What role does the Arctic Fox play in the environment

The arctic fox is a carnivore. he is to keep the population of other small animals low. If there was not a carnivore to keep the population low of lets say rabbits, they would be way to many rabbits. and they would multiply and multiply. after a while there food would run out, and animals share food in this world so other things would die of. they role is to keep other small animals in there place