No, coyote will not become the apex predator but greatly reduces the populations of foxes in order to reduce competition for available resources. Yes, The coyote population will decreases because t
he gray wolf kills coyote to avoid competition for food resources. If another wolf is introduced to fit the same ni
che, the coyote population will decrease because the wolf feeds on coyote. As the number of coyotes increase, the number of beavers will decrease because coyote feeds on beaver.
If the gray wolf became extinct, the coyote population increases in that location due to no predator.