On the group theoretical background of assigning stepwise mutations onto phylogenies
Abstract
In a recent paper, Klaere et al. modeled the impact of substitutions on arbitrary branches of a phylogenetic tree on an alignment site by the so-called One Step Mutation (OSM) matrix. By utilizing the concept of the OSM matrix for the four-state nucleotide alphabet, Nguyen et al. presented an efficient procedure to compute the minimal number of substitutions needed to translate one alignment site into another.The present paper delivers a proof for this computation.Moreover, we provide several mathematical insights into the generalization of the OSM matrix to multistate alphabets.The construction of the OSM matrix is only possible if the matrices representing the substitution types acting on the character states and the identity matrix form a commutative group with respect to matrix multiplication. We illustrate a means to establish such a group for the twenty-state amino acid alphabet and critically discuss its biological usefulness.
Keywords
Cite
@article{arxiv.1110.3943,
title = {On the group theoretical background of assigning stepwise mutations onto phylogenies},
author = {Mareike Fischer and Steffen Klaere and Minh Anh Thi Nguyen and Arndt von Haeseler},
journal= {arXiv preprint arXiv:1110.3943},
year = {2011}
}