# distance

Compute pairwise distance matrices between the genomes stored in an index, optionally build trees (NJ/UPGMA), and optionally derive a central-position SNP model with exports for external phylogenetic tools (TNT, PhyG, IQ-TREE).

```bash
obikmer distance INDEX [OPTIONS]
```

## Arguments

| Argument | Description |
|---|---|
| `INDEX` | Index directory |

## Distance matrix

| Option | Default | Description |
|---|---|---|
| `--metric` | `jaccard` | One of `jaccard`, `mash`, `hamming`, `bray-curtis`, `relfreq-bray-curtis`, `euclidean`, `relfreq-euclidean`, `hellinger`, `hellinger-euclidean` |
| `--presence-threshold` | `1` | Minimum count for a kmer to be considered present, for Jaccard/Mash on a count index |
| `--shared-kmers` | off | Also write the shared-kmer count matrix |
| `--nj` | off | Compute and write a Neighbor-Joining tree (Newick) |
| `--upgma` | off | Compute and write a UPGMA tree (Newick) |
| `-o, --output` | none (stdout) | Output file prefix; without it, the distance matrix is printed to stdout as CSV |

`hamming` requires a presence/absence index. All other metrics work on either index type; on a presence index, `jaccard`/`mash`/`hamming` are the only ones available.

### Metric definitions

- **jaccard**: $D = 1 - \dfrac{|A \cap B|}{|A \cup B|}$ 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 per-genome relative frequencies $p_i = c_i / \sum_j c_j$ 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, $D = \sqrt{2} \times D_{\text{hellinger}}$.

## Central-position SNP model

This is a separate operation from the distance-matrix computation above: if any option below is used, no `--metric` matrix is computed in the same invocation.

A **family** is the set of up to 4 kmers that share identical flanking sequence and differ only at the exact central base. Because $k$ is odd, the central position is well defined and maps to itself under reverse complementation. All computations below first require building the **sibling annex**, an index-wide record of which of the 4 possible central bases are observed at each family, across every genome.

| Option | Default | Description |
|---|---|---|
| `--sibling-annex` | off | Build the sibling presence-mask annex (prerequisite for every option below) |
| `--exclude-genome LABEL` | none | Exclude a genome (repeatable) from every SNP/Sankoff/export computation below |
| `--sibling-stats` | off | Write the family-size (sibling count) distribution, per genome and globally |
| `--raw-snp-distance` | off | Write the single-copy central-SNP p-distance matrix |
| `--raw-snp-counts` | off | Write per-pair diagnostic counts (n_snp, n_shared, n_eligible) instead of a matrix |
| `--snp` | off | Write a SNP-only pseudo-alignment in FASTA, IUPAC-coded |

### Locus eligibility

A family is eligible for a genome pair $(i, j)$ only if genome $i$ carries exactly one of the family's observed forms (single-copy, unambiguous) and genome $j$ also carries exactly one. A genome carrying more than one form at a locus makes that locus ineligible for any pair involving it.

`--raw-snp-distance` tallies, over every eligible locus of every genome pair, $n_{\text{snp}}$ (the two genomes' single forms differ) versus $n_{\text{shared}}$ (they agree — this includes invariant families). The output ratio is $\hat{p} = \dfrac{n_{\text{snp}}}{n_{\text{snp}} + n_{\text{shared}}}$.

`--snp` restricts itself to *variable* families (family size $\ge 2$) and writes one FASTA record per genome, one column per family, IUPAC-coded from each genome's presence mask at that family (a single form → the plain base; several forms → the matching IUPAC ambiguity code; no form → `-`).

`--exclude-genome` removes a genome from these computations, re-checking column variability among the remaining genomes so that a column made monomorphic by the exclusion is dropped rather than kept artificially. It does not affect the `--metric` distance-matrix path.

## Sankoff calibration and phylogenetic exports

| Option | Default | Description |
|---|---|---|
| `--sankoff` | off | Calibrate a 16-state parsimony cost matrix and matching pseudo-alignment |
| `--sankoff-ratio-ceiling` | `0.5` | Exclude genome pairs whose raw SNP ratio exceeds this value from the calibration |
| `--tnt` | off | Also write a TNT script (implies `--sankoff`) |
| `--phyg` | off | Also write PhyG input files (implies `--sankoff`) |
| `--iqtree` | off | Also write an IQ-TREE custom model and alignment (implies `--sankoff`) |
| `--sankoff-cost-scale` | `100` | Integer scaling factor applied to costs before rounding (required by TNT/PhyG's integer-only cost commands) |

### The 16-state model

Each family is treated as a character with 16 possible states: one per subset of the 4 possible central bases actually observed (including the empty subset). Calibration combines two tallies, both restricted to genome pairs at or below `--sankoff-ratio-ceiling`:

- a $5 \times 5$ transition matrix over family cardinality (0–4 observed forms) between paired genomes, and
- a $4 \times 4$ base-substitution transition matrix from unambiguous single-copy loci,

which are combined into a row-normalized $16 \times 16$ transition probability matrix $P$, converted to a symmetric cost matrix via $\text{cost}(a,b) = -\ln P(a,b)$.

`--sankoff` alone writes the cost matrix, the calibration parameters, and a pseudo-alignment recoded so the empty state uses the symbol `0` (never a gap character, to avoid ambiguity with external tools' own gap semantics). It does not run any external tool.

### Exports

All three exports reuse the `--sankoff` calibrated matrix and pseudo-alignment, recoded for the target tool:

- **`--tnt`**: a self-contained TNT script (alignment recoded to TNT's fixed 16-symbol alphabet, integer-scaled cost matrix re-closed to a metric, a default search block).
- **`--phyg`**: a custom cost-matrix file plus a PhyG script reusing the `--sankoff` alignment directly.
- **`--iqtree`**: a custom substitution-model file (exchangeability matrix recovered as $R(a,b) = e^{-\text{cost}(a,b)}$, plus empirical state frequencies) and a matching alignment, for maximum-likelihood inference with real branch lengths (unlike the parsimony step-counts from TNT/PhyG). Only states actually occurring in the alignment are kept and compactly renumbered.

## Output files

With `-o/--output PREFIX`, the relevant subset of the following files is written: `<prefix>_dist.csv`, `<prefix>_shared.csv`, `<prefix>_nj.nwk`, `<prefix>_upgma.nwk`, `<prefix>_siblings.csv`, `<prefix>_rawsnp.csv`, `<prefix>_rawsnp_counts.csv`, `<prefix>_snp.fasta`, `<prefix>_sankoff_matrix.csv`, `<prefix>_sankoff_params.yaml`, `<prefix>_sankoff.fasta`, `<prefix>_sankoff.tnt`, `<prefix>_sankoff.tcm`, `<prefix>_sankoff.pg`, `<prefix>_iqtree.model`, `<prefix>_iqtree.fasta`. Without `-o`, only the plain `--metric` distance matrix is produced, on stdout.