The interesting thing here is that I've seen the same basic stats used to indicate how awful outdoors cats are on native bird population. The flip side is that without 'em, we'd see a lot more rodents eating things up. #ddtb
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What If All the Cats in the World Suddenly Died? | How Cats Impact the Ecosystem | LiveScience
Cats may seem lazy and ineffectual, but in fact they play a vital role in the ecosystem. Without them, the world would be overrun with rats.

I once had a cat who would climb the tree next to our flat roofed garage and wait for birds to land. Then he would pounce down on them. I also had a neighbor who complained about it. I told her the cat hunted mice and moles and kept that population down, but she called the SPCA and the Town anyway. They didn’t listen to her, much to her chagrin.
Our cat Mist had one eye. And a bell on her collar. We figured any bird she caught was an improvement to the gene pool.