## Phylogenetic Invariants for Metazoan Mitochondrial Genome Evolution

David Sankoff[1] (sankoff@ere.umontreal.ca)

Mathieu Blanchette[2] (blanchem@cs.washington.edu)

[1]Centre de recherches mathématiques, Université de Montréal

CP 6128 Succursale Centre-Ville, Montréal, Québec H3C 3J7

[2]Department of Computer Science, University of Washington

Seattle, WA 98195

### Abstract

The method of phylogenetic invariants was developed to
apply to aligned sequence data generated, according to a stochastic substitution
model, for *N* species related through an unknown phylogenetic tree.
The invariants are functions of the probabilities of the observable
*N*-tuples, which are identically zero, over all choices of branch length, for
some trees. Evaluating the invariants associated with all possible trees, using
observed *N*-tuple frequencies over all sequence positions, enables us to rapidly
infer the generating tree.

An aspect of evolution at the genomic level much studied recently is the
rearrangements of gene order along the chromosome from one species to
another. Instead of the substitutions responsible for sequence evolution, we
examine the non-local processes responsible for genome rearrangements such as
inversion of arbitrarily long segments of chromosomes. By treating the potential
adjacency of each possible pair of genes as a ``position", an appropriate
``substitution" model can be recognized as governing the rearrangement process,
and a probabilistically principled phylogenetic inference can be set up. We
calculate the invariants for this process for *N*=5, and apply them to
mitochondrial genome data from coelomate metazoans, showing how they resolve
key aspects of branching order.

*Japanese Society for Bioinformatics*