Depth of Coverage and Callable Bases

Why Depth and Callability Are Different

Sequencing produces reads that overlap genomic positions, but coverage is not necessarily even across a target region. A base with many reads is not automatically well measured, and a base with few reads is not automatically callable. This distinction matters for rare variants: a carrier can have too little usable evidence at a position for the variant to be detected, even when the sample’s average sequencing depth looks adequate.

The earlier material on sequencing errors and mapping artifacts establishes that reads can be misleading as well as sparse. Here the focus is narrower: how much read evidence covers a position, what it means to designate that position callable, and how depth changes the opportunity to detect alternate reads. Callability criteria are operational choices for a study or pipeline, not universal constants.

Definition: The read depth at a genomic base is the number of sequencing reads that cover that base, often after specified read-processing steps. The mean depth over a region is the sum of per-base depths divided by the number of bases in that region. A base is callable under a stated rule if it meets the required coverage and quality criteria. The callable fraction is the number of callable bases divided by the number of bases in the region being assessed.

Depth is a count at a position; it does not by itself describe whether reads are accurate, uniquely mapped, or otherwise suitable for a genotype call. A callability rule may require a minimum depth, acceptable base and mapping quality, and other pre-specified conditions. Some procedures also impose a maximum depth to flag unusually high coverage. The exact thresholds depend on the assay and analysis plan.

Callability is defined relative to a sample and a genomic position, given a particular rule. A region can have high mean depth but still include poorly covered bases. For analyses requiring the same sites across several samples, researchers may also define a joint callable set: bases that meet the rule in every sample being considered. This set can be smaller than the callable set for any one sample.

Applying a Callability Rule

A transparent callability rule states the criteria before results are interpreted. For example, a rule might require depth of at least 10 reads and acceptable base and mapping quality. The word “acceptable” must itself be made operational in an actual analysis, using specified quality thresholds. For the calculations below, quality status is given directly as pass or fail.

Worked Example: Mean Depth and Callable Fraction

Consider a hypothetical ten-base target. Its per-base depths are 12, 8, 20, 15, 9, 11, 30, 14, 6, and 18 reads. Suppose a base is callable only if its depth is at least 10 and its quality criteria pass. Quality passes at bases 1, 3, 4, 5, 6, 8, and 10; it fails at bases 2, 7, and 9.

Mean depth. Add the ten depths and divide by ten:

\bar{D}=\frac{12+8+20+15+9+11+30+14+6+18}{10} =\frac{143}{10}=14.3\text{ reads per base}.

Callable bases. Apply both criteria at each position. Bases 1, 3, 4, 6, 8, and 10 have depth at least 10 and pass quality. Base 5 passes quality but has depth 9, so it is not callable. Base 7 has depth 30 but fails quality, so it is also not callable. Thus 6 of 10 bases are callable.

\text{Callable fraction}=\frac{6}{10}=0.60=60\%.

The region’s mean depth is 14.3 reads per base, yet only 60% of its bases meet the stated rule. Reporting mean depth alone would hide both the low-depth positions and the high-depth position that fails quality.

A base that fails the rule should be recorded as not callable under that rule, rather than silently treated as a confidently observed reference genotype. The distinction is between having evidence that supports a genotype and lacking sufficient evidence to make that assessment. Callability does not guarantee that a genotype call is correct; it says only that the specified minimum conditions have been met.

How Depth Changes the Chance of Seeing Alternate Reads

A simple probability model makes the role of depth explicit. Suppose a true heterozygous variant is sampled by \(d\) independent reads, each of which has probability \(1/2\) of carrying the alternate allele. Let \(X\) be the number of alternate reads. Under this idealized model, \(X\) has a binomial distribution. If a hypothetical detection rule requires at least \(r\) alternate reads, the probability of meeting that read-count requirement is the upper tail of this distribution.

Model: For a true heterozygote, assume independent, unbiased read sampling, so \(X\sim\mathrm{Binomial}(d,1/2)\), where \(d\) is the read depth at the position. If detection requires \(X\ge r\), then the probability of meeting the read-count rule is \(P(X\ge r)\). This model isolates sampling depth; it does not include sequencing error, allele-specific bias, mapping problems, or the full set of a caller’s criteria.

For the illustrative rule \(r=2\), failure to meet the rule means observing either zero or one alternate read. Since each read has alternate-read probability \(1/2\), the probabilities of those two outcomes are \(2^{-d}\) and \(d2^{-d}\). Therefore:

P(X\ge 2) =1-P(X=0)-P(X=1) =1-\frac{1}{2^d}-\frac{d}{2^d} =1-\frac{d+1}{2^d}.

This derivation shows why a higher depth generally raises the chance of satisfying the read-count rule: there are more opportunities to sample alternate reads. It does not imply that every additional read improves all aspects of call quality, or that a site passing a read-count rule must be callable under a broader quality rule.

