Basically, aperture determines DoF.
Correct as usual but I'll add, just in case a few people don't know, it is the actual physical size (the diameter) of the aperture that affects DoF not the f-number (although the f-ratio typically falls out of optical formulae when you end up with an f/d). If it wasn't for diffraction, a tiny aperture would render everything in focus with no need for a lens which is how a pinhole camera works. Yes, in the DoF calculators you must plug in the f-ratio but that is just used (along with focal length) to calculate the diameter (in mm) of the aperture. My turn to wait for a correction from neuro
Question to neuro (because I just tried but quickly gave up playing with the formulas): changes in subject distance and focal have an opposite effect on DoF but is it equally offsetting for the same framing/subject size? There is an article on Luminous Landscape that demonstrates that if camera position changed to keep subject size the same within the frame, DoF remained visually equal regardless of focal length. This makes sense when one understands that the physical size of the aperture is smaller for shorter focal length lenses for the same f-number. But is it mathematically equal at least first order?