feat(phylo): add --iqtree-min-freq to filter rare nucleotide states

Introduces --iqtree-min-freq (default 0.001) to treat low-frequency nucleotide states as missing data during IQ-TREE alignment generation when --free-loss is active. This triggers a recoding pass that folds rare states into the missing symbol, followed by non-informative site removal and alphabet recomputation to maintain output consistency. The change also adds Sankoff model configuration files and updates related tests and documentation.

DevDoc/theory/evolutionary_distances/index.html

@@ -898,6 +898,17 @@
     </span>
   </a>
   
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#-iqtree-min-freq-rare-states-still-perturb-iq-tree-after-the-underflow-fix-implemented-2026-08-15" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        --iqtree-min-freq: rare states still perturb IQ-TREE after the underflow fix (implemented 2026-08-15)
+      
+    </span>
+  </a>
+  
 </li>
       
         <li class="md-nav__item">
@@ -2117,6 +2128,17 @@
     </span>
   </a>
   
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#-iqtree-min-freq-rare-states-still-perturb-iq-tree-after-the-underflow-fix-implemented-2026-08-15" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        --iqtree-min-freq: rare states still perturb IQ-TREE after the underflow fix (implemented 2026-08-15)
+      
+    </span>
+  </a>
+  
 </li>
       
         <li class="md-nav__item">
@@ -4140,6 +4162,49 @@ Covered by <code>cardcomp::tests::underflow_prone_transition_gets_finite_cost_no
 where the old <code>exp()</code>-first code would have underflowed to <code>0.0</code>, cost
 asserted finite). Every pre-existing <code>cardcomp</code> test still passes
 unchanged (numerically identical results when no underflow occurs).</p>
+<h2 id="-iqtree-min-freq-rare-states-still-perturb-iq-tree-after-the-underflow-fix-implemented-2026-08-15"><code>--iqtree-min-freq</code>: rare states still perturb IQ-TREE after the underflow fix (implemented 2026-08-15)</h2>
+<p>After the <code>pairwise_cost_matrix</code> fix above, the user re-checked
+<code>_iqtree_states.csv</code> on the real <code>phyloskims_sal_vac</code> run: no more exact
+zeros, but <code>N</code> (all 4 bases), <code>V</code>/<code>H</code>/<code>D</code> (3 bases each) sit at
+<code>8×10⁻⁵</code>–<code>4×10⁻⁴</code>, and <code>B</code> (3 bases) just above <code>10⁻³</code> — all four
+3-simultaneous-base states plus <code>N</code>, exactly the states the underflow fix
+was papering over the symptom of. <code>iqtree3</code> kept emitting "Numerical
+underflow for lh-derivative" on this same run — a model with several
+near-zero-frequency states is still numerically marginal for ML
+optimisation even once no cost/exchangeability entry is <em>exactly</em>
+infinite/zero.</p>
+<p><strong>Decided and implemented</strong>: extend <code>--free-loss</code>'s existing "sampling
+failure, not true signal" treatment of non-detection to rare
+multi-base states too — biologically, a family showing 3–4 simultaneously
+observed central bases across genomes is far more likely to be
+assembly/detection noise than a genuinely ancestral, widely-preserved
+polymorphism, the same reasoning already used for <code>-</code>.</p>
+<p><strong>Mechanism</strong> (<code>obikmer/src/cmd/phylo/iqtree.rs</code>, <code>write_iqtree</code>): a
+<em>second</em> filtering pass, active only under <code>--free-loss</code>. After the first
+<code>compact_alphabet</code> call (post ascertainment-filtering), any state with
+<code>freq &lt; --iqtree-min-freq</code> (default <code>0.001</code>) has every occurrence recoded
+to <code>-</code> (<code>recode_symbols_as_absent</code>, a new small helper) — reusing the
+<em>existing</em> <code>-</code>→<code>?</code> machinery in <code>compact_alphabet</code>/<code>write_iqtree_alignment</code>
+rather than duplicating it, since a state recoded to <code>-</code> flows through
+exactly the same downstream path a genuinely-absent call already does.
+<code>drop_ascertainment_noninformative</code> then re-runs on the recoded alignment
+(a site can become non-informative once its only distinguishing call was
+the now-recoded rare state), and <code>compact_alphabet</code> is recomputed a third
+time on the result — this final alphabet is what <code>_iqtree_states.csv</code>/
+<code>_iqtree.model</code>/<code>_iqtree.fasta</code> all get built from, so the three files
+stay consistent with each other by construction, same as before this
+change.</p>
+<p>Not a fixed-point loop (recoding one rare state can't, by construction,
+lower another <em>already-above-threshold</em> state's frequency enough to also
+cross the threshold, since removing calls only redistributes mass upward
+among the survivors) — a single extra pass is sufficient.</p>
+<p><code>--iqtree-min-freq 0</code> disables the filter (no state can have frequency
+<code>&lt; 0</code>), recovering the pre-this-change behavior exactly.</p>
+<p>Covered by <code>iqtree::tests::iqtree_min_freq_folds_rare_states_into_missing</code>
+(20 common A/C sites + one site introducing a single, otherwise-informative
+<code>M</code> call at ~1/62 frequency, <code>--iqtree-min-freq 0.05</code>; asserts <code>M</code> absent
+from the written <code>_iqtree_states.csv</code> and <code>A</code>/<code>C</code> still present). Full
+workspace <code>cargo test</code> green.</p>
 <h2 id="references">References</h2>
 <p>The Mash mutation-rate model this discussion contrasts with:
 (Fan <em>et al.</em> 2015; Marbl Lab 2026)<sup id="fnref:Mash-distances-doc"><a class="footnote-ref" href="#fn:Mash-distances-doc">1</a></sup> <sup id="fnref:Fan2015-mash-formula"><a class="footnote-ref" href="#fn:Fan2015-mash-formula">2</a></sup>.</p>

DevDocMD/theory/evolutionary_distances.md

@@ -2132,6 +2132,56 @@ where the old `exp()`-first code would have underflowed to `0.0`, cost
 asserted finite). Every pre-existing `cardcomp` test still passes
 unchanged (numerically identical results when no underflow occurs).
 
