A Fréchet tree distance measure to compare phylogeographic spread paths across trees

Phylogeographic methods reconstruct the origin and spread of taxa by inferring locations for internal nodes of the phylogenetic tree from sampling locations of genetic sequences. This is commonly applied to study pathogen outbreaks and spread. To evaluate such reconstructions, the inferred spread paths from root to leaf nodes should be compared to other methods or references. Usually, ancestral state reconstructions are evaluated by node-wise comparisons, therefore requiring the same tree topology, which is usually unknown. Here, we present a method for comparing phylogeographies across different trees inferred from the same taxa. We compare paths of locations by calculating discrete Fréchet distances. By correcting the distances by the number of paths going through a node, we define the Fréchet tree distance as a distance measure between phylogeographies. As an application, we compare phylogeographic spread patterns on trees inferred with different methods from hemagglutinin sequences of H5N1 influenza viruses, finding that both tree inference and ancestral reconstruction cause variation in phylogeographic spread that is not directly reflected by topological differences. The method is suitable for comparing phylogeographies inferred with different tree or phylogeographic inference methods to each other or to a known ground truth, thus enabling a quality assessment of such techniques.