Operations Research 2025
Abstract Submission

2453. Tropical Location Problems: A Robust Approach to Phylogenetic Consensus

Invited abstract in session TD-4: GOR Young Researchers Awards, stream PC Stream.

Thursday, 14:30-16:00
Room: H6

Authors (first author is the speaker)

1. Andrei Comăneci
TNG Technology Consulting

Abstract

How can we combine conflicting evolutionary trees into a meaningful summary? In evolutionary biology, phylogenetic trees represent hypotheses about species ancestry. But different datasets or inference methods often produce conflicting trees, and synthesizing them into a single, informative consensus tree is a challenging task. Traditional consensus methods tend to ignore features like branch lengths and are sensitive to rogue taxa — species whose positions vary wildly across trees.

In this talk, I present a new approach to this problem using ideas from tropical geometry — a mathematical framework with nonstandard arithmetic but strong geometric properties. We model trees as points in a tropical linear space and explore a class of distances whose balls are tropically convex. This allows us to study location problems where optimal solutions lie in the tropical convex hull of the inputs.

This framework leads to a broad class of tropically convex consensus methods with desirable properties: they incorporate branch lengths, are more robust to rogue taxa, and preserve key structural relationships between taxa present across input trees. These methods are mathematically principled, computationally efficient, and illustrate how geometric reasoning can support robust data summarization — offering new insights into the consensus problem in phylogenetics.

Keywords

Status: accepted

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