There’s a theory that cats mostly domesticated themselves; human settlements and their large grain stores proved to be a reliable source of rodents for them to hunt, and the humans tolerated the cats because they kept the rodent problem in check, but these cats would have lived a semi-domesticated lifestyle around human settlements without initially being kept as household pets. Maybe the feral cats of Istanbul are the closest modern approximation to this.

Definitely in line with the axiom of sits where fits

When I was a kid, that still used to be the norm on farms. There were farm cats and house cats. The farm cats were there to kill rodents and otherwise minded their own buisness. You could not just take them up, they would have bitten you. I think this has gotten out of style, as I have not seen the division nowdays and all cats seem to be gotten tame.

Barn cats are still a thing, but they are typically still owned and kept whereas I was talking more about free roaming cats that live around human settlements. The early free roaming cats would have been about as tame as barn cats; my impression is that the cats of Istanbul are more friendly.

Rodents are an issue of trash and food left around, not a problem of not enough cats.

Cats shit in my garden and leave dead songbirds where I grow food. No, we don’t need more cats.

Do you not think rodents are in your garden … where food is left around?

To be clear, your claims are:

1. An increase in the population of predators will have no effect on the population of the prey.

2. Rats don’t shit and/or aren’t attracted to food.

Are you speaking in jest or do you actually believe those? The fact that your second statement directly contradicts your first doesn’t help.