Building And Interpreting A Manhattan Plot

What a Manhattan Plot Shows

A genome-wide association scan produces a p-value for each tested variant. A Manhattan plot displays those results against genomic position: the horizontal axis orders variants along the chromosomes, and the vertical axis shows how small each association p-value is. A tall point represents a small p-value and therefore stronger statistical evidence against the null hypothesis for that variant, subject to the validity of the analysis that produced it.

The plot is a location-aware view of association results. Unlike the earlier material on the quantile-quantile plot, which compares the overall distribution of observed and expected p-values, a Manhattan plot preserves where along the genome each result arose. That makes it useful for spotting regions with concentrated evidence. It does not, by itself, identify a causal variant or establish a biological mechanism.

Definition: A Manhattan plot is a scatterplot with one point per tested genetic variant. Its horizontal coordinate represents the variant's chromosome and physical position, and its vertical coordinate is \( -\log_{10}(p) \), where \(p\) is the p-value for the variant's association test. Larger vertical values correspond to smaller p-values.

For a p-value \(p\) between 0 and 1, the plotted height is \(y=-\log_{10}(p)\). For example, \(p=0.01\) gives \(y=2\), while \(p=0.0001\) gives \(y=4\). Each tenfold decrease in p-value adds one unit to the vertical coordinate. The transformation makes very small p-values easier to display and compare: they do not all crowd near zero on the axis.

Constructing the Axes

A variant is commonly identified by its chromosome and base-pair position, such as chromosome 2 at position 45,000,000. The simplest horizontal display uses chromosome labels as ordered categories and places each variant within its chromosome according to physical position. A common alternative gives every variant a single cumulative coordinate: positions on later chromosomes are shifted by the lengths of the preceding chromosomes, often with small gaps inserted between chromosomes. Either convention should preserve the within-chromosome order and make chromosome boundaries clear.

The physical positions must use a consistent genome assembly (genome build). Positions from different builds need not refer to the same genomic locations. In a cumulative display, chromosome lengths, offsets, and any gaps determine the displayed x-coordinate; the plot should not imply that an inserted gap is genomic sequence. Alternating colors between chromosomes can make boundaries easier to follow, but color has no inferential meaning. Chromosome labels are often placed at chromosome midpoints.

The vertical axis is calculated separately for every tested variant. A point at \(y=6\), for example, corresponds to \(p=10^{-6}\). If the test reports a p-value rounded to zero because of numerical underflow, then the exact plotted height cannot be recovered from that rounded value. A plotting program should use a more precise reported log p-value, recompute it stably, or mark the value as beyond a stated limit rather than treating \(p=0\) as an ordinary observation.

Worked Example: Converting P-Values to Plot Heights

Suppose three hypothetical variants have association p-values \(0.0025\), \(4.0\times10^{-8}\), and \(0.20\). Their plotted heights are found using \(y=-\log_{10}(p)\).

For the first variant, \(0.0025=2.5\times10^{-3}\), so \(y=-\log_{10}(2.5\times10^{-3})=3-\log_{10}(2.5)=3-0.39794=2.60206\).

For the second, \(y=-\log_{10}(4.0\times10^{-8})=8-\log_{10}(4.0)=8-0.60206=7.39794\).

For the third, \(y=-\log_{10}(0.20)=0.69897\). Thus the second point appears highest because its p-value is smallest. The first and third points are not made less or more associated by their chromosome positions; position tells where each result is located, not how strong its p-value is.

Significance Thresholds on the Plot

A horizontal reference line can show a chosen p-value threshold. Because the vertical coordinate is a negative logarithm, a threshold at p-value \(p_\ast\) is drawn at height \(-\log_{10}(p_\ast)\). Points above that line have p-values smaller than \(p_\ast\); points below it have larger p-values. A threshold should be labelled with its p-value or its rationale, rather than left as an unexplained line.

In a genome-wide scan, many variants are tested, so a nominal threshold such as \(0.05\) does not generally control the probability of at least one false positive across the scan. One conservative choice is the Bonferroni threshold \(\alpha/m\), where \(m\) is the number of tests and \(\alpha\) is the desired upper bound on family-wise error under the global null. Its plotted height is \(-\log_{10}(\alpha/m)\). The commonly used threshold \(5\times10^{-8}\) corresponds to a height of about 7.301; it is a convention often motivated by a large number of genome-wide tests, not a universal threshold for every study design.

Justification: If \(m\) null hypotheses are tested and each test has a valid p-value, the probability of at least one p-value being at most \(\alpha/m\) is no greater than \(\alpha\). Indeed, the event that any test crosses the threshold is the union of the \(m\) individual crossing events, so the union bound gives \(P(\text{at least one crossing})\leq\sum_{j=1}^{m}P(p_j\leq\alpha/m)\leq m(\alpha/m)=\alpha\). This argument does not require the tests to be independent, but the resulting threshold can be conservative. On the Manhattan scale, crossing the threshold is equivalent to \( -\log_{10}(p_j)\geq-\log_{10}(\alpha/m) \).

Worked Example: Calculating a Bonferroni Line

Consider a hypothetical scan testing \(m=800{,}000\) variants, with a family-wise error target \(\alpha=0.05\). The Bonferroni p-value threshold is \(0.05/800{,}000=6.25\times10^{-8}\).

