TY - JOUR AU - Fischer, Mareike AU - Klaere, Steffen AU - Thi Nguyen, Minh Anh AU - Haeseler, Arndt von PY - 2012 DA - 2012/12/15 TI - On the group theoretical background of assigning stepwise mutations onto phylogenies JO - Algorithms for Molecular Biology SP - 36 VL - 7 IS - 1 AB - Recently one step mutation matrices were introduced to model the impact of substitutions on arbitrary branches of a phylogenetic tree on an alignment site. This concept works nicely for the four-state nucleotide alphabet and provides an efficient procedure conjectured to compute the minimal number of substitutions needed to transform one alignment site into another. The present paper delivers a proof of the validity of this algorithm. Moreover, we provide several mathematical insights into the generalization of the OSM matrix to multi-state 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 this approach by looking at Abelian groups over twenty states and critically discuss their biological usefulness when investigating amino acids. SN - 1748-7188 UR - https://doi.org/10.1186/1748-7188-7-36 DO - 10.1186/1748-7188-7-36 ID - Fischer2012 ER -