Can an Army of Feral Cats Help Solve New York City’s Rat Problem?

Answer to all of these questions about predators solving prey problems: no.

if the cats eat all of the rats, there will be no food left for them, so someone will start starving to death and the population of cats will diminish. As the predator population diminishes, there will be fewer cats to eat the rats so the rat population will increase. There will be more food for the cats at that point, so the cat population will increase. This cycle is called Liapunov Stability and it has been extensively studied. Predators do not get rid of their prey for the same reasons that we do not erradicate cows and chickens.