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@@ -203,6 +203,349 @@ implication is that columns should be allowed partial coverage (>=2 resolved
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genomes, not unanimous) rather than requiring every genome to be net
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single-copy at that locus.
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## Context, detectability, and a 3-way ordinal distance per pair
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Empirical follow-up to the pseudo-alignment idea above: `obikmer distance
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--snp` was run on a real 20-genome benchmark index and the resulting FASTA
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fed to `raxml-ng`. Two problems surfaced, both traced back to conflating
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distinct notions under one symbol.
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**"Context", precisely.** Sharing a central base between two genomes is not
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just sharing a nucleotide — it is sharing a **context**: the `2m` flanking
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bases, identical, which is a homology claim about that flanked window
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(guaranteed non-coincidental by k-specificity, Bias 4 above), *not* a claim
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about orthology or paralogy of the copy each genome carries. `A` opposite `C`
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= same context, divergent centre. `A` opposite nothing = **this context is
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not observed in one of the two genomes** — informative, not neutral.
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**Why the IUPAC/DNA encoding used for the first `--snp` test was wrong.**
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Feeding IUPAC-coded ambiguity into a standard DNA model (`raxml-ng --model
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GTR+G`) is a semantic mismatch: Felsenstein-pruning ML treats an ambiguous
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tip as "exactly one true state, unknown which" (a uniform partial-likelihood
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vector over compatible bases), not "these states are simultaneously
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present". The two encodings look identical (same IUPAC letters) but the
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software reads them backwards from what was intended — this invalidates the
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literal branch lengths from that first experiment (topology-level groupings
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by genus were still informative, see the worked example further down).
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**Why `-` (absence) must not be scored as similarity, but also must not be
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scored as a shared character between two absences.** Two genomes both
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lacking a context are not observed to resemble each other at that locus —
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neither is observed to differ from the other either. It is a symmetric
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non-observation, uninformative for that pair, and should contribute nothing
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(not a small positive nor a small negative signal) to their distance. A
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genome carrying a state (`A`) against one carrying none is a different case
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entirely: informative, and should not be scored as neutral "missing data"
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the way a generic DNA/ML pipeline would.
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**Detectability vs existence — a deliberate simplification, accepted.**
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"Context not observed" conflates two different biological events: (1) true
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loss of the locus, (2) the locus still exists but a mutation/indel *outside*
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the centre, anywhere in the `2m` flanks, broke k-mer recognition. The design
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adopts a rigorist stance on purpose: any flank-breaking mutation counts as
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"this context no longer exists", full stop — because both causes (1) and (2)
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independently require *at least* one more mutational event than a lone
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central substitution would. This licenses treating "context absent in one of
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the two genomes" as a **lower bound** on distance strictly greater than a
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plain central SNP, without needing to know which of the two causes applies.
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Coarser than a true event count, and accepted as such (fine substitution-type
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modelling, e.g. transition/transversion weighting, is a secondary
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refinement, not required for this to be useful).
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**Resulting ordinal distance between two genomes at one family/context:**
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| Comparison | Distance | Meaning |
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|---|---|---|
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| same centre (`A`/`A`) | `0` | identical |
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| different centre, both single-copy (`A`/`C`) | `1` | plain central SNP |
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| one genome has a state, the other has none | `>1` (lower bound) | context undetectable in one genome — at least one extra mutational event, of unknown type |
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| neither genome has any state (`∅`/`∅`) | excluded | symmetric non-observation, not comparable, contributes nothing |
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This is a direct extension of `KmerIndex::raw_snp_distance` (`obikindex/src/siblings.rs`),
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which today only implements the `0`/`1` rows and silently drops everything
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else (including the informative `>1` row) rather than scoring it.
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**Open, not yet resolved:**
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- Calibrating `>1` to a real number for tools expecting continuous distances
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(NJ/UPGMA, ML branch lengths), rather than an arbitrary placeholder.
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Natural route: estimate `p_hat` from the resolved (`0`/`1`) sites first,
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then use the already-derived ascertainment formula (`P(usable window
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showing a central SNP) = p * (1-p)^(2m)`, Bias 1 above) to derive a
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model-consistent value for the `>1` bucket instead of guessing a constant.
