Of course they do. They’re cats
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Of course. They’re not bunny rabbits. I read about one South American country, one of the smaller ones in the south, that when Europeans got there and set up shop, the place was soon overrun with rats. Turns out there were ZERO cats around there. They impported some cats, and voila! Rats stopped running the show.
Without cats, rats and mice would rule the world.
My eternal gratitude to our feline benefactors.