+## `--iqtree-min-freq`: rare states still perturb IQ-TREE after the underflow fix (implemented 2026-08-15)
+
+After the `pairwise_cost_matrix` fix above, the user re-checked
+`_iqtree_states.csv` on the real `phyloskims_sal_vac` run: no more exact
+zeros, but `N` (all 4 bases), `V`/`H`/`D` (3 bases each) sit at
+`8×10⁻⁵`–`4×10⁻⁴`, and `B` (3 bases) just above `10⁻³` — all four
+3-simultaneous-base states plus `N`, exactly the states the underflow fix
+was papering over the symptom of. `iqtree3` kept emitting "Numerical
+underflow for lh-derivative" on this same run — a model with several
+near-zero-frequency states is still numerically marginal for ML
+optimisation even once no cost/exchangeability entry is *exactly*
+infinite/zero.
+
+**Decided and implemented**: extend `--free-loss`'s existing "sampling
+failure, not true signal" treatment of non-detection to rare
+multi-base states too — biologically, a family showing 3–4 simultaneously
+observed central bases across genomes is far more likely to be
+assembly/detection noise than a genuinely ancestral, widely-preserved
+polymorphism, the same reasoning already used for `-`.
+
+**Mechanism** (`obikmer/src/cmd/phylo/iqtree.rs`, `write_iqtree`): a
+*second* filtering pass, active only under `--free-loss`. After the first
+`compact_alphabet` call (post ascertainment-filtering), any state with
+`freq < --iqtree-min-freq` (default `0.001`) has every occurrence recoded
+to `-` (`recode_symbols_as_absent`, a new small helper) — reusing the
+*existing* `-`→`?` machinery in `compact_alphabet`/`write_iqtree_alignment`
+rather than duplicating it, since a state recoded to `-` flows through
+exactly the same downstream path a genuinely-absent call already does.
+`drop_ascertainment_noninformative` then re-runs on the recoded alignment
+(a site can become non-informative once its only distinguishing call was
+the now-recoded rare state), and `compact_alphabet` is recomputed a third
+time on the result — this final alphabet is what `_iqtree_states.csv`/
+`_iqtree.model`/`_iqtree.fasta` all get built from, so the three files
+stay consistent with each other by construction, same as before this
+change.
+
+Not a fixed-point loop (recoding one rare state can't, by construction,
+lower another *already-above-threshold* state's frequency enough to also
+cross the threshold, since removing calls only redistributes mass upward
+among the survivors) — a single extra pass is sufficient.
+
+`--iqtree-min-freq 0` disables the filter (no state can have frequency
+`< 0`), recovering the pre-this-change behavior exactly.
+
+Covered by `iqtree::tests::iqtree_min_freq_folds_rare_states_into_missing`
+(20 common A/C sites + one site introducing a single, otherwise-informative
+`M` call at ~1/62 frequency, `--iqtree-min-freq 0.05`; asserts `M` absent
+from the written `_iqtree_states.csv` and `A`/`C` still present). Full
+workspace `cargo test` green.
+
 ## References
 
 The Mash mutation-rate model this discussion contrasts with:

UserDocMD/usage/phylo.md

@@ -124,6 +124,7 @@ The first `phylo` run on a given index that uses `--entropy`/`--entropy-sd` pays
 | `--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`) |
+| `--iqtree-min-freq` | `0.001` | With `--iqtree --free-loss`: also treat as missing any state rarer than this in the alignment |
 | `--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
@@ -232,9 +233,13 @@ Matrix layout (`_dist.csv`, `_shared.csv`, and every other "CSV matrix" below):
 
 **`_iqtree.model`** (`--iqtree`) — lower-triangular exchangeability matrix $R(a,b) = e^{-\text{cost}(a,b)}$ (one row of increasing length per state, whitespace-separated, PAML order), followed by one line of empirical state frequencies. Only states actually occurring in the alignment are kept, compactly renumbered `0..k-1`.
 
-**`_iqtree.fasta`** (`--iqtree`) — alignment recoded to that same compact `0..k-1` alphabet (symbols `0-9A-F`). Under `--free-loss`, non-detection becomes `?` and columns left non-informative once missing calls are ignored are dropped first (required for `+ASC`). Run with:
+**`_iqtree.fasta`** (`--iqtree`) — alignment recoded to that same compact `0..k-1` alphabet (symbols `0-9A-F`). Under `--free-loss`, non-detection becomes `?` and columns left non-informative once missing calls are ignored are dropped first (required for `+ASC`); with `--iqtree-min-freq` also set (the default), any state rarer than that threshold is folded into the same `?` treatment, and non-informative columns are re-checked and dropped again after that. Run with:
 ```
 iqtree3 -s <prefix>_iqtree.fasta --seqtype MORPH -m <prefix>_iqtree.model+ASC --prefix <prefix>_iqtree -T AUTO
 ```
 
