Defining phylogenetic networks using ancestral profiles

TL;DR

This paper investigates the conditions under which ancestral profiles uniquely determine rooted phylogenetic networks, showing that stack-free orchard networks guarantee uniqueness, while allowing high in-degree vertices introduces ambiguity.

Contribution

It clarifies the conditions needed for ancestral profiles to uniquely identify orchard networks, emphasizing the importance of the stack-free restriction.

Findings

Stack-free orchard networks have unique ancestral profiles.

Lifting the stack-free restriction leads to non-uniqueness due to high in-degree vertices.

Provides a refined understanding of reconstructing phylogenetic networks from ancestral data.

Abstract

Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is to consider its `ancestral profile' (the number of paths from each ancestral vertex to each leaf). In general, this information does not uniquely determine the underlying phylogenetic network. A recent paper considered a new class of phylogenetic networks called `orchard networks' where this uniqueness was claimed to hold. Here we show that an additional restriction on the network, that of being `stack-free', is required in order for the original uniqueness claim to hold. On the other hand, if the additional stack-free restriction is lifted, we establish an alternative result; namely, there is uniqueness within the class of orchard networks up to the resolution of vertices of high in-degree.