Using the “mock character-trait matrix of wheeled vehicles” produced by creationist John Woodmorappe (found here), I generated a morphology-based phylogeny using IQ-TREE (thanks, @davecarlson!). Here is the result, both unrooted and outgroup-rooted* (visualized at iTOL: Vehicles):
This tree actually displays the same strange topology as the ‘random’ trees, as all of the vehicle ‘taxa’ fall along a single line rather than creating a branching pattern. The bootstrap values are high, but I suspect that this is only because Woodmorappe purposely cherry-picked features of these vehicles that fall along such a pattern. If we did a comprehensive morphological analysis of these vehicles, the tree would undoubtedly have more ‘noise’ and less ‘signal.’
Ideally, this should put to rest the creationist claim that vehicles produce a nested hierarchy like common ancestry (cough @scd cough) but sadly it’s very likely that this myth will continue to be perpetuated. At least now, when creationists make this claim, I can direct them to this post which shows that even in the best-case scenario (using Woodmorappe’s cherry-picked morphological data), the topology of the vehicle phylogeny is actually far closer to ‘random’ trees than the branching pattern produced by common ancestry.
* The outgroup is “unicycle.”