Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks

Transformations to Simplify Phylogenetic Networks

The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or lateral gene transfer events between lineages, and so the history of life is more accurately described by a rooted phylogenetic network. Nevertheless, phylogenetic networks may be complex and difficult to interpret, so biologists sometimes prefer a tree that summarises the central tree-like trend of evolution. In this paper, we formally investigate methods for transforming an arbitrary phylogenetic network into a tree (on the same set of leaves) and ask which ones (if any) satisfy a simple consistency condition. This consistency condition states that if we add additional species into a phylogenetic network (without otherwise changing this original network) then transforming this enlarged network into a rooted phylogenetic tree induces the same tree on the original set of species as transforming the original network. We show that the LSA (lowest stable ancestor) tree method satisfies this consistency property, whereas several other commonly used methods (and a new one we introduce) do not. We also briefly consider transformations that convert arbitrary phylogenetic networks to another simpler class, namely normal networks.

Distinct-Cluster Tree-Child Phylogenetic Networks and Possible Uses to Study Polyploidy

As phylogenetic networks become more widely studied and the networks grow larger, it may be useful to "simplify" such networks into especially tractable networks. Recent results have found methods to simplify networks into normal networks. By definition, normal networks contain no redundant arcs. Nevertheless, there may be redundant arcs in networks where speciation events involving allopolyploidy occur. It is therefore desirable to find a different tractable class of networks that may contain redundant arcs. This paper proposes distinct-cluster tree-child networks as such a class, here abbreviated as DCTC networks. They are shown to have a number of useful properties, such as quadratic growth of the number of vertices with the number of leaves. A DCTC network is shown to be essentially a normal network to which some redundant arcs may have been added without losing the tree-child property. Every phylogenetic network can be simplified into a DCTC network depending only on the structure of the original network. There is always a CSD map from the original network to the resulting DCTC network. As a result, the simplified network can readily be interpreted via a "wired lift" in which the original network is redrawn with each arc represented in one of two ways.