People think cats might be controlling rats but that’s just not the case. If you took cats – wild and domestic – away the rat numbers wouldn’t increase because there’s no more food for them. Certainly cats take a few rats from time to time but they are not actually controlling the population.
Studies have shown that rats cannot break into large eggs – eg hen size and larger. They are unlikely to take on an adult bird so what they do is wait until the eggs hatch and then take the chick in the first 24 hours. This is what decimates our seabird populations.