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- Where multi-copy/ambiguous states (the IUPAC case: a genome carrying more
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than one form) fit into this ordinal scheme — plausibly also `>1` by the
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same "at least one extra event" argument (a second form appearing is a
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gain, itself an event), but not yet worked out.
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**Practical alternative validated for the pseudo-alignment output itself**
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(orthogonal to the ordinal-distance question above, useful regardless of how
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`>1` ends up calibrated): re-encode each family as 4 independent binary
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presence/absence characters (`A`,`C`,`G`,`T` columns) instead of one IUPAC
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column, feed to a `BIN`-type model instead of `DNA`. `∅` becomes an explicit
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`0000` state (identity with another `0000`, not missing data) rather than a
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gap — removes the semantic mismatch above by construction. Known cost,
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accepted for now: a plain central substitution (`A` -> `C`) becomes 2 binary
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flips (`1000` -> `0100`), overweighting substitutions relative to true
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gain/loss events, and the 4 sub-characters of one family are not
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statistically independent the way a generic `BIN` model assumes. A proper
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fix (single 16-state alphabet, i.e. the powerset of `{A,C,G,T}`, with a
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substitution-rate structure that respects the subset lattice rather than a
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fully general 16x16 GTR-analogue) is very likely not expressible in
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`raxml-ng`'s `MULTI` datatype as-is (Mk or fully-general rates only) and a
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fully general 16-state rate matrix is almost certainly unidentifiable here
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(states of cardinality >=3 are ~2% of sites in the benchmark run). Treated as
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a longer-term research question, not a near-term implementation target.
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## Sankoff parsimony as the resolution of the 16-state model problem
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The "longer-term research question" just above (a 16-state alphabet — the
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powerset of `{A,C,G,T}` — with a substitution structure that respects the
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subset lattice) turns out to have a near-term answer, once the *unification*
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question below is worked through.
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**Distance methods (NJ/UPGMA/ME) vs. character methods (parsimony/ML): not a
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deep philosophical divide, but a real practical distinction for this
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project.** Historically "phenetic" (characters -> distances -> tree) and
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"cladistic" (characters -> tree directly) approaches were presented as
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opposed schools; the modern view is a mathematical continuity, not a
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dichotomy — Minimum Evolution (ME: find the tree minimizing total branch
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length from a distance matrix) and Maximum Parsimony (MP: find the tree
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minimizing total character-state changes) are both instances of "minimise a
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global explanatory cost", and coincide under simple encodings (see Farris
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1983, "The Logical Basis of Phylogenetic Analysis"; the MP/ME connection is
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developed in the Minimum Evolution / Balanced Minimum Evolution literature,
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e.g. Nei and colleagues — citations not independently re-verified here, flag
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before quoting further). NJ's own agglomeration step already uses the whole
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distance matrix jointly (the Q-matrix), not just the pair being merged — an
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earlier claim in this discussion that distance methods are "blind" to
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cross-taxon structure at every stage was too strong.
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What *does* remain a real, structural distinction for this project: in a
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character method, a given character's cost is **re-evaluated per candidate
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topology** during tree search (the same family can cost 1 change under one
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topology, 2 under another). In a pairwise-distance pipeline
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(`raw_snp_distance` as it exists today), each family's contribution to
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`d(i,j)` is computed **once**, independent of any candidate topology, before
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NJ/UPGMA ever runs — so a question like "does this shared `∅` look like a
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synapomorphy under topology T" can never be posed in that pipeline, for any
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T. That question is only answerable by a method that tests candidate
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topologies and re-scores characters under each — i.e. a character method.
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**Sankoff parsimony directly resolves the `∅`/gain-loss/substitution
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question, without the identifiability problem of a fitted 16-state model.**
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Sankoff's algorithm generalises Fitch parsimony to an arbitrary
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user-supplied cost matrix between states (`obikseq`/`obikindex` would treat
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each family as a `2^{4}`-state character, state = subset of `{A,C,G,T}`
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observed in that genome, `∅` included as a real state, not a gap). The
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previous 16-state idea failed specifically because *fitting* a full 16x16
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rate matrix by ML is unidentifiable at this data volume; Sankoff sidesteps
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that because the cost matrix is **fixed a priori from domain knowledge**, not
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estimated — e.g. `c({A},{C}) = 1` (a substitution), `c({A},{A,C}) = 1` (a
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gain), `c({A,C},{A}) = 1` (a loss), `c({A,C},{G,T}) = 2` (two changes) — no
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estimation, no overparameterisation. This reframes gain/loss and central
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substitution as two cost categories with independently chosen weights,
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exactly the "two families of parameters" (`mu_substitution`, `mu_gain/loss`)
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floated earlier in this discussion, now with an actual algorithmic home.
