The problem with having an invasive species in the area is the replacement of the natural wild animal.  I'm not saying that this is perhaps a problem with turkeys.  An example of domesticated animals being introduced into the wild is rabbits.  Rabbits are not hares.  They are domesticated even the cottontail rabbit is a hare.  The balance of nature becomes disturbed when the less elusive "rabbit" is introduced into nature.  They are easier game for predators to catch because they don't have the instinct and blending ability that hares do.  Example of this is a black rabbit in the snow.  It might freeze but it can be seen!  What happens is the snowshoe hare becomes overpopulated because they are harder to catch by prey animals.  This leads to damage or loss of eatable items to support new hares.  Voila! When the starvation occurs what happens to the predators that have eaten all the rabbits and the hares have starved which decreases the population for predators to eat!  Make sense?