Coyotes don't decrease deer or turkey populations. We've seen that in the past 40 years both deer and turkey populations have exploded across the country. In fact, predation causes prey populations to increase in the long term. But this isn't Population Dynamics 101 so I'll stop there.

If you want any reason to kill coyotes at least be educated about it. The reason to control coyote numbers is to help foxes, endangered birds and endangered small mammals (like Pygmy Rabbits). Fox populations have decreased substantially almost everywhere they occur in conjuction with coyotes.