Worked Example: Detection Probability at Two Depths

Suppose a hypothetical heterozygous rare variant is assessed using the model above, and the simplified read-count requirement is at least two alternate reads. Compare depth 4 with depth 8. The assumptions are independent, unbiased sampling and a true heterozygote; the calculation does not model other quality filters.

At depth 4, the probability of at least two alternate reads is:

P(X\ge 2\mid d=4) =1-\frac{4+1}{2^4} =1-\frac{5}{16} =\frac{11}{16} =0.6875.

At depth 8, it is:

P(X\ge 2\mid d=8) =1-\frac{8+1}{2^8} =1-\frac{9}{256} =\frac{247}{256} \approx0.9648.

Under these assumptions, the chance of obtaining at least two alternate reads rises from 68.75% at depth 4 to about 96.48% at depth 8. These are probabilities of satisfying the specified read-count condition, not probabilities that a reported variant is true and not guarantees of a final genotype call.

Comparing Detection Across a Group of Carriers

The same calculation can describe expected detection across hypothetical carriers when their depths are known. For each carrier, calculate the probability of satisfying the read-count rule at that person’s depth. Add those probabilities to obtain the expected number detected. This expectation does not require every carrier to have the same probability, but it does rely on the model being a reasonable description for each person.

Worked Example: Expected Carrier Detection at Two Depths

Imagine a hypothetical set of 30 people who truly carry the same heterozygous rare variant. Compare two sequencing designs in which every carrier has depth 4 or, alternatively, depth 8 at the variant position. Use the same simplified requirement of at least two alternate reads, and assume independent, unbiased sampling for each carrier.

From the preceding calculations, the probability of meeting the read-count rule is \(11/16=0.6875\) at depth 4 and \(247/256\approx0.9648\) at depth 8. If \(I_i\) equals 1 when carrier \(i\) meets the rule and 0 otherwise, the total number meeting it is \(\sum_{i=1}^{30} I_i\). By adding the expected values of these indicators:

E\!\left[\sum_{i=1}^{30} I_i\right] =\sum_{i=1}^{30}E[I_i] =30P(\text{meets rule}).

At depth 4, the expected number meeting the rule is:

30\left(\frac{11}{16}\right)=20.625\text{ carriers}.

At depth 8, the expected number is:

30\left(\frac{247}{256}\right) =\frac{7410}{256} \approx28.95\text{ carriers}.

Thus, under this simplified model, the expected count meeting the read threshold is about 8.32 carriers higher at depth 8. These are expected counts, not promises about the observed counts in a particular sample. Real data can differ because depths vary by person and position, and because the model omits factors such as allele imbalance and quality filters.

Interpreting Depth Without Overstating It

Depth is useful for assessing how much read sampling is available at a base, and the binomial model shows one way that more depth can increase the opportunity to observe alternate reads. But a mean depth for a region or sample is a summary, not a substitute for examining the positions relevant to an analysis. Two regions with the same mean can have different distributions of per-base depth and different callable fractions.

A practical assessment should therefore report the rule used to define callability and summarize both coverage and the resulting callable bases. When comparing samples or designs, it is helpful to be explicit about whether depth is reported at individual positions, averaged over a target, or summarized only across positions that passed filters. Those quantities answer different questions.

Specify the target and rule.
State which bases are assessed and the minimum coverage and quality conditions required for callability.

Assess positions, not just averages.
Apply the rule base by base; then summarize the callable count and callable fraction for the target.

Interpret depth-based detection carefully.
Use a stated sampling model to compare chances of observing alternate reads, while distinguishing that calculation from a complete genotype-calling decision.

Common mistake: “The sample has mean depth 30, so every position is callable and a rare variant would have been detected.” This reasoning treats a region-wide average as if it were the depth at every base and treats read count as if it settled quality. The correction is to inspect the relevant base’s coverage and quality against the stated callability rule. If the base fails that rule, the data do not support calling it reference simply because no variant was reported.

Key takeaway: Depth counts reads at a position; callability classifies whether the available evidence meets explicit coverage and quality requirements. Greater depth can raise the modeled chance of observing alternate reads, but neither high mean depth nor a read-count probability alone establishes that every base is callable or every genotype is reliable.

Check Your Understanding

Use the definitions and assumptions in this tutorial to answer the following.

A target has mean depth 25 reads per base, but one position has depth 5. Explain why the mean does not determine whether that position is callable.
Under the illustrative heterozygote model, calculate the probability of at least two alternate reads at depth 6 using \(1-(d+1)/2^d\).
A base has depth above the minimum threshold but fails the stated mapping-quality criterion. Is it callable under that rule? Explain.
Why should a position that fails callability criteria not automatically be interpreted as a reference genotype?
State two assumptions of the binomial read-sampling model and one real-data feature it leaves out.