Comparing and simplifying distinct-cluster phylogenetic networks

TL;DR

This paper studies a special class of phylogenetic networks called distinct-cluster networks, introduces a metric on them, and explores a cluster-preserving simplification process that can uniquely determine networks.

Contribution

It defines a metric on the set of distinct-cluster networks and analyzes a simplification process that preserves clusters, potentially leading to unique network representations.

Findings

Defined a metric on DC(X) networks

Introduced a cluster-preserving simplification process

Identified conditions for unique network determination

Abstract

Phylogenetic networks are rooted acyclic directed graphs in which the leaves are identified with members of a set X of species. The cluster of a vertex is the set of leaves that are descendants of the vertex. A network is "distinct-cluster" if distinct vertices have distinct clusters. This paper focuses on the set DC(X) of distinct-cluster networks whose leaves are identified with the members of X. For a fixed X, a metric on DC(X) is defined. There is a "cluster-preserving" simplification process by which vertices or certain arcs may be removed without changing the clusters of any remaining vertices. Many of the resulting networks may be uniquely determined without regard to the order of the simplifying operations.