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**Caveat, not blocking for this project's scope.** Sankoff is still
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parsimony: in principle exposed to Felsenstein's statistical-inconsistency
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result under long-branch attraction (already invoked earlier against
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`D_F = min(a,b)`) — parsimony and ML only provably coincide in the
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short-branch regime. This is not a practical concern here because it is
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exactly this estimator's declared target (closely related genomes, short
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branches) — the regime where parsimony's known failure mode does not apply —
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but worth stating explicitly as a scope guard rather than leaving it
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implicit.
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**Cheapest next experiment: don't write a Sankoff tree-search engine, use
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one that exists.** The hard part of a from-scratch implementation is not the
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Sankoff DP itself (a straightforward dynamic program over a *fixed* tree) but
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the topology search (SPR/NNI with incremental re-scoring) that comes for
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free with `raxml-ng` on the ML side. **TNT** (Tree analysis using New
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Technology, free, standard in morphological cladistics) already implements
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Sankoff parsimony with a custom cost matrix plus topology search — the
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family-state matrix (already close to what `--snp` produces, minus the
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IUPAC/DNA-model mismatch) could be fed there directly, no new code required,
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before considering a bespoke engine.
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**The concrete comparison this unlocks:** run both pipelines on the same
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family data —
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`k-mer families -> D_ij -> NJ/ME/UPGMA` (phenetic, what exists today) vs.
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`k-mer families -> characters -> argmin_T Sankoff-cost(T)` (cladistic, via
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TNT) — and compare the resulting topologies. Agreement would validate that
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the pairwise-distance projection preserves the phylogenetic signal;
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disagreement would pinpoint exactly what the projection to a single number
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per pair loses. Not yet run.
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### A concrete Sankoff cost matrix for the 16-state alphabet
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**Set-edit-distance formula.** For two states `X, Y ⊆ {A,C,G,T}`, split into
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`seulement_X = X \ Y` (size `a`) and `seulement_Y = Y \ X` (size `b`).
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Elements present in both cost nothing. Pair up to `min(a,b)` of the
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remaining elements as **substitutions** (cheaper than treating them as an
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unrelated loss + gain whenever `c_sub < 2*c_gl`, which any sane parameter
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choice satisfies); whatever is left over after pairing is a pure
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**gain/loss**:
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```
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cost(X,Y) = min(a,b)*c_sub + |a-b|*c_gl
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```
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Worked examples (`c_sub = c_gl = 1`): `{A}->{C}` = 1 (one substitution);
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`{A}->{A,C}` = 1 (one gain, no substitution pair available since nothing is
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only-in-Y that matches an only-in-X element after the shared `A` is
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excluded); `{A,C}->{G,T}` = 2 (two substitution pairs, `A/C` vs `G/T`, both
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same-size sets share nothing); `{A,C,G}->{A,C,T}` = 1 (`G`/`T` is the only
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mismatched pair, `A,C` shared).
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**`∅` is a flat-cost special case, not a instance of the general formula.**
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Applying the formula naively to e.g. `{A,C,G} -> ∅` would charge `3*c_gl`
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(three independent losses). Reject that: total context disappearance
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(flank-breaking, or true structural loss) is plausibly **one** event, not
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`|X|` of them, so:
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```
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cost(X, ∅) = cost(∅, X) = c_ctx (constant, independent of |X|)
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cost(∅, ∅) = 0
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```
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`c_ctx` should not be guessed — it is exactly the value already derived for
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the `>1` bucket in "Context, detectability, and a 3-way ordinal distance per
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pair" above (`(2m*p_hat)/(1-(1-p_hat)^(2m)) + p_hat`), reused rather than
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invented.