-**`_iqtree_states.csv`** (`--iqtree`) — one row per state actually kept in `_iqtree.model`/`_iqtree.fasta` (header `iqtree_symbol,canonical_symbol,frequency`): `iqtree_symbol` is the compact `0-9A-F` symbol as written in those two files, `canonical_symbol` is the matching `_sankoff_matrix.csv` state, `frequency` is that state's empirical frequency at full precision (`_iqtree.model`'s own frequency line is rounded to 6 decimals). Under `--free-loss`, absent (`0`/`?`) is never a kept state, so it never appears here. Use this file to identify which real state a given row/column of `_iqtree.model`'s matrix corresponds to — e.g. to check whether a state showing zero exchangeability with everything else is expected (a state combination that never co-occurs with anything else in this data) or worth investigating further.
+**`_iqtree_states.csv`** (`--iqtree`) — one row per state actually kept in `_iqtree.model`/`_iqtree.fasta` (header `iqtree_symbol,canonical_symbol,frequency`): `iqtree_symbol` is the compact `0-9A-F` symbol as written in those two files, `canonical_symbol` is the matching `_sankoff_matrix.csv` state, `frequency` is that state's empirical frequency at full precision (`_iqtree.model`'s own frequency line is rounded to 6 decimals). Under `--free-loss`, absent (`0`/`?`) is never a kept state, so it never appears here — nor does any state `--iqtree-min-freq` folded away for being too rare. Use this file to identify which real state a given row/column of `_iqtree.model`'s matrix corresponds to — e.g. to check whether a state showing zero exchangeability with everything else is expected (a state combination that never co-occurs with anything else in this data) or worth investigating further.
+
+### Rare states and `--iqtree-min-freq`
+
+States that combine 3 or 4 central bases at once (IUPAC `V`/`H`/`K`.../`N`) are inherently rare — and, on real data, rare enough that they can make `iqtree3` itself numerically unstable ("Numerical underflow for lh-derivative" warnings, near-degenerate likelihood optimization). They're also more likely to be assembly/detection noise than genuine, widely-shared multi-way polymorphism, the same "sampling failure, not true signal" reasoning `--free-loss` already applies to non-detection. With `--free-loss` set, `--iqtree-min-freq` (default `0.001`, i.e. one in a thousand) extends that same missing-data treatment to any state below this frequency, not just absence. Check `_iqtree_states.csv` to see exactly which states survived and at what frequency; set `--iqtree-min-freq 0` to disable this and keep every state that occurs at all (the old behavior). Has no effect without `--free-loss` — there is no missing-data symbol to fold rare states into otherwise.

aloss_nofl_sankoff_params.yaml

@@ -0,0 +1,167 @@
+ratio_ceiling: 0.5
+cardinality_transitions:
+- from: 0
+  to: 0
+  count: 122014779
+  probability: 0.870049812090934
+- from: 0
+  to: 1
+  count: 17966272
+  probability: 0.12811195254940888
+- from: 0
+  to: 2
+  count: 233683
+  probability: 0.001666321505518981
+- from: 0
+  to: 3
+  count: 24109
+  probability: 0.00017191385413811494
+- from: 0
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 1
+  to: 0
+  count: 17966272
+  probability: 0.967023782579572
+- from: 1
+  to: 1
+  count: 602798
+  probability: 0.03244523972983381
+- from: 1
+  to: 2
+  count: 9562
+  probability: 0.0005146688978673966
+- from: 1
+  to: 3
+  count: 303
+  probability: 0.00001630879272681669
+- from: 1
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 2
+  to: 0
+  count: 233683
+  probability: 0.9585500516842502
+- from: 2
+  to: 1
+  count: 9562
+  probability: 0.039222603245442765
+- from: 2
+  to: 2
+  count: 438
+  probability: 0.0017966429848885097
+- from: 2
+  to: 3
+  count: 105
+  probability: 0.00043070208541847837
+- from: 2
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 3
+  to: 0
+  count: 24109
+  probability: 0.9827171564831044
+- from: 3
+  to: 1
+  count: 303
+  probability: 0.012350711286838137
+- from: 3
+  to: 2
+  count: 105
+  probability: 0.004279949455834998
+- from: 3
+  to: 3
+  count: 16
+  probability: 0.0006521827742224758
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+  to: 4
+  count: 0
+  probability: 0.0
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+- from: 4
+  to: 1
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+  probability: 0.0
+- from: 4
+  to: 2
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 3
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 4
+  count: 0
+  probability: 0.0
+composition_transitions:
+- from: 'A'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'A'
+  to: 'C'
+  count: 0
+  probability: 0.0
+- from: 'A'
+  to: 'G'
+  count: 0
+  probability: 0.0
+- from: 'A'
+  to: 'T'
+  count: 0
+  probability: 0.0
+- from: 'C'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'C'
+  to: 'C'
+  count: 96389
+  probability: 0.9663832688335907
+- from: 'C'
+  to: 'G'
+  count: 1290
+  probability: 0.012933368089671353
+- from: 'C'
+  to: 'T'
+  count: 2063
+  probability: 0.020683363076737984
+- from: 'G'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'G'
+  to: 'C'
+  count: 1290
+  probability: 0.005696948820201646
+- from: 'G'
+  to: 'G'
+  count: 222720
+  probability: 0.9835848381669073
+- from: 'G'
+  to: 'T'
+  count: 2427
+  probability: 0.010718213012891003
+- from: 'T'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'T'
+  to: 'C'
+  count: 2063
+  probability: 0.007305266661709142
+- from: 'T'
+  to: 'G'
+  count: 2427
+  probability: 0.008594223067362136
+- from: 'T'
+  to: 'T'
+  count: 277909
+  probability: 0.9841005102709287

