Geodesics to characterize the phylogenetic landscape

Phylogenetic trees are fundamental for understanding the evolutionary history of a set of species. The local neighborhoods of a phylogenetic tree provide important information, but since trees are high-dimensional objects, characterizing these neighborhoods is difficult. Based on the Billera-Holmes-Vogtmann (BHV) distance between pairs of trees, we describe a method to generate intermediate trees on the shortest path between two arbitrary trees, called pathtrees. These pathtrees give a structured way to investigate intermediate neighborhoods between trees of interest in the BHV treespace and can also be used to find high likelihood trees independently of traditional heuristic search mechanisms. We implemented our algorithm in the Python package Pathtrees, which enables the construction of the continuous tree landscape interior of the convex hull of starting trees, low-dimensional visualization of the generated tree landscape, identifying clusters of trees with the same topologies, and searching for the best tree.