SarasotaClucker: As a professional wildlife biologist, I have to weigh in here. The idea that keeping chickens would increase predator populations is unreasonable and inaccurate. First of all, is inappropriate to lump all predators in the same category. Each species varies with diet, territory size, and population density. While it is true that increased availability of READILY AVAILABLE food can increase density, one must not consider a backyard chicken coop as readily available food. The availability of dog food, cat food and bird feeders are a steady supply of food for many of these wildlife species, and usually goes undetected. In urban areas, the direct, intentional feeding of wildlife is much more prone to increasing populations than opportunistic food availability. The difference is that backyard flocks are traditionally small and enclosed. Owners of backyard flocks typically do not tolerate the presence of meso-mammals (coons, possums, coyotes, skunks, etc), and such intolerance (aversive conditioning) has been proven to decrease presence of many species. Additionally, if a chicken is eaten, unlike dog food, that "food source" is lost and they have to go elsewhere to find the next meal the following night. Even if a whole flock is lost, that feeds 1 or 2 animals for a few nights. Such limited food source is hardly enough to 1) sustain an increased population or 2) increase reproductive output such that the numbers are increased.
Also consider the myth that just having wildlife near urban areas will lead to an attack. Coyotes have to be tolerated and basically hand-fed before their behavior becomes worrisome. Much work by Dr. Stanley Gehrt in Chicago and others (new book Urban Carnivores is EXCELLENT) has shown that urban coyote diets typically are made up of less than 6% "urban" type items, including trash, feral cats, etc. They are much more likely to eat fruits, berries, roadkill, rats, mice, snakes, etc in parks or undeveloped land.
There's much much more to write, but I'll spare you my rant!