# On the definition of sequence identity

Sequence identity is a way to measure the similarity between two sequences. For sequencing data, it is often thought as the opposite of sequencing error rate. When we say “the sequence divergence between two species is ABC” or “the sequencing error rate is XYZ”, we assume everyone knows how to compute identity. In fact, there are more than one ways to compute identity. This blog post discusses a few definitions and how minimap2 implements it.

I will start with the following example: what is the identity between the two sequences?

```
CCAGTGTGGCCGATACCCCAGGTTGGCACGCATCGTTGCCTTGGTAAGC
CCAGTGTGGCCGATGCCCGTGCTACGCATCGTTGCCTTGGTAAGC
```

The classical way to find identity is to perform alignment first. If match=1, mismatch=-2, gapOpen=-2 and gapExt=-1, we get the following alignment:

```
Ref+: 1 CCAGTGTGGCCGATaCCCcagGTtgGC-ACGCATCGTTGCCTTGGTAAGC 49
|||||||||||||| ||| || || ||||||||||||||||||||||
Qry+: 1 CCAGTGTGGCCGATgCCC---GT--GCtACGCATCGTTGCCTTGGTAAGC 45
```

Here we have 43 matching bases, 1 mismatch, 5 deletions and 1 insertion to the
first/Ref sequence. The CIGAR is `18M3D2M2D2M1I22M`

.

### Gap-excluded identity

With this definition, we exclude all gapped columns from the alignment. The identity equals “#matches / (#matches + #mismatches)”. In the example able, the gap-excluded identity is 43/(43+1)=97.7%.

An obvious problem with this definition is that it doesn’t count gaps. However, it is an often used definition. We may hear that the chimpanzee and human genome differ by a couple of percent. Here we are referring to such gap-excluded identity. The exact sentence in the first chimpanzee genome paper is “Single-nucleotide substitutions occur at a mean rate of 1.23% between copies of the human and chimpanzee genome”.

### BLAST identity

BLAST identity is defined as the number of matching bases over the number of alignment columns. In this example, there are 50 columns, so the identity is 43/50=86%. In a SAM file, the number of columns can be calculated by summing over the lengths of M/I/D CIGAR operators. The number of matching bases equals the column length minus the NM tag. Here is a Perl one-liner to calculate BLAST identity:

```
perl -ane 'if(/NM:i:(\d+)/){$n=$1;$l=0;$l+=$1 while/(\d+)[MID]/g;print(($l-$n)/$l,"\n")}'
```

where variable `$n`

is the sum of mismatches and gaps and `$l`

is the alignment
length. In the PAF format, column 10 divived by column 11 gives the
BLAST identity.

BLAST identity is perhaps the most common definition, but it should be used with caution when we filter alignments by identity. Suppose we are aligning 1000bp query sequence that has a ~300bp ALU insertion in the middle. The alignment will have a BLAST identity around 70% and is likely to get filtered out. In evolution, an ALT insertion is created by one event. It should not be counted as 300 independent differences.

### Gap-compressed identity

At least for filtering, a better definition of sequence identity is the following: we count consecutive gaps as one difference. By compressing gaps in the example above, we are effectively dealing with this alignment:

```
Ref+: CCAGTGTGGCCGATaCCCcGTtGCTACGCATC-TTGCCTTGGTAAGC
|||||||||||||| ||| || |||||||||| ||||||||||||||
Qry+: CCAGTGTGGCCGATgCCC-GT-GCTACGCATCgTTGCCTTGGTAAGC
```

The identity is 43/(50-2-1)=91.5%. I have been using this definition for
various tasks. The latest minimap2 at github outputs such identity at a new
`de:f`

tag. There is a Perl one-liner for this as well:

```
perl -ane 'if(/NM:i:(\d+)/){$n=$1;$m=$g=$o=0;$m+=$1 while/(\d+)M/g;$g+=$1,++$o while/(\d+)[ID]/g;print(1-($n-$g+$o)/($m+$o),"\n")}'
```

where `$m`

is the sum of `M`

operations, `$g`

the sum of `I`

and `D`

operations
and `$o`

the number of gap opens.

### Effect of scoring

Scoring affects alignment and thus sequence identity. For the same pair of sequences, if we change gapOpen=-4, we end up with a different alignment

```
Ref+: 1 CCAGTGTGGCCGATaCCCcaggtTGgcACGCATCGTTGCCTTGGTAAGC 49
|||||||||||||| ||| || ||||||||||||||||||||||
Qry+: 1 CCAGTGTGGCCGATgCCC----gTGctACGCATCGTTGCCTTGGTAAGC 45
```

The BLAST identity is 83.7% and the gap-compressed identity is 89.1%. **Even if
we stick with one definition, the identity can be different if we change the
scoring.**

### Concluding remarks

The estimate of sequence identity varies with definitions and alignment scoring. When you see someone talking about “sequencing error rate” next time, ask about the definition and scoring in use to make sure that is the error rate you intend to compare. If you want to estimate error rate or identity on your own, try the following command line

```
minimap2 -c ref.fa query.fa \
| perl -ane 'if(/tp:A:P/&&/NM:i:(\d+)/){$n+=$1;$m+=$1 while/(\d+)M/g;$g+=$1,++$o while/(\d+)[ID]/g}END{print(($n-$g+$o)/($m+$o),"\n")}'
```

Remember that for fair comparisons, use the same scoring.

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