What is the permaculture method for controlling varmints?

Farmers and ranchers oftentimes resort to poisoning or shooting animals they classify as varmints that threaten their crops or livestock.  Unless the varmint population has increased from consuming crops or livestock, they are integral to a balanced ecosystem.  Therefore, killing varmints that don't rely on crops or livestock creates ecosystem imbalance.  Ranchers are allowed to roam their livestock, and of course predators prey on the livestock. Ranchers are allowed to kill predators that threaten their livestock and kill burrowing animals whose holes may injure the legs of livestock when they step in the holes.

Do permaculture farming and livestock rearing methods reduce or eliminate damage to crops or livestock from wild mammals?  Thank for any replies.          

We have an unnatural population of varmits in our area. Oil drilling pushed all the ground animals toward the houses. We went from no noticeable ground squirrels to so many I can't barely raise anything. Our big dogs, while fenced, do discourage most predator action on our property. As such, rabbits abound. Our various piles of building material also help the rabbits out. I don't even want to get into wild birds. I know most people love them but I am fighting them hard in two structures that I just don't want them in and they will not leave alone. They keep nesting in the kids clubhouse and it's not ideal for nesting so baby birds fall out and die and this is a kids clubhouse so bird crap, debri and dead baby birds just really are not acceptable. I can't seem to keep the damn things out. I put up some metal in the roof gaps. I spray foamed it. I nailed some wood up. It seems like every time I block an entrance they find a new one and I'm so done with the damn birds in the clubhouse and greenhouse.

As far as how we control it, well we do shoot them if we can. We shoot a fair number of bunnies. We collect bull snakes and I love to put them down the ground squirrel holes. We've had a weasel out on murdering sprees. We encourage raptors with random telephone pole placement. We have a badger. A very prolific badger. Holes everywhere. He makes me nervous. The kids are under strict orders not to stick any appendages in any holes. This badger has been about our property for over a year now. We haven't seen it and that's fine. It can kill whatever it wants so long as it's not us.

we have an adopted cat that is helping us out with some of it as well.