Wald Space for Phylogenetic Trees

The recently introduced wald space models phylogenetic trees from an evolutionary perspective. We show that it is a stratified space and propose algorithms to compute geodesics. In application we compute a Frechet mean of three trees of different topologies that is fully resolved, unlike in BHV-space. Both, preliminary results on geodesics and on means suggest that wald space features less stickiness than BHV-space, making it an alternative model for statistical investigations.