From Wired Science which notes why man has succeeded in breeding big turkeys when evolution failed–it’s not as complicated as you might think:
…the key technical advance was artificial insemination, which came into widespread use in the 1960s, right around the time that turkey size starts to skyrocket. The reason is that turkeys over 30 pounds are “inefficient” breeders: It’s difficult for them to actually perform the natural mating act. With artificial insemination, the largest birds can still be used as sires, even if they have a hard time walking, let alone engaging in sexual reproduction.
Hat tip: @m_sendhil.