Title: Behind Every Great Tree is a Great (Phylogenetic) Network,
Abstract: In Francis and Steel (2015), it was shown that there exists non-trivial
networks on $4$ leaves upon which the distance metric affords a metric on a
tree which is not the base tree of the network. In this paper we extend this
result in two directions. We show that for any tree $T$ there exists a family
of non-trivial HGT networks $N$ for which the distance metric $d_N$ affords a
metric on $T$. We additionally provide a class of networks on any number of
leaves upon which the distance metric affords a metric on a tree which is not
the base tree of the network.
The family of networks are all "floating" networks, a subclass of a novel
family of networks introduced in this paper, and referred to as "versatile"
networks. Versatile networks are then characterised.
Additionally, we find a lower bound for the number of `useful' HGT arcs in
such networks, in a sense explained in the paper. This lower bound is equal to
the number of HGT arcs required for each floating network in the main results,
and thus our networks are minimal in this sense.