Whole-index distance metrics

These metrics operate on the kmer sets or counts stored in an index directly — no per-locus SNP calling, no sibling annex required. A/B denote the two genomes being compared; c_i^A / c_i^B are their raw counts at kmer i, p_i^A / p_i^B the corresponding relative frequencies (p_i = c_i / \sum_j c_j).

Metric	Definition
jaccard	`D = 1 - \dfrac{\lvert A \cap B \rvert}{\lvert A \cup B \rvert}` over the sets of kmers present in each genome
mash	derived from the Jaccard distance via `D = -\dfrac{1}{k} \ln\!\left(\dfrac{2J}{1+J}\right)` where `J = 1 - D_{\text{jaccard}}` and `k` is the index's kmer size; clamped to 1.0 when `J \le 0`
hamming	number of kmer positions where presence differs between the two genomes (presence index only, not normalized): `D = \sum_i \mathbb{1}[a_i \ne b_i]`
bray-curtis	`D = 1 - \dfrac{2 \sum_i \min(c_i^A, c_i^B)}{\sum_i c_i^A + \sum_i c_i^B}` on raw per-kmer counts
relfreq-bray-curtis	the same formula computed on relative frequencies `p_i` instead of raw counts
euclidean	`D = \sqrt{\sum_i (c_i^A - c_i^B)^2}` on raw counts
relfreq-euclidean	the same formula on relative frequencies
hellinger	`D = \dfrac{1}{\sqrt{2}} \sqrt{\sum_i \left(\sqrt{p_i^A} - \sqrt{p_i^B}\right)^2}` on relative frequencies, bounded in `[0, 1]`
hellinger-euclidean	the unnormalized variant, `D = \sqrt{2} \times D_{\text{hellinger}}`

hamming requires a presence/absence index; the others work on either index type.

See phylo for how to select a metric and the output formats.

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Theory

Kmer indexing

Phylogeny

Kmer-based

Whole k-mer set distances

Whole-index distance metrics

Wiki sidebar

Theory

Kmer indexing

Phylogeny

Kmer-based

SNP-based

Usage

Formats