aloss_sankoff_params.yaml

@@ -0,0 +1,167 @@
+ratio_ceiling: 0.5
+cardinality_transitions:
+- from: 0
+  to: 0
+  count: 13019012
+  probability: 0.8682962128540935
+- from: 0
+  to: 1
+  count: 1945560
+  probability: 0.12975810913150784
+- from: 0
+  to: 2
+  count: 26381
+  probability: 0.0017594670310852958
+- from: 0
+  to: 3
+  count: 2792
+  probability: 0.000186210983313375
+- from: 0
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 1
+  to: 0
+  count: 1945560
+  probability: 0.9666005228573729
+- from: 1
+  to: 1
+  count: 66078
+  probability: 0.03282912341401421
+- from: 1
+  to: 2
+  count: 1123
+  probability: 0.0005579331334776772
+- from: 1
+  to: 3
+  count: 25
+  probability: 0.000012420595135300028
+- from: 1
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 2
+  to: 0
+  count: 26381
+  probability: 0.9567346050627402
+- from: 2
+  to: 1
+  count: 1123
+  probability: 0.04072677159643142
+- from: 2
+  to: 2
+  count: 51
+  probability: 0.0018495684340320592
+- from: 2
+  to: 3
+  count: 19
+  probability: 0.0006890549067962574
+- from: 2
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 3
+  to: 0
+  count: 2792
+  probability: 0.9841381741275996
+- from: 3
+  to: 1
+  count: 25
+  probability: 0.008812125484666901
+- from: 3
+  to: 2
+  count: 19
+  probability: 0.0066972153683468455
+- from: 3
+  to: 3
+  count: 1
+  probability: 0.00035248501938667606
+- from: 3
+  to: 4
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 0
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 1
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 2
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 3
+  count: 0
+  probability: 0.0
+- from: 4
+  to: 4
+  count: 0
+  probability: 0.0
+composition_transitions:
+- from: 'A'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'A'
+  to: 'C'
+  count: 0
+  probability: 0.0
+- from: 'A'
+  to: 'G'
+  count: 0
+  probability: 0.0
+- from: 'A'
+  to: 'T'
+  count: 0
+  probability: 0.0
+- from: 'C'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'C'
+  to: 'C'
+  count: 10771
+  probability: 0.9619540948468339
+- from: 'C'
+  to: 'G'
+  count: 163
+  probability: 0.014557470751094042
+- from: 'C'
+  to: 'T'
+  count: 263
+  probability: 0.023488434402071982
+- from: 'G'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'G'
+  to: 'C'
+  count: 163
+  probability: 0.006662851536952256
+- from: 'G'
+  to: 'G'
+  count: 24073
+  probability: 0.9840173315892741
+- from: 'G'
+  to: 'T'
+  count: 228
+  probability: 0.009319816873773708
+- from: 'T'
+  to: 'A'
+  count: 0
+  probability: 0.0
+- from: 'T'
+  to: 'C'
+  count: 263
+  probability: 0.008464484567603231
+- from: 'T'
+  to: 'G'
+  count: 228
+  probability: 0.007338032248720672
+- from: 'T'
+  to: 'T'
+  count: 30580
+  probability: 0.9841974831836761

doc/usage/phylo/index.html

@@ -946,6 +946,17 @@
     </span>
   </a>
   
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#rare-states-and-iqtree-min-freq" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        Rare states and --iqtree-min-freq
+      
+    </span>
+  </a>
+  
 </li>
         
       </ul>
@@ -1510,6 +1521,17 @@
     </span>
   </a>
   
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#rare-states-and-iqtree-min-freq" class="md-nav__link">
+    <span class="md-ellipsis">
+      
+        Rare states and --iqtree-min-freq
+      
+    </span>
+  </a>
+  
 </li>
         
