Matrix data (which genomes carry each kmer, or with what count) is often mostly empty — most kmers are present in only a handful of genomes out of the whole collection. The default (dense) packed format stores one entry per genome for every kmer regardless of how many genomes actually carry it; `--sparse` instead stores each kmer's genome list directly. For presence/absence matrices, identical genome lists shared by many kmers are also deduplicated (common in real data, since kmers from the same conserved region tend to be carried by the same genomes); for count matrices, the genome list is deduplicated the same way but each kmer's actual counts are kept per-kmer, since two kmers sharing the same genome list rarely carry the same counts.
On real genome collections this has measured at roughly 7x smaller on disk than the dense format for presence/absence, and single-kmer lookups (the shape `phylo`'s sibling-annex/entropy/Sankoff computations use) are typically faster too, since the smaller files mean less data to read from disk. The trade-off: reading a whole genome column at once (used by `--distance` matrix computations) is much slower on the sparse format than on the dense one, since there is no native column layout to read sequentially — prefer the dense format (the default, no `--sparse`) for indexes you mainly query with `phylo`'s `--distance` matrices.
`--sparse` applies to both presence/absence and count matrices — a count index (`--distance` matrix computations included) is packed sparse the same as a presence index.