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**Better construction method: shortest path in a small state graph, not the
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closed-form formula directly.** Build a graph on the 16 states with two edge
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types — substitution edges between same-cardinality sets differing by one
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element (weight `c_sub`, or `c_ts`/`c_tv` if split further below), and
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gain/loss edges between sets whose cardinality differs by one (weight
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`c_gl`) — then define `cost(X,Y)` as shortest-path distance in that graph,
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precomputed once (16 nodes, trivial) into a dense 16x16 matrix before
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feeding it to Sankoff/TNT. Verified equivalent to the closed-form formula
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above in the uniform-cost case (checked by hand on `{A}->{C,G,T}`: both give
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`c_sub + 2*c_gl`). The graph construction is not just a reformulation for
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its own sake: it is the version that generalises correctly once substitution
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costs stop being uniform (next point) — the closed-form's `min(a,b)`
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counting silently assumes *any* pairing costs the same, which breaks the
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moment `c_sub` depends on which two bases are involved.
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**Transition/transversion refinement.** Split `c_sub` into `c_ts` (A<->G or
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C<->T) and `c_tv` (the other four pairs) — already well-defined in canonical
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space (see "Canonical invariance" above: a transition maps to a transition,
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a transversion to a transversion, regardless of orientation). This turns
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"pick `min(a,b)` substitution pairs" into a genuine (tiny, <=4 elements per
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side, trivially enumerable) minimum-cost bipartite matching problem instead
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of a plain count — the state-graph shortest-path construction handles this
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automatically, no separate logic needed. Calibration is not a guess either:
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the "Sufficient statistic: 4x4 base-pair tally" section below already plans
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to collect the joint `(centre_i, centre_j)` distribution over resolved (`0`
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or `1`) sites — that tally directly gives the empirical Ts/Tv ratio, from
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which `c_ts`/`c_tv` follow (e.g. `cost ∝ -log(observed rate)`, the standard
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generalised-parsimony step-weighting heuristic), reusing a statistic already
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planned rather than adding a new one.
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**`gamma`/`mu` (i.e. `c_gl`/`c_sub`) sensitivity sweep before calibration.**
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No strong prior on whether gain/loss events should cost more or less than a
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point substitution — duplication/deletion rates are not a priori equal to
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point-mutation rates, but the direction isn't obvious, and setting it too
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high risks the parsimony search *eliminating* exactly the
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heterozygosity/paralogy signal the design is meant to tolerate (see
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"Heterozygosity, ploidy..." below). Cheap first step: run the topology at a
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handful of ratios (`0.5, 1, 2, 5`) and check whether it's stable — a robust
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topology across that range is far more trustworthy than one built on a
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single, unvalidated guess. Empirical calibration of `c_gl` from the
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family-size distribution already available (`sibling_annex_stats`) is a
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natural follow-up once the sensitivity sweep shows the topology is worth
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refining further.
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**Caveat carried over from the `D_F = min(a,b)` rejection earlier:** this
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cost matrix is only valid as **Sankoff step-cost input**, re-evaluated for
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every branch of every candidate topology during tree search. Reusing
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`cost(leaf_A, leaf_B)` directly as a standalone pairwise distance (bypassing
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the tree) would reintroduce the exact circularity already rejected — the
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`min(a,b)` pairing here is a locally-defined edit distance between two
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states, not a claim about the true evolutionary history between two
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specific genomes.
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**Feasibility confirmed:** TNT's `costs` command accepts custom step
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matrices for multistate characters, so this whole construction (16x16
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matrix derived from the state graph, `c_ts`/`c_tv`/`c_gl`/`c_ctx` as
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tunable parameters) is directly usable there — no new tooling required
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before testing it.
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### Experiment: TNT run on real data (2026-08-11)
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**Status:** validated at genus/family/order scale within Bacteria; not
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informative across domains with this character type. Exploratory only —
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run entirely outside the repo (`/tmp/tnt_run`, TNT installed locally under
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`TNT/`), no new Rust code. Kept here as the record of what was learned.
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**Pipeline.** `obikmer distance --snp` emits one IUPAC-coded pseudo-alignment
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row per genome (`snp_pseudo_alignment`, one column per family with
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`family_size() >= 2`). A small external Python script decodes IUPAC back to
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the 16-state bitmask, applies the set-edit-distance formula above, and
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emits a complete TNT script (`xread` matrix + `smatrix` step-matrix + `hold`/
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`mult` search). No new Rust code was needed for this pass.