       </ul>
@@ -1790,6 +1812,11 @@
 <td>Also write an IQ-TREE custom model and alignment (implies <code>--sankoff</code>)</td>
 </tr>
 <tr>
+<td><code>--iqtree-min-freq</code></td>
+<td><code>0.001</code></td>
+<td>With <code>--iqtree --free-loss</code>: also treat as missing any state rarer than this in the alignment</td>
+</tr>
+<tr>
 <td><code>--sankoff-cost-scale</code></td>
 <td><code>100</code></td>
 <td>Integer scaling factor applied to costs before rounding (required by TNT/PhyG's integer-only cost commands)</td>
@@ -2051,10 +2078,12 @@
 <p><strong><code>_sankoff.tcm</code></strong> (<code>--phyg</code>) — first line: the 16-symbol alphabet plus a trailing gap symbol (17 total). Each following line: one row of the integer-scaled, metric-closed cost matrix (17 values — the extra gap column/row reuses the cost to/from the empty state <code>0</code>, since it's never actually triggered).</p>
 <p><strong><code>_sankoff.pg</code></strong> (<code>--phyg</code>) — script: <code>read(prefasta:..., tcm:...)</code> against <code>_sankoff.fasta</code>/<code>_sankoff.tcm</code>, a default 300s/4-instance <code>search</code>, <code>report(...)</code> writing <code>&lt;prefix&gt;_sankoff.tre</code> (bare numeric labels, as for <code>--tnt</code>). Run with <code>phyg</code> from the output directory (the script uses relative file names). Feed the tree plus <code>_sankoff.fasta</code> into <a href="../name-tree/"><code>name-tree</code></a> for taxon names.</p>
 <p><strong><code>_iqtree.model</code></strong> (<code>--iqtree</code>) — lower-triangular exchangeability matrix <span class="arithmatex">\(R(a,b) = e^{-\text{cost}(a,b)}\)</span> (one row of increasing length per state, whitespace-separated, PAML order), followed by one line of empirical state frequencies. Only states actually occurring in the alignment are kept, compactly renumbered <code>0..k-1</code>.</p>
-<p><strong><code>_iqtree.fasta</code></strong> (<code>--iqtree</code>) — alignment recoded to that same compact <code>0..k-1</code> alphabet (symbols <code>0-9A-F</code>). Under <code>--free-loss</code>, non-detection becomes <code>?</code> and columns left non-informative once missing calls are ignored are dropped first (required for <code>+ASC</code>). Run with:
+<p><strong><code>_iqtree.fasta</code></strong> (<code>--iqtree</code>) — alignment recoded to that same compact <code>0..k-1</code> alphabet (symbols <code>0-9A-F</code>). Under <code>--free-loss</code>, non-detection becomes <code>?</code> and columns left non-informative once missing calls are ignored are dropped first (required for <code>+ASC</code>); with <code>--iqtree-min-freq</code> also set (the default), any state rarer than that threshold is folded into the same <code>?</code> treatment, and non-informative columns are re-checked and dropped again after that. Run with:
 <div class="highlight"><pre><span></span><code>iqtree3 -s &lt;prefix&gt;_iqtree.fasta --seqtype MORPH -m &lt;prefix&gt;_iqtree.model+ASC --prefix &lt;prefix&gt;_iqtree -T AUTO
 </code></pre></div></p>
-<p><strong><code>_iqtree_states.csv</code></strong> (<code>--iqtree</code>) — one row per state actually kept in <code>_iqtree.model</code>/<code>_iqtree.fasta</code> (header <code>iqtree_symbol,canonical_symbol,frequency</code>): <code>iqtree_symbol</code> is the compact <code>0-9A-F</code> symbol as written in those two files, <code>canonical_symbol</code> is the matching <code>_sankoff_matrix.csv</code> state, <code>frequency</code> is that state's empirical frequency at full precision (<code>_iqtree.model</code>'s own frequency line is rounded to 6 decimals). Under <code>--free-loss</code>, absent (<code>0</code>/<code>?</code>) is never a kept state, so it never appears here. Use this file to identify which real state a given row/column of <code>_iqtree.model</code>'s matrix corresponds to — e.g. to check whether a state showing zero exchangeability with everything else is expected (a state combination that never co-occurs with anything else in this data) or worth investigating further.</p>
+<p><strong><code>_iqtree_states.csv</code></strong> (<code>--iqtree</code>) — one row per state actually kept in <code>_iqtree.model</code>/<code>_iqtree.fasta</code> (header <code>iqtree_symbol,canonical_symbol,frequency</code>): <code>iqtree_symbol</code> is the compact <code>0-9A-F</code> symbol as written in those two files, <code>canonical_symbol</code> is the matching <code>_sankoff_matrix.csv</code> state, <code>frequency</code> is that state's empirical frequency at full precision (<code>_iqtree.model</code>'s own frequency line is rounded to 6 decimals). Under <code>--free-loss</code>, absent (<code>0</code>/<code>?</code>) is never a kept state, so it never appears here — nor does any state <code>--iqtree-min-freq</code> folded away for being too rare. Use this file to identify which real state a given row/column of <code>_iqtree.model</code>'s matrix corresponds to — e.g. to check whether a state showing zero exchangeability with everything else is expected (a state combination that never co-occurs with anything else in this data) or worth investigating further.</p>
+<h3 id="rare-states-and-iqtree-min-freq">Rare states and <code>--iqtree-min-freq</code></h3>
+<p>States that combine 3 or 4 central bases at once (IUPAC <code>V</code>/<code>H</code>/<code>K</code>.../<code>N</code>) are inherently rare — and, on real data, rare enough that they can make <code>iqtree3</code> itself numerically unstable ("Numerical underflow for lh-derivative" warnings, near-degenerate likelihood optimization). They're also more likely to be assembly/detection noise than genuine, widely-shared multi-way polymorphism, the same "sampling failure, not true signal" reasoning <code>--free-loss</code> already applies to non-detection. With <code>--free-loss</code> set, <code>--iqtree-min-freq</code> (default <code>0.001</code>, i.e. one in a thousand) extends that same missing-data treatment to any state below this frequency, not just absence. Check <code>_iqtree_states.csv</code> to see exactly which states survived and at what frequency; set <code>--iqtree-min-freq 0</code> to disable this and keep every state that occurs at all (the old behavior). Has no effect without <code>--free-loss</code> — there is no missing-data symbol to fold rare states into otherwise.</p>
 
 
 

src/obikmer/src/cmd/phylo/args.rs

@@ -267,6 +267,25 @@ pub struct PhyloArgs {
     #[arg(long)]
     pub iqtree: bool,
 
