Sketches

For sequences to be compared with mash, they must first be sketched, which creates vastly reduced representations of them. This will happen automatically if 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.

k-mer size

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 specified with -k, and sketch files must have the same k-mer size to be compared with 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:

\[p = \frac 1 {\frac {\left(\overline\Sigma\right)^k} g + 1}\]

...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:

\[\left({\overline\Sigma}\right)^k \leq 2^{32}\]

...which becomes \(k \leq 16\) for nucleotides (the default) and \(k \leq 7\) for amino acids.

sketch size

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:

\[\sqrt{\frac{1}{s}}\]

Sketch size is specified with -s. Sketches of different sizes can be compared with mash dist, although the comparison will be restricted to the smaller of the two sizes.

Strand and alphabet

By default, 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 specified with -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, -r 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 with -m (e.g. -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 (-b) 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 inspected with 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.