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**Calibration ("quick option").** Rather than modifying
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`write_raw_snp_distance_csv` to emit raw counts, `c_ctx` was approximated as
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the unweighted mean of the pairwise `snp/(snp+shared)` ratios already
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present in `rawsnp.csv`, restricted to the relevant taxon subset. Used
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values: `mu = gamma = 10`, `c_ctx = 18` (ratio `c_ctx/mu = 1.8`, consistent
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with the observed pairwise ratios for genomes within Enterobacteriaceae/
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Eubacteria, which cluster around 1.5-2 and barely move as the taxon set
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widens — the context signal is stable, not sensitive to which subset is
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chosen). The more principled route (raw counts, weighted `p_hat`, Ts/Tv
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split) remains a follow-up, not yet done.
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**Run 1 — Enterobacteriaceae (11 taxa: 4 *E. coli*, 4 *Salmonella enterica*,
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3 *Klebsiella pneumoniae*).** All three genera recovered as monophyletic.
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Initial read of the exported (unrooted, TNT/Nexus `[&U]`) tree as showing a
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genus-arrangement disagreement with known systematics (*Escherichieae*:
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*Escherichia*+*Salmonella* sister vs. more distant *Klebsielleae*) was
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**wrong** — diagnosed via `force = (taxa);` monophyly-constraint test
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(identical score constrained vs. free ⟹ no real disagreement). Root cause of
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the misreading: with exactly 3 clades and no outgroup, an unrooted tree has
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only **one possible topology** (a single trifurcation) — there is no
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internal arrangement to get right or wrong. This run cannot test
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inter-genus relationships at all; it can only test intra-genus monophyly
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(which held).
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**Run 2 — Eubacteria (18 taxa: run 1 + *Acidobacterium capsulatum*,
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*Opitutus terrae*, *Bacillus subtilis*, *Shouchella clausii*, *Wolbachia*
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endosymbiont, *Proteus mirabilis*, *Yersinia ruckeri*).** The
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Enterobacteriaceae substructure from run 1 is reproduced identically, now
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correctly rooted by real outgroups, resolving the tribal arrangement left
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undetermined in run 1: *Escherichia*+*Salmonella* sister, *Klebsiella* more
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distant — matching known systematics. Outgroup placement: `(Bacillus,
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Shouchella)` sister pair (Firmicutes/*Bacillales*) splits from all
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Proteobacteria — a correct phylum-level split; `Wolbachia`
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(Alphaproteobacteria) splits from the Gammaproteobacteria block
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(`Proteus`, `Yersinia`, Enterobacteriaceae) — a correct class-level split.
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Lower confidence: the fine nested order `(Proteus, (Yersinia,
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|
Enterobacteriaceae))` and the relative position of `Acidobacterium` vs.
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`Opitutus` — plausible, not independently verified against current
|
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Enterobacterales family-level literature.
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**Run 3 — full domain set (20 taxa: run 2 + *Candidozyma auris* [yeast] and
|
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*Saccharolobus islandicus* [archaeon]).** The bacterial clade from run 2 is
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reproduced **unchanged and intact** — a real robustness signal, the method
|
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|
does not fragment the ingroup when unrelated deep taxa are added. But the
|
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result carries **no information on Bacteria/Archaea/Eukarya relationships**:
|
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|
with exactly one eukaryote, one archaeon and one bacterial clade, the
|
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unrooted tree is again forced into the single 3-clade trifurcation from run
|
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|
1's caveat — there is no second representative of either outgroup domain to
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resolve internal arrangement, so nothing about their relative position can
|
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|
be read from the topology (a "ladder" ordering in the exported tree is
|
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|
|
serialization, not signal). Independently, `rawsnp.csv` shows *why* this
|
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|
|
character type cannot reach further: pairwise ratios involving
|
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|
|
*Candidozyma*/*Saccharolobus* are almost all `NA` (no central-position
|
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|
|
family shared at all) or saturated at `1.0` (every shared family differs) —
|
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|
|
central-position families require literal 31 bp context conservation, which
|
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|
|
simply does not survive domain-level divergence. Cross-domain placement
|
|
|
|
|
would need conserved-marker characters (rRNA, ribosomal proteins), not this
|
|
|
|
|
estimator.
|
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|
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|
|
|
|
## Heterozygosity, ploidy, and consensus-assembly inputs
|
|
|
|
|
|
|
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|
|
A within-genome multiplicity signal (more than one of the 4 central forms
|
|
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|
|