The corresponding height is \(-\log_{10}(6.25\times10^{-8})=8-\log_{10}(6.25)=8-0.79588=7.20412\). The reference line would therefore be drawn at about \(7.204\). A variant with \(p=5.0\times10^{-8}\) has height \(8-\log_{10}(5)=8-0.69897=7.30103\), which is above the line and passes this particular Bonferroni threshold. A variant with \(p=1.0\times10^{-7}\) has height 7 and is below the line. These classifications apply to the stated testing family and threshold, not to every possible analysis of the data.

Reading Points, Peaks, and Regions

An individual point represents the test result for one variant. A peak is a local concentration of relatively high points in a genomic region. Such a pattern may arise because nearby variants are correlated through linkage disequilibrium: they can carry similar association information even when only one, or a subset, is most relevant to the underlying association. Consequently, a group of tall points is not necessarily a group of independent discoveries. The plot gives a useful regional overview, but it does not show the correlation structure needed to distinguish among nearby variants.

A visible peak is also not itself a formal definition of a locus. The choice of how to group nearby variants into loci requires additional rules or analyses, and a Manhattan plot alone does not supply those rules. A reported lead variant is often the variant with the smallest p-value in a region, but its status as the tallest point does not prove that it is causal. A signal can also be missed or obscured if variants were not tested, if positions were misaligned, or if the axis is truncated.

Worked Example: Interpreting a Regional Peak

Suppose a hypothetical scan uses a threshold of \(5\times10^{-8}\), corresponding to \(y=7.301\). In one region, the smallest p-value is \(2.0\times10^{-9}\), and several nearby variants have p-values around \(1.0\times10^{-7}\). The tallest point has height \(-\log_{10}(2.0\times10^{-9})=9-\log_{10}(2)=9-0.30103=8.69897\). The nearby points at \(1.0\times10^{-7}\) have height 7.

The tallest point exceeds the stated threshold; the nearby points do not. The pattern is consistent with a strong association signal concentrated in that region, with nearby variants also showing smaller p-values. The display alone cannot tell whether the tallest variant is causal, whether another correlated variant is responsible, or whether the nearby points represent independent effects. Those questions require further analysis and relevant biological or design information.

Assumptions, Diagnostics, and Limitations

The plotting transformation itself requires only a usable p-value and a genomic position for each variant. Its interpretation, however, depends on the inputs: the association tests must be appropriate for the data and their p-values must be calibrated under their null hypotheses. If quality control, sample structure, genotype coding, or the fitted association model creates distorted p-values, a precisely drawn plot will still display misleading evidence. A Manhattan plot cannot diagnose every cause of invalid results.

Before interpreting peaks, check that each point corresponds to the intended test, that chromosome and position fields are present and ordered correctly, and that all coordinates use a consistent genome build. Confirm that the plotted number of tests matches the stated testing family and threshold. Inspect the y-axis range and any clipping: a capped plot can make distinct extreme values look tied. Check also whether some variants were omitted or whether missing p-values were silently dropped. A line at a conventional threshold does not remedy invalid p-values or account automatically for every analysis decision.

A Manhattan plot is best treated as an overview, not a complete association report. It emphasizes p-values and genomic locations, but generally does not display effect direction, effect size, uncertainty, sample size, allele frequency, or the quality of each variant. Two points with similar heights can have different estimated effects or precision. For interpretation of a particular result, the corresponding estimates, uncertainty measures, variant information, and analysis details are needed.

Common Mistakes

Reading taller as a larger effect. Height encodes the p-value, not the effect size. A small p-value can reflect a precise estimate as well as a substantial effect.
Calling every point above a line a causal discovery. Crossing a threshold is evidence under the specified test and multiplicity procedure; it does not establish causality or a mechanism.
Treating all points in a peak as independent signals. Nearby variants may be correlated. A visual cluster does not show how many distinct underlying effects exist.
Using a threshold without stating its basis. A line based on a conventional genome-wide threshold, a Bonferroni correction, or another procedure has meaning only in relation to the stated testing family and error criterion.
Plotting rounded zeros as infinite evidence. A reported value rounded to zero is not necessarily a true zero p-value; use adequate numerical precision or explicitly indicate a plotting limit.

Key takeaway: A Manhattan plot maps each variant's association p-value to a genomic position and displays its strength of statistical evidence as \( -\log_{10}(p) \). Peaks help locate regions for follow-up, while significance thresholds depend on the testing procedure and a plot alone cannot establish which variant is causal.

Check Your Understanding

Try each question, then compare your reasoning with the solutions below.

What plotted height corresponds to a p-value of \(10^{-6}\), and what p-value corresponds to height 5?
A scan tests 100,000 variants with a Bonferroni family-wise error target of \(0.05\). Find its p-value threshold and approximate plotted height.
Two neighboring variants form high points in the same peak. Why is it not justified to conclude from the plot alone that there are two independent causal variants?
What does a point above a stated genome-wide threshold support, and what does it not establish?
Why can a plotted p-value of zero be misleading, and what should be done instead?

Solutions. (1) The height is \(-\log_{10}(10^{-6})=6\); height 5 corresponds to \(p=10^{-5}\). (2) The threshold is \(0.05/100{,}000=5\times10^{-7}\). Its height is \(-\log_{10}(5\times10^{-7})=7-\log_{10}(5)=6.301\). (3) Nearby variants may be correlated through linkage disequilibrium, and the plot does not show whether their association information is independent. (4) It supports evidence against the tested null under the stated threshold and valid-test assumptions; it does not establish causality, mechanism, or effect size. (5) Zero may result from rounding or numerical underflow rather than a true zero p-value. Use a precise p-value or log p-value, or report an explicit display limit rather than treating zero as an ordinary value.