A new hypothesis on bat ancestry: seems odd…

Halliday, Upchurch and Goswami (2015)
report they have resolved the relationships of Paleocene placental mammals. That includes bats, of course (subset of their cladogram in Fig. 1).

From their abstract “the affinities of most Paleocene mammals have remained unresolved, despite significant advances in understanding the relationships of the extant orders, hindering efforts to reconstruct robustly the origin and early evolution of placental  mammals. Here we present the largest cladistic analysis of Paleocene placentals to date, from a data matrix including 177 taxa (130 of which are Palaeogene) and 680 morphological characters.”

The ancestry of bats
has been a traditional problem in paleontology. Pterosaur Heresies resolved that to a certain extent here and here. Halliday et al. put forth a new and odd sister taxon, Apatemys (Fig. 2), a small chisel-toothed mammal. Unfortunately the only time Apatemys is mentioned in the text is in the cladogram figure.

As readers may recall, 
the large reptile tree nested bats with the extinct arboreal carnivores, Vulpavus and Chriacus (Fig. 3) and the small extant mammal Ptilocercus, which we looked at here. In the Halliday et al. tree, Vulpavus nests on a nearby busy branch. Chriacus nests much farther away. Ptilocercus nests as a very basal mammal with Plesiadapis, Notharctus and other primates, far from Tupaia, which nests with Cynocephalus (just the opposite of what the large reptile tree recovered, which aligned Tupaia with rabbits and Ptilocercus with flying lemurs like Cynocephalus.

A more generalized and bat-like dentition
is found in Chriacus and Protictis (Fig. 3). Unfortunately the fossils are few in the ancestry of bats. We have to work with what we have.

The next most proximal outgroups to bats
in the Halliday et al. cladogram include the digging taeniodont Onychodectes and the basal pangolin Escavadodon (Fig. 1, 4). Again, these are all much more derived than a sister to bats needs to be. They are not at all ‘bat-like’. Not sure why the Halliday team arrived at such an odd nesting. It doesn’t appear to make sense. I don’t see any gradual accumulation of derived traits leading up to bats here.

On the other hand
Ptiilocercus (Fig. 5) is still the best example of what a bat ancestor must have looked like, as we examined previously here, here and here.

Ptilocercus is the right size,
the right niche, and it has lots of bat-like traits, like that rotating wrist, flat ribs and that high floating scapula.

References
Halliday TJD, Upchurch P and Goswami A 2015. Resolving the relationships of Palaeocene placental mammals. Biological Reviews first published Dec 21, 2015.