It's the same in the Galapagos islands too. I wonder how it is that rats are so fierce that they destroy everything they touch...
We use a bigger version to catch possums. Its hard to tell how many we catch though, as the feral pigs like to carry off and eat the dead ones. Its really a fascinating logistical problem trying to eradicate a broad spectrum of pests.
That being said, wild rats are very destructive because of their hardiness and intelligence. Raccoons may be the top animal for intelligence in urban environments, but they can't match rats for their destructive potential.
Many predators live in balance with the population of their preys. When the predators are too successful, the prey population will diminish, which causes the predator population to shrink, which is good for the preys, etc.
But omnivores like rats can wipe out an entire prey population and then just switch to some other source of food.