Phylogenetic network classes through the lens of expanding covers

Andrew Francis; Daniele Marchei; Mike Steel

doi:10.1007/s00285-024-02075-y

Phylogenetic network classes through the lens of expanding covers

J Math Biol. 2024 Apr 8;88(5):58. doi: 10.1007/s00285-024-02075-y.

Authors

Andrew Francis^{1

2}, Daniele Marchei^{3

4}, Mike Steel⁵

Affiliations

¹ Centre for Research in Mathematics and Data Science, Western Sydney University, Sydney, Australia. a.francis@unsw.edu.au.
² School of Mathematics and Statistics, University of New South Wales, Sydney, Australia. a.francis@unsw.edu.au.
³ Centre for Research in Mathematics and Data Science, Western Sydney University, Sydney, Australia.
⁴ Computer Science, University of Camerino, Camerino, Italy.
⁵ Biomathematics Research Centre, University of Canterbury, Christchurch, New Zealand.

Abstract

It was recently shown that a large class of phylogenetic networks, the 'labellable' networks, is in bijection with the set of 'expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call 'spinal' phylogenetic networks.

Keywords: Algorithms; Characterising network classes; Encoding; Expanding cover; Partition; Phylogenetic network; Spanning tree.

MeSH terms

Algorithms*
Humans
Models, Genetic*
Phylogeny