FULL RECONSTRUCTION OF MARKOV-MODELS ON EVOLUTIONARY TREES - IDENTIFIABILITY AND CONSISTENCY

A Markov model of evolution of characters on a phylogenetic tree consi sts of a tree topology together with a specification of probability tr ansition matrices on the edges of the tree. Previous work has shown th at, under mild conditions, the tree topology may be reconstructed, in the sense that the topology is identifiable from knowledge of the join t distribution of character states at pairs of terminal nodes of the t ree. Also, the method of maximum likelihood is statistically consisten t for inferring the tree topology. In this article we answer the analo gous questions for reconstructing the full model, including the edge t ransition matrices. Under mild conditions, such full reconstruction is achievable, not by using pairs of terminal nodes, but rather by using triples of terminal nodes. The identifiability result generalizes pre vious results that were restricted either to characters having two sta tes or to transition matrices having special structure. The proof deve lops matrix relationships that may be exploited to identify the model. We also use the identifiability result to prove that the method of ma ximum likelihood is consistent for reconstructing the full model.