15" to 16"?
 

Can I replace my 15" stock alloy wheels on my 2011 ranger 4x4 with 16" stock alloy wheels from my 2001 ranger 4x4? Will it cause any problems with transmission shift or operation?

go for it. wont harm anything at all. rim size changes nothing in terms of speedo/odometer. its the tire size that matters

The 15" rims have 235/75: the 16" have 255/70

Using this link: Tire Size Calculator - Compare Tire Sizes

Your speedometer will be off by about 4%. It will read 4% slower because you are going to a larger diameter tire. When your speedometer says 50mph, you'll really be traveling 52mph. Not that much of an issue and will not have any adverse effects on transmission or anything else. In fact Ford speedometers tend to read a little on the high side compared to actual speed anyway.

Also, 255/70R16 is the factory size on '03+ 4x4's with 16" rims. Prior to that, they were 245/75R16 (a little skinnier but the same overall height). You'll be fine. SWAP AWAY!!