P mode means the camera chooses the aperture and shutter speed for you. When you turn the dial in P mode, you're applying exposure compensation, and actually, the camera will decide whether to shift aperture or shutter speed (usually it shifts both if you apply 2/3-stop or more). A Canon dSLR behaves the same way in P mode.
If you want to use the dial to change aperture, that's Av mode. Select Av from the menu and leave it there. You pick the aperture you want for DoF, the camera picks the shutter speed (and ISO if that's set to Auto).
Are you referring to turning the wheel thingy beside the shutter button (dslr)? If I turn than in P mode in my t2i it will shift the exposure reading. It will be the same exposure but the camera will assign a new combination of av and tv. So if you shift AV a stop smaller, then the camera will slow down Tv 1 stop. Now not quite sure this exactly what happens if Iso is set to auto. I can confirm when I get back home and play a little. But if ISO is set to a fixed value, I'd expect the behavior I described.
This is a trick I do to alter dof when in P. I do shoot in av too but in this case I was in P while using the M.
It actually works in the M as I described but very hard to do. Half press the shutter and when focus and exposure is confirmed, turn the d pad wheel and you will see the Av and Tv value shift. The shutter must be half pressed while you turn the wheel and that what makes it almost impossible to do. You have to use 2 hands! On the dslr the confirmed exposure info stays on the vf or lv longer and gives you time to lift your index finger off the shutter and use it to turn the small wheel to shift the calculated exposure.
Bodies: Canon 6D, 70D, T2i gripped, EOS 5, EOS 100, EOS M
Lenses:EF 24-105 F4L, EF 70-200 F2.8L mkII, EF 100 F2.8L, EF 50 F1.8, EF-S 18-55mm, EF 28-80 USM, EF-M 22, Rokinon 8mm HD Fisheye, M mount adapter
Other : 540EZ, 320EX, 430EX II, Yongnuo triggers & strobist stuff