Tree Topologies along a Tropical Line Segment

Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because tropical metric some nice properties such as convexity in terms of metric. One challenges applications is difficulty interpreting outcomes This paper focuses on combinatorics topologies along a line segment, an intrinsic geodesic metric, between two phylogenetic trees space and we show segment trees. Specifically that probability randomly chosen going through origin (the star tree) zero if number leave greater than four, also given differ only one nearest neighbor interchange (NNI) move, then topology them same these possible branch lengths.