Western slope (Palisade) here!
The higher the altitude the lower the cylinder pressure, so the lower the octane needed. Very general decsription put loosely in laymans terms for most people out there.
Ambient temperature also has a lot to do with this. Engines are more prone to 'ping' or 'knock' (detonate) at higher temperatures, mostly to do with combustion chamber design and what goes on inside when detonation (sometimes called preignition) takes place. For example, my late model high-performance vehicle (2000 Dakota R/T 5.9) will tolerate 85 octane in the dead middle of winter and 87 octane in the early spring and late fall. As soon as the ambient temperature gets above about 85*F, I must go to 91 octane fuel, or it pings like crazy on hills and under part throttle acceleration. And yes, I've checked its OBDII system thoroughly!
Most late model vehicles have knock sensors in their engine management systems to avoid damage when detonation or preignition occurs, but when the knock sensor sees this condition the first thing that it does is to retard the ignition timing to pull the engine out of trouble. This causes a lack of power and loss of fuel milage among other things. Not good. An extreme case of detonation will also cause the fuel management system to go to full rich condition and will basically put the system in a 'limp home' mode. Also not good.
There is no hard and fast rule for octane requirement at high (govt says over 4000ft) altitude driving. Internal combustion engines vary at least as much as our AR's do from one to the next. Two points of octane rating lower that what's recommended at sea level is a good rule of thumb for the uniniated to use, but that's not carved in stone. Use your brains. If your car is knocking on 85 go up a grade until it doesn't knock anymore. Never mind what the owners manual says. Remember the adage - YMMV!