What would be some innate behaviors for an arctic fox?

the artic fox, although beautiful, relies on hearing, movement under snow, and mostly scavenging from polor bears..

Explanation:

this is just how they are programmed to survive..they are opportunistic, in a desolate environment with prey that take a lot of they're energy to track down, more energy is spent hunting mice, rabbit, and finding carrion..

if the hares very faster than they are now, and thus the lynx's hunting success rate drops because it will be harder to catch them, the rate that will change will be the pray-rate. the pray-rate will change because more hares will be able to survive, thus more individuals for reproduction, so the end result will be increasing population of hares.

the predator-rate will remain pretty much the same because there will be more than enough pray, but the hunting success rate is stagnant.