calling every local peak the scan-wide maximum. A local peak need only be at least as high as nearby values. Reserve “global maximum” or “scan-wide peak” for the largest value across the whole scan.
- Treating the peak coordinate as the causal location. It is the position with the highest observed statistic under the scan, not a direct identification of the causal variant.
- Calling a chosen near-peak band a confidence interval. A descriptive threshold does not provide a coverage guarantee. Use “descriptive band” unless a formal inferential method justifies interval language.
- Equating a narrow genetic span with a narrow physical span. Genetic and physical distances are different maps; report the scale and units for each.
- Reading a plotted value as if IBD were known with certainty. Genotypes and pedigree information can leave uncertainty about sharing states, which contributes to how sharply a scan distinguishes nearby positions.
Check Your Understanding
Answer these questions using the definitions and examples above.
- A position has a statistic larger than the values immediately around it but smaller than a distant position elsewhere in the scan. What should each position be called?
- Why does a broad, relatively flat linkage peak provide limited localization, even when its values are elevated?
- What additional information is conveyed by neighboring-marker results, and why do they not necessarily pinpoint one physical coordinate?
- A researcher defines an interval as all listed markers with statistics at least 2.0. Why is that interval not automatically a confidence interval?
- In one or two sentences, explain why a strong linkage peak does not by itself identify a causal variant.