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We give a non-technical introduction to convergence-divergence models, a newmodeling approach for phylogenetic data that allows for the usual divergence ofspecies post speciation but also allows for species to converge, i.e. becomemore similar over time. By examining the $3$-taxon case in some detail weillustrate that phylogeneticists have been "spoiled" in the sense of not havingto think about the structural parameters in their models by virtue of thestrong assumption that evolution is treelike. We show that there are not alwaysgood statistical reasons to prefer the usual class of treelike models over moregeneral convergence-divergence models. Specifically we show many $3$-taxondatasets can be equally well explained by supposing violation of the molecularclock due to change in the rate of evolution along different edges, or bykeeping the assumption of a constant rate of evolution but instead assumingthat evolution is not a purely divergent process. Given the abundance ofevidence that evolution is not strictly treelike, our discussion is anillustration that as phylogeneticists we often need to think clearly about thestructural form of the models we use.

Distinguishing between convergent evolution and violation of the molecular clock