Algorithms for Searching and Analyzing Sets of Evolutionary Trees

The evolutionary relationships between organisms are represented as phylogenetic trees. These trees have important implications for understanding biodiversity, tracking disease, and designing medicine. Since the evolutionary process that led to modern biodiversity was not directly recorded, phylogenetic trees are inferred from modern observations. Inferring accurate phylogenies is computationally difficult and many inference algorithms produce multiple phylogenetic trees of equal quality. The common method for presenting a set of trees is to summarize their common features into a single consensus tree. Consensus methods make it easy to tell which features are common to a set of trees, but how do you explore the hypotheses that are not the majority of trees? This question is best answered by a search algorithm.

We present algorithms to query a set of trees based on their internal structure. Trees can be queried based on their bipartitions, quartets, clades, subtrees, or taxa, and we present a new concept which unifies edge based relationships for search functions. To extend the power of our search functions we provide the ability to combine the results of multiple searches using set operations.

We also explore the differences between sets of trees. Clustering algorithms can detect if there are multiple distinct hypotheses within a set of trees. Decision tree depth and distinguishing bipartitions can be used to measure the similarity between sets of trees. For situations where a set of trees is made up of multiple distinct sets, we present p-support which is a measure to quantify the impact of the individual sets on a single consensus tree.

The algorithms are presented within the context of TreeHouse. This is my open source platform for querying and analyzing sets of trees. One goal of TreeHouse was to unite query and analysis algorithms under a single user interface. The seamless interaction between fast filtering and analysis algorithms allows users to the explore their data in a way not easily accomplished elsewhere. We believe that the algorithms in this document and in TreeHouse can shed new light on often unexplored territory.