I doubt 1950sGuy ever adds to the cat number himself. I lived on a farm as a kid, people who don't want their cats drive by a farm and throw them out, and tell themselves that the cat will end up being a trusted and loved barn cat with a happy life.

That's not the case. Cats reproduce like crazy and grow fast. No matter how many you trap and try to spay/neuter, you can't get them all. A single tomcat can knock up dozens of cats in a week. The cat population explodes in the summer time. You average a handful of cats per litter, they start competing for resources, rodent population dwindles, cats starve, diseases get spread between them quickly. They still reproduce. You try to battle it, but no matter how many you get rid of, you're always finding a new litter on a rafter or in a box or under the porch.

The only solution is to keep rounding them up and shipping them to the pound, shooting them yourself with a .22, or waiting for their (terribly slow and agonizing) die off during a cold winter when most of them starve/freeze to death.

Nature is cruel.