Wikipedia reports:
“For many years, there has been a large debate as to whether Purgatorius is a primitive member of the Primates or a basal member of the Plesiadapiforms.” Here (Fig. 1) taxa from the Plesiadapiformes have giant procumbent (rat-like) incisors followed by a long diastema, followed by flat molars…completely UNLIKE Purgatorius. So what were they thinking?
Halliday et al. 2015
nested Purgatorius outside crown group placentals with Protunugulatum (Fig 1). That seems reasonable, though it is twice the size. However, the large reptile tree (LRT, 1044 taxa) was not able to replicate most of the Halliday team’s cladogram, which nested hyraxes with elephant shrews…and horses… and that clade with pre-odontocetes and an early artiodactyl. It just gets worse after that. Protunugulatum was originally allied with condylarths, large plant-eating mammals. Halliday et al. nested it outside the placentals. Wible et al. 2007 nested it with whales + artiodactyls (a clade not validated by the LRT).
Purgatorius is another one of those fossils
known from an incompleted mandible with teeth and little else. Based on a lack of other bones, this is the sort of fossil the LRT cannot successfully resolve and it does not make it onto the list. So we go to plan #2: visual comparisons.
Figure 1. Purgatorius compared to other basal and often Paleocene mammals. Given these choices, Purgatorius looks more like Palaechthon, the basal dermopteran, than any other taxa in the LRT. Taxa in yellow nest together in the LRT with primates. Taxa in pink nest with rats and rabbits. Maelestes is a basal marsupial.
Rat-sized Purgatorius unio
(Valen and Sloan 1965; Latest Cretaceous/Earliest Paleocene) gained some early notoriety as the earliest known primate. Ankle bones found in association with Purgatorius, but not articulation, show signs of being flexible like those of primates (Kaplan 2012).
I can describe Purgatorius in the simplest of terms
based on comparisons to related basal mammal taxa (Fig. 1) and without describing any molar cusps (except one).
- small in overall size (skull < 2cm in length)
- robust mandible with convex dorsal and ventral rims and straight in occlusal view
- incisors likely procumbent, but not large
- canine tiny
- three robust premolars and three robust molars with one very tall cusp
- Premolar #3 taller than other teeth
Based on a visual comparison
of candidate taxa (Fig. 1), Purgatorius looks more like Protungulatum and even more like Palaechthon. The latter nests with flying lemurs like Cynocephalus. So we’re close to the base of primates, but closer to their cousins, and far from plesiadapiformes.
Best I can do for now…
References
Halliday TJD, Upchurch P and Goswami A 2015. Resolving the relationships of Paleocene placental mammals Biological Reviews. | doi = 10.1111/brv.12242
Kaplan M 2012. Primates were always tree-dwellers. Nature. doi:10.1038/nature.2012.11423
Van Valen L and Sloan R 1965. The earliest primates. Science. 150(3697): 743–745.
Wible JR, Rougier GW, Novacek MJ and Asher RJ 2007. Cretaceous eutherians and Laurasian origin for placental mammals near the K/T boundary.” Nature volume 447: 1003-1006
The Pterosaur Heresies 
Lower incisors are not known for Purgatorius–what you’ve got pictured there is a reconstruction based on only partially complete alveoli. It is very much open to interpretation. Halliday’s analysis has the same problem as the Wible et al. analysis that also found a relationship between Purgatorius and Protungulatum–an insufficiency of other plesiadapiforms and of characters appropriate to properly placing primitive euarchontans. The Chester et al., 2015 analysis rectified these problems to some degree, and found Purgatorius to be a primitive primate.
And it is a primitive primate that was nowhere near rat-sized. Much smaller.
Oh, and no analysis that is well sampled with relatives of Palaechthon has ever found a close relationship with dermopterans.
Good to know. Which relatively complete taxa are closer to dermopterans? I’d like to add them.