Sounds like a lot of coyotes. We found a fur buyer in our area who will buy our pelts taken from Nov. to mid March. If we don't want to skin stretch and sew the hide he will give us 50% of what we get from the prepared hide. We don't hunt them just in the winter we hunt them 7 days a week 12 months a year. Most of our summer hunting are problem coyotes cattle and sheep farmers call us to take care of.
Down below I have recipes for coyote. We only take parts of young ones to cook and they are as tasty as any thing when cooked properly.
Once you take out a goodly number and put enough pressure on the coyotes they will leave the area. the other game animals will rebound with no coyotes to eat the turkey eggs and little chicks before they can fly. The fawns will live to grow into adult deer and if does have babies of their own.
I second hunt and kill every coyote you can. You can make some pretty good money if you learn to skin stretch and sew and have a fur buyer to sell to.

Al