We had loads of rabbits for many years before Katrina. After Katrina, the swamps around our area had so much activity in them with contractors building levees to prevent flooding in the next hurricane that they ran all the wildlife out of the swamps and into our areas. We had more deer than we had ever seen plus fox that we had never seen before and more coyotes than a thousand road runners could kill. The coyotes cleaned out the rabbit population and then started on the cats, small dogs and chickens.
They worked their way into the suburban areas and got the residents angry and complaining that something needs to be done. The politicians found articles that stated that killing the coyotes just leads to even more coyotes being born and increases the population. They encouraged everyone not to shoot the coyotes. With ever increasing complaints about the coyotes, they voted to hire trappers to start trapping them but the trappers all said it would be a never ending battle getting rid of them and advised the politicians to inform the public to bring in their small animals at night and to never leave food out at night for pets.
I've lost several barn cats and many chickens, most during the day, and have resumed hunting them but it isn't easy. You can sit in a stand for 6 nights straight and go relax on the 7th night and the next morning go out and count your losses. With my dogs and so many neighbors dogs around, poisoning them is out of the question. I have wondered if some type of birth control pill could be used to control the population.