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.
