They achieve that "natural equilibrium" by starving en masse. It's why I started hunting deer in my country - no natural predators, so they'll breed until they

They achieve that "natural equilibrium" by starving en masse. It's why I started hunting deer in my country - no natural predators, so they'll breed until they outbreed the carrying capacity of the forests they browse, and then they'll suffer long and agonising deaths, and in their desperation will devastate the forest, eating anything that's remotely edible, seedlings gone, bark stripped from adult trees.