Tropical medians, transportation, and consensus trees

Using data from protein or DNA sequences, evolutionary biologists seek the true ancestral relations among species which is represented in the form of a tree. The space of phylogenetric trees is a tropical linear space which motivates a tropical approach to analyze evolutionary data.

In this talk, we will focus on the Fermat--Weber problem under an asymmetric tropical distance, emphasizing its geometric and computational aspects. In particular, we will show its connection to the transportation problem from operations research. These properties lead to an efficient consensus method for phylogenetics.

The talk is based on joint work with Michael Joswig.