Breathing and Running in Primates

[CDarwin]

I know that in horses, breathing while running is coupled to the strides, so that a horse can only breath once per stride. In humans, this is decoupled, so that humans can breath as much as they want per stride, and this is often cited as some very monumental thing in human evolution.

 

My question, if you will forgive its naive obviousness, is whether-or-not this has coupling has actually been demonstrated in quadrupedal primates or if its just a thing in striding animals like horses and carnivores and the like. Those are the only animals I've ever heard actually spoken of as having linked breathing and running.

[Glider]

It might have something to do with the swallow reflex. Humans have to stop breathing to swallow (saliva etc.) and as humans breathe both through nose and mouth, breathing would have to be decoupled to allow a panting human to swallow without choking. Horses, on the other hand, can't breathe through their mouths and so can swallow and breathe at the same time.