Bounding the number of reticulation events for displaying multiple trees in a phylogenetic network

TL;DR

This paper investigates upper bounds on the reticulation number in phylogenetic networks that display multiple trees, extending understanding beyond the well-studied case of two trees to three or more trees.

Contribution

The paper provides new non-trivial upper bounds on reticulation numbers for three or more phylogenetic trees, advancing theoretical understanding in phylogenetics.

Findings

Established new upper bounds for reticulation numbers with three or more trees

Extended theoretical results beyond the two-tree case

Contributed to the mathematical understanding of phylogenetic network complexity

Abstract

Reconstructing a parsimonious phylogenetic network that displays multiple phylogenetic trees is an important problem in theory of phylogenetics, where the complexity of the inferred networks is measured by reticulation numbers. The reticulation number for a set of trees is defined as the minimum number of reticulations in a phylogenetic network that displays those trees. A mathematical problem is bounding the reticulation number for multiple trees over a fixed number of taxa. While this problem has been extensively studied for two trees, much less is known about the upper bounds on the reticulation numbers for three or more arbitrary trees. In this paper, we present a few non-trivial upper bounds on reticulation numbers for three or more trees.