Combinatorial Aspects of Phylogenetic Analysis
- Alex Grossmann (Centre national de la recherche scientifique, Paris, France)
Ranks of amino acid mutabilities as phylogenetic markers
Consider an arbitrary set on square matrices with non-negative entries. One may ask whether they can be represented in a way that mimics the logarithmic-scale display of one-dimensional data. Such a representation can be obtained by the use of elementary properties of matrix-valued logarithms.
The set of matrices may consist of the count matrices obtained from pairwise subalignments of an alignment of N sequences. The method associates a "rate" matrix to any pair of sequences, and makes it possible to consider two artificial continuous "evolutions" leading from one sequence to the other - if these "evolutions" exist.
The negative trace of the "rate" matrix is the LogDet distance between the two sequences.
The information contained in a "rate" matrix is richer than just the trace.The aim of this work is to exploit this additional information. This is can be done e.g. by focusing on the order of values in the entries of the "rate" matrix, i.e. by rank methods.
We have used this method on proteins coded by a set 123 mitochondrial genomes of metazoa.
Report on Rank-based Analyses of B Subtilis Micro Array Dat