Beyond representing orthology relations by trees

TL;DR

This paper introduces a novel approach to represent complex orthology relations in genomics using phylogenetic networks instead of trees, and presents an algorithm for constructing such networks.

Contribution

It proposes the { extsc{Network-Popping}} algorithm for level-1 phylogenetic network construction from orthology data, expanding the representational framework beyond trees.

Findings

The { extsc{Network-Popping}} algorithm effectively constructs level-1 networks.

Characterization of orthology relations with level-1 network representations.

Identification of natural properties for orthology relations to be representable by networks.

Abstract

Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple operations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view they are also attractive from a theoretical perspective in that e. g. a characterization is known for when such a relation is representable by a certain type of phylogenetic tree. For an orthology relation inferred from real biological data it is however generally too much to hope for that it satisfies that characterization. Rather than trying to correct the data in some way or another which has its own drawbacks, as an alternative, we propose to represent an orthology relation $\delta$ in terms of a structure more general than a phylogenetic tree called a phylogenetic network. To compute such a network in the form of a level-1 representation for $\delta$, we introduce the novel {\sc Network-Popping} algorithm which has several attractive properties. In addition, we characterize orthology relations $\delta$ on some set $X$ that have a level-1 representation in terms of eight natural properties for $\delta$ as well as in terms for level-1 representations of orthology relations on certain subsets of $X$.