+    /// Under `--iqtree --free-loss`, also recode to `?` (the same
+    /// missing-data treatment as `-`) any state whose empirical frequency
+    /// in the alignment falls below this threshold — not just genuinely
+    /// absent calls. States encoding 3 or 4 simultaneously-observed
+    /// central bases (IUPAC `V`/`H`/`K`.../`N` for 3, `N` for 4) are rare
+    /// by construction and, on real data, land in exactly this low-frequency
+    /// range — more likely assembly/detection noise than a genuine,
+    /// widely-preserved multi-way polymorphism, the same "sampling failure,
+    /// not true signal" reasoning `--free-loss` already applies to absence.
+    /// Confirmed on real data to matter: `iqtree3`'s own "Numerical
+    /// underflow for lh-derivative" warnings and the exact-zero
+    /// exchangeability rows this was meant to fix (see
+    /// `DevDocMD/theory/evolutionary_distances.md`) both trace back to
+    /// states this thin. No effect without `--free-loss` (there is no
+    /// missing-data symbol to recode to otherwise). `<prefix>_iqtree_states.csv`
+    /// reports the frequency actually used to decide.
+    #[arg(long, default_value = "0.001")]
+    pub iqtree_min_freq: f64,
+
     /// Scale factor applied before rounding real-valued costs to the
     /// integers both `--tnt`'s smatrix/cost commands and `--phyg`'s `tcm:`
     /// matrix require. Keep this small: the total tree score is this scale

src/obikmer/src/cmd/phylo/iqtree.rs

@@ -107,6 +107,19 @@ fn drop_ascertainment_noninformative(alignment: &SnpAlignment) -> SnpAlignment {
     SnpAlignment { sequences }
 }
 
+/// Recode every occurrence of a byte in `symbols` to `-` — the same
+/// "absent" byte `drop_ascertainment_noninformative`/`compact_alphabet`
+/// already treat specially under `--free-loss` (recoded to `?` further
+/// downstream). Used by `--iqtree-min-freq` to fold rare, likely-noisy
+/// states into the missing-data treatment before a second
+/// `compact_alphabet` pass, without duplicating that treatment's logic.
+fn recode_symbols_as_absent(alignment: &SnpAlignment, symbols: &[u8]) -> SnpAlignment {
+    let sequences = alignment.sequences.iter()
+        .map(|seq| seq.iter().map(|&b| if symbols.contains(&b) { b'-' } else { b }).collect())
+        .collect();
+    SnpAlignment { sequences }
+}
+
 fn compact_alphabet(alignment: &SnpAlignment, free_loss: bool) -> CompactAlphabet {
     let iupac_to_state = state_index_table();
 
@@ -240,6 +253,7 @@ pub(super) fn write_iqtree(
     labels: &[String],
     output: &Option<PathBuf>,
     free_loss: bool,
+    min_freq: f64,
 ) {
     let filtered;
     let alignment = if free_loss {
@@ -257,7 +271,41 @@ pub(super) fn write_iqtree(
         alignment
     };
 
-    let alphabet = compact_alphabet(alignment, free_loss);
+    let mut alphabet = compact_alphabet(alignment, free_loss);
+
+    // `--iqtree-min-freq`: fold rare (likely-noisy) states into the same
+    // missing-data treatment `-` already gets under `--free-loss`, then
+    // recompute the alphabet on the further-filtered alignment — see
+    // `args.rs`'s docs on `--iqtree-min-freq` and
+    // `DevDocMD/theory/evolutionary_distances.md` for why (real data:
+    // states encoding 3-4 simultaneous central bases land in exactly this
+    // low-frequency range and correlate with `iqtree3`'s own numerical
+    // instability warnings).
+    let refiltered;
+    let alignment = if free_loss {
+        let low_freq_symbols: Vec<u8> = alphabet.compact_to_old.iter().zip(alphabet.freq.iter())
+            .filter(|&(_, &f)| f < min_freq)
+            .map(|(&old, _)| STATE_SYMBOL[old as usize] as u8)
+            .collect();
+        if low_freq_symbols.is_empty() {
+            alignment
+        } else {
+            let recoded = recode_symbols_as_absent(alignment, &low_freq_symbols);
+            let before = recoded.sequences.first().map(|s| s.len()).unwrap_or(0);
+            refiltered = drop_ascertainment_noninformative(&recoded);
+            let after = refiltered.sequences.first().map(|s| s.len()).unwrap_or(0);
+            info!(
+                "--iqtree-min-freq {min_freq}: {} rare state(s) ({}) recoded as missing, {before} → {after} sites",
+                low_freq_symbols.len(),
+                low_freq_symbols.iter().map(|&b| b as char).collect::<String>(),
+            );
+            alphabet = compact_alphabet(&refiltered, free_loss);
+            &refiltered
+        }
+    } else {
+        alignment
+    };
+
     let states_path = write_iqtree_states_csv(&alphabet, output);
     let model_path = write_iqtree_model(matrix, &alphabet, output);
     let (fasta_path, n_sites) = write_iqtree_alignment(alignment, labels, &alphabet, output, free_loss);
@@ -349,4 +397,39 @@ mod tests {
         assert_eq!(lines.next(), Some("1,G,0.5"));
         assert!(lines.next().is_none());
     }
+
+    #[test]
+    fn iqtree_min_freq_folds_rare_states_into_missing() {
+        // 20 common A/C sites (60 calls total across 3 genomes) plus one
+        // site where genome 0 carries the rare ambiguity state `M` and
+        // genome 1 carries `A` (kept informative by the first
+        // ascertainment filter: two distinct non-`-` calls) — `M` ends up
+        // at 1/62, well below the 0.05 threshold used here.
+        let mut sequences: Vec<Vec<u8>> = vec![Vec::new(); 3];
+        for i in 0..20 {
+            let (a, b, c) = if i % 2 == 0 { (b'A', b'C', b'A') } else { (b'C', b'A', b'C') };
+            sequences[0].push(a);
+            sequences[1].push(b);
+            sequences[2].push(c);
+        }
+        sequences[0].push(b'M');
+        sequences[1].push(b'A');
+        sequences[2].push(b'-');
+        let alignment = SnpAlignment { sequences };
+        let labels = vec!["g1".to_string(), "g2".to_string(), "g3".to_string()];
+        let matrix = [[0.0f64; 16]; 16];
+        let prefix = std::env::temp_dir().join(format!("obikmer_test_iqtree_minfreq_{}", std::process::id()));
+        let output = Some(prefix.clone());
+
+        write_iqtree(&matrix, &alignment, &labels, &output, true, 0.05);
+
+        let states_path = format!("{}_iqtree_states.csv", prefix.display());
+        let csv = std::fs::read_to_string(&states_path).unwrap();
+        assert!(!csv.contains(",M,"), "M (freq ~1/62) must be folded into missing under --iqtree-min-freq 0.05, got:\n{csv}");
+        assert!(csv.contains(",A,") && csv.contains(",C,"), "A/C must survive (well above threshold), got:\n{csv}");
+
+        for suffix in ["_iqtree_states.csv", "_iqtree.model", "_iqtree.fasta"] {
+            std::fs::remove_file(format!("{}{suffix}", prefix.display())).ok();
+        }
+    }
 }

