Information Metrics for Phylogenetic Trees via Distributions of Discrete and Continuous Characters

A wide range of metrics between phylogenetic trees are used in evolutionary molecular biology. They are typically based directly on the branching patterns and edge lengths represented by the trees. Metrics have recently been proposed which are based on the information content of distributions of genetic characters induced by the trees. We first show how these metrics lead to a change to the topology of the underlying tree space. Next we show via computational methods that the metrics are stable under changes to the Markov process used to generate characters, at least in the case of 5 taxa. As a result, a Gaussian process defined over the edges of trees can be used to compute the metrics, leading to a substantial computational efficiency over DNA nucleotide-valued Markov process models.