Why Alternate Reads Are Not Automatically Variants
A sequenced read is an observation produced by a measurement process, not a perfect copy of the underlying DNA. A base caller can substitute one nucleotide for another, and the chance of a substitution can depend on base-call quality, sequence context, read position, and sequencing orientation. Consequently, a few reads carrying an alternate base do not by themselves establish that the sample contains an alternate allele.
The key question is comparative: are the observed alternate reads more compatible with the error expected when the true sequence is reference, or with a model in which some DNA molecules carry the alternate allele? Read depth matters because even a small error probability can generate occasional incorrect calls across many reads. Read quality and strand pattern matter because error probabilities may not be uniform.
A Simple Read-Count Error Model
Suppose a site is truly reference in every sequenced DNA molecule. Let \(n\) be the number of reads covering the site, and let \(X\) be the number of those reads reported as the alternate base. If each read independently has the same reference-to-alternate error probability \(e\), then
This model says that each read has two outcomes for this calculation: it is reported as alternate with probability \(e\), or it is not. Its expected alternate-read count is \(ne\), and its standard deviation is \(\sqrt{ne(1-e)}\). These are expectations under the stated error model, not guarantees about any particular sequencing run.
A base-call quality score can help specify an error probability. Under the conventional Phred definition, a base with quality score \(Q\) has estimated error probability
For example, \(Q=30\) corresponds to an estimated error probability of \(10^{-3}=0.001\), or one error per 1,000 calls of that quality on average. This is a probability estimate for a base call, not a statement that every site or substitution has exactly that error rate. In particular, the probability of a specific reference-to-alternate substitution may differ from the probability of any incorrect base call.
If a fraction \(f\) of the sequenced DNA molecules truly carries the alternate allele, and errors are symmetric with probability \(e\) in either direction, a read is reported as alternate either because it came from an alternate molecule and was called correctly, or because it came from a reference molecule and was miscalled. Thus the observed alternate probability is
The formula makes an important point: even when an allele is truly present, the observed alternate fraction need not equal the fraction of molecules carrying it. More generally, if the reference-to-alternate error probability is \(e_{RA}\) and the alternate-to-reference error probability is \(e_{AR}\), then
The simple binomial model assumes independent reads with a common error probability and a correctly specified mapping and base-call process. Those assumptions can fail: reads may share systematic errors, error rates may vary by position or sequence context, and correlated reads can make the observed count more variable than the binomial model predicts. A calculated tail probability is therefore only as credible as its error model.
Worked Example: A Few Alternate Reads at a Reference Site
In a hypothetical sample, 100 reads cover a site believed to be reference. Suppose calibration for this substitution and read-quality range supports a reference-to-alternate error probability of \(e=0.005\). Three reads report the alternate base. What does the simple model say?
Under the reference-only model, \(X\sim\operatorname{Binomial}(100,0.005)\), with expected count \(100(0.005)=0.5\). The probability of observing three or more alternate reads is
The observed count is higher than the expected count of 0.5, and the model assigns about a 1.41% probability to a count of at least three if the site is truly reference and the assumptions hold. This is evidence against that particular reference-only error model, but it is not proof of a true variant. A site-specific error rate higher than 0.005, correlated errors, or a strand-specific artifact could make three alternate reads less surprising than the calculation suggests. The count alone does not resolve those possibilities.
Low-Frequency Alleles and the Scale of Expected Error
A low alternate fraction can be meaningful when read depth is high and the expected error count is small, but the fraction must be assessed against an appropriate error model. Comparing an observed fraction only with zero is not useful: ordinary base-calling errors make the probability of at least one alternate read positive. Instead, compare the observed count with the distribution expected under a reference-only model, while checking whether the model's error rate is plausible for the relevant reads.
Worked Example: Eight Alternate Reads at High Depth
Consider a hypothetical site with 1,000 reads. Assume, for illustration, that the relevant reference-to-alternate error probability is \(e=0.001\), and that eight reads report the alternate base. Under a reference-only model, \(X\sim\operatorname{Binomial}(1000,0.001)\), so the expected count is \(1000(0.001)=1\). The probability of eight or more alternate reads is
Eight alternate reads among 1,000 correspond to an observed fraction of \(8/1000=0.008\), or 0.8%. Under the assumed error model, that count is unusual. For comparison, if a true fraction \(f=0.008\) of molecules carries the allele and errors are symmetric with \(e=0.001\), then
So eight reads are also on the scale expected under this illustrative true-allele model. This contrast shows why the error rate matters. It does not establish that the allele is real: the calculation assumes that \(e=0.001\) applies at this site and that reads behave independently. A context-specific error rate or shared artifact could invalidate that comparison. Read quality, orientation, and the local sequence should be reviewed before interpreting the count as biological evidence.
Strand-Specific Artifacts
Sequencing artifacts can be associated with read orientation. For example, a substitution may be observed mainly among reads from one strand because of a directional chemistry or processing problem. A true allele will often be observed on both strands when both are adequately represented, although real library and mapping processes can also create strand imbalance. Therefore, strand support is a diagnostic clue, not a stand-alone proof.
