Perfect Phylogeny¶
A tree that jointly displays character states without repeated introductions under a stated model.
Core Idea¶
A perfect phylogeny is one tree that jointly displays a declared set of discrete characters: for each character, every state occupies a connected region distinct from its other states. One topology must satisfy all included characters; fitting a different tree to each column is insufficient. “Perfect” names exact fit under a stated model, not a directly observed evolutionary history or proof that recurrence and error never occurred.[ref-5bce4557b59a][ref-dafdd4fdedaa]
Scope of Application¶
This formal phylogenetic model applies when discrete character states and one tree are assessed under declared assumptions:
- Unrooted multistate construction: one tree T1 displays three specified partitions on eight formal labels.[^ref-5bce4557b59a]
- Tumor clone inference: a rooted, binary infinite-sites tree represents compatible inferred clone patterns.[^ref-dafdd4fdedaa]
Clarity¶
The question is whether one tree displays the whole declared matrix, rather than whether each character individually has some tree. In the eight-label construction, T1 fits the selected three characters, but the full four-character set has no common witness; a successful local check is therefore not a general multistate certificate.[^ref-5bce4557b59a] In the tumor case, the compatible tree is inferred from mixed samples under additional assumptions, so compatibility is not confirmation of each actual mutation event.[^ref-dafdd4fdedaa]
Manages Complexity¶
The role map—objects and states, candidate tree, connected state regions, joint witness, model assumptions—compresses many proposed histories into one exact compatibility question. A fitting tree organizes all included characters at once; if no such tree exists, fitting separate columns cannot rescue the full matrix. Binary local tests have their own bounded theorem, while multistate and noisy cases require attention to their declared conditions; the exact model can reject observations that a recurrence-tolerant explanation might accommodate.[ref-5bce4557b59a][ref-dafdd4fdedaa]
Abstract Reasoning¶
Use a witness test by asking whether every character's state regions can be made connected and distinct on the same tree, then an obstruction test by checking whether a larger character set defeats an apparently successful subset. Use a model counterfactual when a fit fails: reconsider the permitted recurrence, error or clone assumptions without treating a relaxed account as the same exact result. A failed compatibility check is not a historical verdict; it is a result relative to the chosen character representation.[ref-5bce4557b59a][ref-dafdd4fdedaa]
Knowledge Transfer¶
The joint-display question transfers literally from formal taxon partitions to rooted tumor mutation patterns, although the former is unrooted and multistate while the latter uses a binary infinite-sites clone model.[ref-5bce4557b59a][ref-dafdd4fdedaa] Tree (Graph Theory) is the broader kind: each witness is connected and acyclic, but an arbitrary tree need not display the declared characters. Its path and bridge properties do not make perfect-phylogeny inference easy or establish actual lineage history. Tree Structure's designated root belongs to the tumor specialization, not every perfect phylogeny; beyond character/tree modeling, “one structure fits many constraints” is only an analogy.
Relationships to Other Abstractions¶
Current abstraction Perfect Phylogeny Domain-specific
Parents (1) — more general patterns this builds on
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Perfect Phylogeny is a kind of Tree (Graph Theory) Domain-specific
A perfect phylogeny is a graph-theoretic tree specialized by joint connected-state display of a declared character matrix.
Hierarchy path (1) — routes to 1 parentless root
- Perfect Phylogeny → Tree (Graph Theory) → Network
Neighborhood in Abstraction Space¶
Perfect Phylogeny sits in a moderately populated region (59th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Unclustered & Miscellaneous (2721 abstractions)
Nearest neighbors
- Maximum Parsimony — 0.89
- Nested Set Model — 0.85
- Self-Verifying Finite Automaton — 0.84
- Gray Code — 0.84
- Generalized blockmodeling of binary networks — 0.84
Computed from structural-signature embeddings · 2026-10-17
References¶
[^ref-5bce4557b59a]: Leo van Iersel, Mark Jones and Steven Kelk, “A Third Strike Against Perfect Phylogeny,” Systematic Biology 68(5):814–827 (2019), Introduction, “Example for Eight Taxa,” Figure 2 caption and incompatible-four discussion, and “Mathematical Definitions,” https://academic.oup.com/sysbio/article/68/5/814/5319938. Original publisher full text was inspected; Figure 2's detailed image pixels were not independently analyzed. [^ref-dafdd4fdedaa]: Mohammed El-Kebir, Layla Oesper, Hannah Acheson-Field and Benjamin J. Raphael, “Reconstruction of clonal trees and tumor composition from multi-sample sequencing data,” Bioinformatics 31(12):i62–i70 (2015), Abstract, §2.1 Definitions 1–3 and perfect-phylogeny matrix discussion, and §3 Results, https://academic.oup.com/bioinformatics/article/31/12/i62/216528. Original publisher full text was inspected; the inferred tree remains conditional on the paper's model and mixed-sample measurements.