Are molecular studies proof? Or evidence?
Evidence.
Some bat-centered molecular studies use impressive numbers of taxa.
And what is the final measure in head-to-head competition.
Final measure? In science? ~:-|
Pettigrew et al. gives a really convincing account, including reams of soft tissue data that is well worth a read.
Long answer: Recent molecular studies have thoroughly refuted the hypothesis that bats are diphyletic, with megabats closer to primates. Last I heard, molecular evidence was even indicating that Microchiroptera is actually paraphyletic with respect to Megachiroptera,
Yep. That's the one with the many OTUs.
and that bats are on a totally different branch (no pun intended) from primates on the placental tree (hanging out with shrews, true ungulates, carnivores, and pangolins).
Old news (2001 at least).
>> In the above paper is a ref [not copied] for some soft-tissue > cladistic work describing a close association between lagomorphs and > primates.
Interesting. Molecular evidence also indicates that rabbits + rodents are close to primates + tree shrews + colugos.
> 1. Do eurymlids have a large diastema like Gomphos, lagomorphs and > rodents do?
Not familiar with them.
> 2. I know that a basal primate, Plesiadapis, has a large diastema, > among other interesting characters.
May not be a primate; possibly closer to dermapterans,
though (AFAIK) still an archontan.
> 3. Did the two large diastemas, so close to each other on the tree, > develop convergently? Or is there another connection? > > And in a worst-case scenario, wouldn't that be weird?
Not really. Highly related to food processing; diastemata appear to have arisen many times among mammals.