src/obikmer/src/cmd/phylo/mod.rs

@@ -249,7 +249,7 @@ pub fn run(args: PhyloArgs) {
             write_sankoff_phyg(&matrix, &args.output, args.sankoff_cost_scale);
         }
         if args.iqtree {
-            write_iqtree(&matrix, &alignment, &kept_labels, &args.output, args.free_loss);
+            write_iqtree(&matrix, &alignment, &kept_labels, &args.output, args.free_loss, args.iqtree_min_freq);
         }
     }
 

src/obikphylo/src/siblings/tests.rs

@@ -15,7 +15,7 @@ use super::cardinality::CardinalityExt;
 use super::distance::DistanceExt;
 use super::entropy::ShannonEntropyExt;
 use super::entropy_annex::{EntropyAnnex, ENTROPY_ANNEX_FILE_NAME};
-use super::helpers::is_minorant;
+use super::helpers::{central_base, is_minorant};
 use super::sankoff_bundle::SankoffBundleExt;
 use super::stats::SiblingStatsExt;
 use super::subsample::EntropyBias;
@@ -457,6 +457,44 @@ fn sankoff_bundle_matches_old_separate_calls() {
     assert_eq!(bundle.alignment.sequences, expected_alignment.sequences);
 }
 
+#[test]
+fn base_pair_tally_accumulates_base_a_diagnostic() {
+    // Diagnostic for a user-reported observation on real data:
+    // `composition_transitions`'s row/column for base 'A' (index 0) was
+    // *entirely* zero, including the diagonal (`same[0]`, "A stays A"),
+    // despite 'A' appearing at ~6% frequency in the pseudo-alignment
+    // itself. g1/g2 are identical (both central base 'A'), g3 differs
+    // (central base 'C') at the same family — makes the family variable
+    // (family_size=2) while g1/g2 form an eligible (ratio 0), ordinary
+    // pair both resolving `single_form` to `Some(0)` = 'A'.
+    let dir = tempdir().unwrap();
+    let g1 = build_single_genome_index(dir.path(), "g1", b"AAAAAAAAAAA");
+    let g2 = build_single_genome_index(dir.path(), "g2", b"AAAAAAAAAAA");
+    let g3 = build_single_genome_index(dir.path(), "g3", b"AAAAACAAAAA");
+    let mut rep = Reporter::new();
+    let merged = KmerIndex::merge(
+        &dir.path().join("merged.idx"),
+        &[&g1, &g2, &g3],
+        MergeMode::Presence,
+        false,
+        false,
+        1.0,
+        &mut rep,
+    ).expect("merge");
+    merged.build_sibling_annex().expect("build_sibling_annex");
+
+    let n_genomes = merged.meta().genomes.len();
+    let exclude_mask = vec![false; n_genomes];
+    let bundle = merged.sankoff_bundle(None, None, 0.5, &exclude_mask).expect("sankoff_bundle");
+
+    assert!(
+        bundle.base_pair_tally.same[0] >= 1,
+        "base 'A' (index 0) must accumulate in BasePairTally.same for an identical, included g1/g2 \
+         pair both resolving to 'A' — got same={:?}, counts={:?}",
+        bundle.base_pair_tally.same, bundle.base_pair_tally.counts,
+    );
+}
+
 #[test]
 fn entropy_annex_builds_on_demand_and_biases_selection() {
     // Same fixture, same single non-monomorphic family, known entropy15 =
@@ -537,6 +575,132 @@ fn diag_real_index_layer_distribution() {
     println!("top10 counts: {:?}", &sorted_counts[..10.min(sorted_counts.len())]);
 }
 
