The SNPR neighbourhood of tree-child networks

TL;DR

This paper derives exact formulas and bounds for the size of the SNPR neighbourhood in tree-child networks, aiding efficient exploration of phylogenetic network spaces.

Contribution

It provides the first explicit expressions and bounds for SNPR neighbourhood sizes in tree-child networks, considering network size and topology.

Findings

Exact formulas for SNPR neighbourhood sizes in tree-child networks.

Upper and lower bounds for neighbourhood sizes.

Insights into network topology's impact on neighbourhood size.

Abstract

Network rearrangement operations like SNPR (SubNet Prune and Regraft), a recent generalisation of rSPR (rooted Subtree Prune and Regraft), induce a metric on phylogenetic networks. To search the space of these networks one important property of these metrics is the sizes of the neighbourhoods, that is, the number of networks reachable by exactly one operation from a given network. In this paper, we present exact expressions for the SNPR neighbourhood of tree-child networks, which depend on both the size and the topology of a network. We furthermore give upper and lower bounds for the minimum and maximum size of such a neighbourhood.