It is thought by some historians that the turkeys served by the Pilgrims were actually Mexican turkeys brought over on the boat.
Mexican "bred for eating" turkeys had already completely taken over from the peacock (ostentacious, but not very good eating) as the festival bird throughout Europe. The wild turkeys of the day would have been very hard to hunt, tough and not very meaty. It is descendents of Mexican turkeys that we eat today.