Yeah Stef., it is all about shutter speed and you take what aperture the cameras offers. (You do not have to stop action as noted by the flutteirng on your greater Antillean grackle. Wing blur can be very effective--provided the head is sharp.)
The head has to be in dead focus and that is why we shoot digital these days--on moving stuff I shoot a LOT for two reasons. 1) As good as AF is, it is not perfect. 2) As good as I think I am, my aim is not perfect. See below.
I get about one good shot per 100 images on flying birds. I've had days where nothing works. I recall one day two years ago I took around 800 images and got about 20 good pcitures--and a handful of top-drawer images ...one I sold recently. Digital rocks. I'd quit taking serious pictures before DSLRs came out. It is all good.
One more thing. If the light/lens is too slow then boost the ISO...or come back tomorrow when conditions improve. You are better off with a noisy image than a blurry image--or NO image. Case in point about high ISO salvaging a "one of" chance.
The moose is blurry from panning, but high ISO salvaged the actual moose shot.
OOPS ... it is the aim
(And, yes, that is a skim of ice on the background pond! Been cold here again!)