+#[test]
+#[ignore]
+fn diag_real_index_base_a_representation() {
+    // Diagnostic for a user-reported observation, reproduced on two
+    // unrelated real datasets (a plant and this bacterial index):
+    // `composition_transitions`'s row/column for base 'A' is entirely
+    // zero, even though 'A' appears at real (~6-22%) frequency in the
+    // pseudo-alignment itself. A minimal synthetic reproduction
+    // (`base_pair_tally_accumulates_base_a_diagnostic`) showed the
+    // pairwise tally mechanism itself works correctly for base A in
+    // isolation — so this checks one level lower, purely structural
+    // (annex bits only, no cross-partition/genome-level resolution): does
+    // base A even show up as *present* in minorant families' own
+    // `FamilyMask`s at all, at a rate proportional to the other 3 bases?
+    // If yes, the anomaly is specific to the pairwise/`single_form`
+    // resolution stage; if `has_base[0]` is itself near-zero here, the
+    // anomaly originates earlier, in `build_sibling_annex`/`central_base`.
+    let idx = KmerIndex::open("/Users/coissac/Sync/travail/__MOI__/obikmer/benchmark/global_index_presence")
+        .expect("open real index");
+    let layer_dirs = super::family_scan::sibling_layer_dirs(&idx).expect("layer dirs");
+    let mut has_base = [0u64; 4];
+    let mut minorant_total = 0u64;
+    let mut minorant_central_a = 0u64;
+    for layer_dir in &layer_dirs {
+        let annex = SiblingAnnex::open(&layer_dir.join(ANNEX_FILE_NAME)).unwrap();
+        for slot in 0..annex.len() {
+            let Some(mask) = annex.get(slot) else { continue };
+            if !mask.is_minorant() {
+                continue;
+            }
+            minorant_total += 1;
+            for b in 0..4u8 {
+                if mask.has(b) {
+                    has_base[b as usize] += 1;
+                }
+            }
+        }
+        // Cross-check: for a sample of this layer's minorants, is the
+        // slot's *own* central base ever actually 'A' (bit 0)? — reads
+        // the real k-mer via the layer's MPHF, not just the mask.
+        let meta = PartitionMeta::load(layer_dir.parent().unwrap()).unwrap();
+        let mphf = MphfLayer::open(layer_dir, &meta.mode).unwrap();
+        for (order, kmer) in mphf.enumerate_kmers().take(2_000_000) {
+            let Some(mask) = annex.get(order) else { continue };
+            if mask.is_minorant() && central_base(kmer, idx.kmer_size()) == 0 {
+                minorant_central_a += 1;
+            }
+        }
+    }
+    println!(
+        "minorant_total={minorant_total} has_base(A,C,G,T)={has_base:?} minorant_central_a_sampled={minorant_central_a}"
+    );
+}
+
+#[test]
+#[ignore]
+fn diag_real_index_sankoff_bundle_base_a() {
+    // Structural check (`diag_real_index_base_a_representation`) shows
+    // base A fully, proportionally represented at the family level (~23M
+    // minorants, the *highest* of the four bases) — so the anomaly must
+    // be downstream, in `sankoff_bundle`'s actual pairwise resolution.
+    // Reproduces through the real cross-partition code path (not the
+    // minimal synthetic fixture, which showed the mechanism working in
+    // isolation), bounded by `--subsample` to stay fast.
+    let idx = KmerIndex::open("/Users/coissac/Sync/travail/__MOI__/obikmer/benchmark/global_index_presence")
+        .expect("open real index");
+    let n_genomes = idx.meta().genomes.len();
+    let exclude_mask = vec![false; n_genomes];
+    let bundle = idx.sankoff_bundle(Some(1_000_000), None, 0.5, &exclude_mask).expect("sankoff_bundle");
+    println!("base_pair_tally.same={:?}", bundle.base_pair_tally.same);
+    println!("base_pair_tally.counts={:?}", bundle.base_pair_tally.counts);
+    let alignment_a_count: usize = bundle.alignment.sequences.iter()
+        .map(|seq| seq.iter().filter(|&&b| b == b'A').count())
+        .sum();
+    println!("alignment raw 'A' byte count={alignment_a_count}");
+}
+
+#[test]
+#[ignore]
+fn diag_real_index_genome_mask_for_base_a_families() {
+    // Directly inspects the raw `genome_mask` array `sankoff_bundle`'s
+    // closures see, for the first few variable families where base A is
+    // present — to check whether A ever co-occurs as `single_form` in two
+    // *different* genomes at the same family at all (the precondition for
+    // `bp_same`/`bp_counts` to ever increment for base A), rather than
+    // reasoning about it further.
+    use std::sync::Arc;
+    let idx = KmerIndex::open("/Users/coissac/Sync/travail/__MOI__/obikmer/benchmark/global_index_presence")
+        .expect("open real index");
+    let n_parts = idx.n_partitions();
+    let n_genomes = idx.meta().genomes.len();
+    let with_counts = idx.meta().config.with_counts;
+    let k = idx.kmer_size();
+    let n_bits = n_parts.trailing_zeros() as usize;
+    let partition = obikpartitionner::KmerPartition::open_with_config(
+        idx.root_path(), idx.kmer_size(), idx.minimizer_size(), n_bits,
+    ).unwrap();
+    let cache = Arc::new(super::cache::PartitionCache::build(&partition, n_parts, with_counts).unwrap());
+    let layer_dirs = super::family_scan::sibling_layer_dirs(&idx).unwrap();
+
+    let mut printed = 0usize;
+    for layer_dir in &layer_dirs {
+        super::family_scan::scan_layer_families(
+            layer_dir, n_parts, n_genomes, with_counts, k, &cache, &super::family_scan::Selection::All,
+            |_family_idx, mask, genome_mask| {
+                if printed >= 15 || !mask.has(0) || mask.family_size() < 2 {
+                    return;
+                }
+                let single_a: Vec<usize> = (0..n_genomes).filter(|&g| genome_mask[g] == 1).collect();
+                let others: Vec<(usize, u8)> = (0..n_genomes)
+                    .filter(|&g| genome_mask[g] != 0 && genome_mask[g] != 1)
+                    .map(|g| (g, genome_mask[g]))
+                    .collect();
+                println!(
+                    "family bits={:#06b} size={} single_A_genomes={:?} other_nonzero_genomes={:?}",
+                    mask.bits(), mask.family_size(), single_a, others,
+                );
+                printed += 1;
+            },
+        ).unwrap();
+        if printed >= 15 {
+            break;
+        }
+    }
+}
+
 #[test]
 #[ignore]
 fn diag_plant_index_presence_matrix_sparsity() {