Flouri et al.'s MSci identifiability conjecture, for clock-JC data with long loci
Flouri, Jiao, Rannala and Yang ask whether, with multiple sampled sequences and multiple sites per locus, parameters of the multispecies coalescent with introgression are identifiable from sequence alignments exactly when they are identifiable from gene-tree topologies and coalescent times. The present entry makes the observation channel and site-length quantifier explicit: complete labelled contemporaneous haploid alignments, homogeneous stationary molecular-clock JC mutation in mutation-scaled units, and sufficiently long finite loci within each fixed finite MSci model.
- Result
- Proved(see note)
- Status
- Variant only
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Mathematical statistics; algebraic identifiability; coalescent phylogenetics
- Posed by
- Flouri, Jiao, Rannala and Yang, MBE 37(4):1211–1223, DOI 10.1093/molbev/msz296 (online 6 Dec 2019; issue 2020). Restated by Yang and Flouri, MBE 39:msac083 (2022).
- Year posed
- 2019
- Years open
- 7y
- Solved
- 2026-10-05
- Model
- OpenAI assistant (dot; underlying model unspecified)
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
For every fixed finite admitted MSci model and its unchanged labelled sample panel, a finite site cutoff works uniformly over parameter pairs: complete sequence laws agree exactly when route-marginal timed-genealogy laws agree. All identifiable functionals and all genuine ambiguities transfer. Multiple introgressions, expansions, equal rates, rank-deficient routing and source-allowed inheritance endpoints are covered. The A–D compiler preserves tied ages and current-lineage routing. Trees end at the sample MRCA; route flags are marginalized.
The channel is complete contemporaneous haploid data under homogeneous stationary clock-JC in mutation units. No arbitrary short-locus claim, universal cutoff over unbounded complexity, or general demographic uniqueness is made. Unknown locus-rate mixtures, unphased genotypes and other mutation/clock channels remain separate. No calendar calibration, finite-data accuracy or reliable numerical inference is supplied.
What the AI did
Under the user's research direction, dot (OpenAI) developed the mathematical observation bridge, finite-site arguments and source-specific MSci compiler, wrote the proof and exact rational controls, and performed separate AI correctness/source-scope reviews. The finite-generation method builds on classical polynomial-family identifiability and finite exponential recurrence ideas, with attribution in the proof. The biological model and conjecture are existing research. No human expert endorsement is claimed.
Verification
Read by this site on 6 October 2026. The source sentence was checked in the 2020 paper (Discussion, Identifiability of MSci models) and in Yang and Flouri's 2022 restatement. The submission's event-compiler check passed when re-run here; it verifies small rational routing compositions, not identifiability. The identifiability transfer rests on a written proof (bridge/THEOREM.md) that was not read here. Both review records are by the same AI agent. No Lean formalisation.
Sources
Submitted by ZestyDingo473 on