For sequences to be compared with
mash, they must first be sketched,
which creates vastly reduced representations of them. This will happen
mash dist is given raw sequences. However, if multiple
comparisons will be performed, it is more efficient to create sketches with
mash sketch first and provide them to
mash dist in place of the
raw sequences. Sketching parameters can be provided to either tool via
command line options.
Reduced representations with MinHash tables¶
Sketches are used by the MinHash algorithm to allow fast distance estimations with low storage and memory requirements. To make a sketch, each k-mer in a sequence is hashed, which creates a pseudo-random identifier. By sorting these identifiers (hashes), a small subset from the top of the sorted list can represent the entire sequence (these are min-hashes). The more similar another sequence is, the more min-hashes it is likely to share.
As in any k-mer based method, larger k-mers will provide more specificity, while
smaller k-mers will provide more sensitivity. Larger genomes will also require
larger k-mers to avoid k-mers that are shared by chance. K-mer size is
-k, and sketch files must have the same k-mer size to be
mash dist. When
mash sketch is run, it
automatically assesses the specified k-mer size against the sizes of input
genomes by estimating the probability of a random match as:
...where \(g\) is the genome size and \(\Sigma\) is the alphabet (ACGT
by default). If this probability exceeds a threshold (specified by
-w; 0.01 by default) for any input genomes, a warning will be given
with the minimum k-mer size needed to get within the threshold.
For large collections of sketches, memory and storage may also be a
consideration when choosing a k-mer size. Mash will use 32-bit hashes, rather
than 64-bit, if they can encompass the full k-mer space for the alphabet in use.
This will (roughly) halve the size of the size of the sketch file on disk and
the memory it uses when loaded for
mash dist. The criterion for using a
32-bit hash is:
...which becomes \(k \leq 16\) for nucleotides (the default) and \(k \leq 7\) for amino acids.
Sketch size corresponds to the number of (non-redundant) min-hashes that are kept. Larger sketches will better represent the sequence, but at the cost of larger sketch files and longer comparison times. The error bound of a distance estimation for a given sketch size \(s\) is formulated as:
Sketch size is specified with
-s. Sketches of different sizes can be
mash dist, although the comparison will be restricted to
the smaller of the two sizes.
Strand and alphabet¶
mash uses a nucleotide alphabet (ACGT), is case-insensitive,
and will ignore strandedness by using canonical k-mers, as done in
Jellyfish. This works by using the reverse complement of a k-mer if it comes
before the original k-mer alphabetically. Strandedness can be preserved with
-n (non-canonical) and case can be preserved with
-Z. Note that
the default nucleotide alphabet does not include lowercase and thus will filter
out k-mers with lowercase nucleotides if
-Z is specified. The amino acid
alphabet can be specified with
-a, which also changes the default k-mer
size to reflect the denser information. A completely custom alphabet can also be
-z. Note that alphabet size affects p-value calculation
and hash size (see Assessing significance with p-values and k-mer size).
Sketching read sets¶
When sketching reads instead of complete genomes or assemblies,
should be specified, which will estimate genome size from k-mer content
rather than total sequence length, allowing more accurate p-vlaues. Genome
size can also be specified directly with
-g. Additionally, Since
MinHash is a k-mer based method, removing unique or low-copy k-mers usually
improves results for read sets, since these k-mers are likely to represent
sequencing error. The minimum copies of each k-mer required can be specified
-m 2 to filter unique). However, this could
lead to high memory usage if genome size is high and coverage is low, such as
in metagenomic read sets. In these cases a Bloom filter can be used (
to filter out most unique k-mers with constant memory. If coverage is high (e.g.
>100x), it can be helpful to limit it to save time and to avoid repeat errors
appearing as legitimate k-mers. This can be done with
-c, which stops
sketching reads once the estimated average coverage (based on k-mer
multiplicity) reaches the target.
Working with sketch files¶
The sketch or sketches stored in a sketch file, and their parameters, can be
mash info. If sketch files have matching k-mer sizes,
their sketches can be combined into a single file with
mash paste. This
allows simple pairwise comparisons with
mash dist, and allows sketching
of multiple files to be parallelized.