2021/11/29 by Jandre Snyman, Snyman, Jandre, Colin Fox +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · #Evolution and Paleontology Studies #FOS: Biological sciences #Genetic diversity and population structure #Genomics and Phylogenetic Studies #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2111.14961
openalex publication_date 2021/11/29 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
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 rℓT(A|B), where r is the number of states and ℓT(A|B) is the parsimony length of the binary character separating A and B. This result corrects an earlier published formula and opens up new applications for old parsimony theorems. Since completing this work, we have learnt that an equivalent result has been proved much earlier by Casanellas and Fernández-Sánchez, using a different proof strategy.