## Recovering a tree from the lengths of random subtrees

#### Steven EvansUniversity of California, Berkeley (UC Berkeley)Statistics

Suppose that we sample the leaves of edge-weighted tree with n leaves in a uniform random order and record the lengths of the subtrees spanned by the first k leaves (that is, in biological terms, the phylogenetic diversity of the first k taxa) for k between 2 and n. In joint work with Daniel Lanoue (UC Berkeley) we consider the question, Can we reconstruct the tree (up to isomorphism) from the joint probability distribution of this random increasing sequence of lengths?" The answer is affirmative if we know a priori that the tree belongs to one of a number of families, but the general question is still open.

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