and your professional experience on this matter is what??
HOW many folks actually have HEN HOUSES anymore? and those that do, , do you really think don;'t have protection for there animals they keep ion them??
Typically in nature
when there is a lack of food for predators, , predators either move to find greener pastures, or they DIE , due to lack of enough food to sustain themselves!
and when there are TOO many rodents, it normally is due to HUMANS and NO lat of predators
humans waste more food and allow rodents to explode into high numbers, mostly a problem in places where natural predators are NOT a viable option to TRY to control them and once the population of rodents get too high, even natural predators cannot keep up with them to control them!
this typically is where science and chemicals tend to be needed to restore things to lower levels!