A simple reference model with one shared error probability does not describe strand-specific error. If forward and reverse reads have different error probabilities, they should be considered separately: under a reference-only model, the forward alternate count can have a binomial distribution using the forward error rate, and the reverse count can have one using the reverse error rate. If the error rates are unknown or poorly calibrated, a small count on one strand cannot be judged reliably by pretending both strands have the same error probability.
Worked Example: Ten Alternate Reads on One Strand
In a hypothetical set of 200 reads, 10 report the alternate base; all 10 are forward-strand reads, while reverse-strand reads report reference. Suppose that, conditional on seeing 10 alternate reads from a true allele, the reads are equally likely to be forward or reverse. Under that specific assumption, the number of forward reads among the 10 alternate reads has a \(\operatorname{Binomial}(10,0.5)\) distribution. The probability of all 10 being on either one strand is
This is a strong warning of strand imbalance under the equal-orientation assumption. It does not show that the signal must be an artifact: a true allele can be imbalanced by chance, and library preparation or mapping can make orientation probabilities unequal. The next checks are whether both strands have adequate coverage, whether base qualities and read positions differ, and whether a plausible orientation-specific error process is known. If the assumed equal-orientation model is not justified, the numerical probability is not a valid measure of evidence.
How to Assess Read-Level Evidence
A defensible assessment separates observations from assumptions. First record the total depth and alternate-read count, then examine the quality and orientation of those reads. Next, state a reference-only error model that is relevant to the substitution and sequencing context, and compare the observed count with its predicted distribution. Finally, ask whether the features of the alternate reads fit a true allele or a known failure mode. The following sequence keeps those steps explicit.
Record total depth, alternate-read count, observed alternate fraction, and the distribution of alternate reads across strands. These are summaries of observations, not proof of a genotype.
State the relevant reference-to-alternate error probability, whether it differs by strand or context, and whether read independence and a common probability are reasonable approximations.
Calculate the probability of the observed count or a more extreme count under that model. Interpret it as a probability conditional on the model, not as the probability that the site is a variant.
Check whether alternate reads have lower base quality, occur at particular read positions, or are concentrated on one strand. Such patterns can reveal that the assumed error model is inadequate.
Read-level evidence is more informative when the observations supporting the alternate base have good base-call quality, occur across both strands where coverage permits, and are not concentrated at a problematic read position or sequence context. Conversely, low-quality alternate calls, pronounced strand concentration, and a count that is plausible under a context-specific error process weaken the case for a true allele. None of these checks is decisive in isolation.
Common Pitfalls and Limits
- Treating every read as error-free. The wrong reasoning is that any alternate read proves the DNA carries the alternate allele. The correction is that read calls have nonzero error probabilities; compare the evidence with a relevant error model.
- Using expected count as a cutoff. The wrong reasoning is that a count above \(ne\) must indicate a variant. The expected count is an average, not a maximum. Use the count distribution to describe how unusual the observation is under the model.
- Reading a small tail probability as the probability the site is false. The wrong reasoning is that \(P(X\geq x)\) under the reference-only model is the probability that the reference-only explanation is true. The calculation is conditional on that model; it does not give the probability of a hypothesis or account for alternative explanations by itself.
- Calling strand imbalance conclusive. A one-strand pattern can be an artifact warning, but true alleles can be imbalanced and library processes can produce unequal strand representation. Check the assumptions behind any strand calculation.
- Assuming all errors are independent and identical. Systematic or correlated errors can create more alternate reads than a binomial model predicts. A nominally small binomial tail probability can therefore overstate how surprising the data are.
The binomial calculation is useful for making assumptions visible and for comparing read counts with an expected error scale. Its limitations are equally important: a read-level calculation does not establish the biological origin of a signal, repair a miscalibrated error rate, or replace context-specific review. When evidence remains ambiguous, additional data or an independent measurement can help distinguish a true low-frequency allele from a systematic artifact.
Check Your Understanding
Answer each question using the stated assumptions. Short solutions follow the questions.
- At a reference site, \(n=500\) reads have a reference-to-alternate error probability \(e=0.002\). What is the expected number of alternate reads under the reference-only model?
- Why does observing one alternate read not, by itself, establish that a true alternate allele is present?
- Under a true-allele model with \(f=0.01\) and symmetric error \(e=0.001\), calculate the observed alternate probability \(q\).
- If six alternate reads are all forward-strand reads, what probability does the equal-orientation true-allele model assign to all six being on either one strand?
- Name two assumptions whose failure could make a binomial tail probability misleading for a site with several alternate reads.
Solutions. (1) The expected count is \(ne=500(0.002)=1\) alternate read. (2) The probability of an alternate call is nonzero under the reference-only model, so an observed alternate read can be an error. (3) \(q=f(1-e)+(1-f)e=0.01(0.999)+0.99(0.001)=0.01098\), or 1.098%. (4) The probability is \(2(1/2)^6=2/64=0.03125\), assuming independent equal strand probabilities conditional on six alternate reads. (5) Examples include correlated reads, a site-specific error probability different from the assumed value, and different forward- and reverse-strand error rates.