Parsimony and the rank of a flattening matrix.

Jandre Snyman, Colin Fox, David Bryant

Open access · hybridAbstract read

In one paragraph

Article in Journal of mathematical biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

0numbers the graph read from it

0cells of the map it votes in

1citing papers in PubMed

0.3field-weighted citation impact, top 38% of its field

1 · What the graph read from it

What it found

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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

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3 · Its place in the literature

Who cites it

1 citing paper in PubMed, 2 citations in OpenAlex.

Phylogenetic Network Models as Graphical Models.Bulletin of mathematical biology · 2026
Article

4 · The record

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5 · Who and what money

Authors and funding

3 authors at 1 institution in 1 country.

Jandre SnymanDepartment of Mathematics and Statistics, University of Otago, Dunedin, New Zealand.

Colin FoxDepartment of Physics, University of Otago, Dunedin, New Zealand.

David BryantDepartment of Mathematics and Statistics, University of Otago, Dunedin, New Zealand. david.bryant@otago.ac.nz.ORCID 0000-0003-1963-5535

University of Otago · NZ

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

The standard models of sequence evolution on a tree determine probabilities for every character or site pattern. A flattening is an arrangement of these probabilities into a matrix, with rows corresponding to all possible site patterns for one set A of taxa and columns corresponding to all site patterns for another set B of taxa. Flattenings have been used to prove difficult results relating to phylogenetic invariants and consistency and also form the basis of several methods of phylogenetic inference. We prove that the rank of the flattening equals [Formula: see text], where r is the number of states and [Formula: see text] is the minimum size of a vertex cut separating A from B. When T is binary the rank of the flattening equals [Formula: see text] where [Formula: see text] equals the parsimony length of the binary character separating A and B. We provide a direct proof that requires little more than undergraduate algebra, but note that the formula could also be derived from work by Casanellas and Fernández-Sánchez (2011) on phylogenetic invariants.

Indexed as

AlgorithmsPhylogenyProbabilityMarkov models on treesPhylogenetic invariantsPhylogenyRank formulaTensor flattening

Identifiers

PMID36757460

DOI10.1007/s00285-023-01875-y

PMCPMC9911492

OpenAlexW3214954443

What OpenQuestion holds

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LicenceCC BY

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.