  We give a non-technical introduction to convergence-divergence models, a new
modeling approach for phylogenetic data that allows for the usual divergence of
species post speciation but also allows for species to converge, i.e. become
more similar over time. By examining the $3$-taxon case in some detail we
illustrate that phylogeneticists have been "spoiled" in the sense of not having
to think about the structural parameters in their models by virtue of the
strong assumption that evolution is treelike. We show that there are not always
good statistical reasons to prefer the usual class of treelike models over more
general convergence-divergence models. Specifically we show many $3$-taxon
datasets can be equally well explained by supposing violation of the molecular
clock due to change in the rate of evolution along different edges, or by
keeping the assumption of a constant rate of evolution but instead assuming
that evolution is not a purely divergent process. Given the abundance of
evidence that evolution is not strictly treelike, our discussion is an
illustration that as phylogeneticists we often need to think clearly about the
structural form of the models we use.
