Georgia Institute of Technology College of Sciences

Phylogenetic trees  are  the fundamental  mathematical  representation  of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the  complication that  their  discrete  geometric  structure  results  in  a  non-Euclidean phylogenetic  tree  space,  which  poses  computational  and   statistical limitations.

In this  talk, I  will compare  the geometric  and statistical  properties between a  well-studied framework  -  the BHV  space, and  an  alternative framework that  we  propose, which  is  based on  tropical  geometry.  Our framework exhibits analytic,  geometric, and  topological properties  that are desirable for  theoretical studies in  probability and statistics,  as well  as  increased  computational  efficiency.  I  also  demonstrate  our approach on an example of seasonal influenza data.