The phrase "alpha dog" refers to someone who is the most dominant, powerful, and influential person in a group or situation. They are usually seen as the leader and tend to take charge and make decisions. Full definition
As newborns, their mother plays the role of alpha dog. (puppy-basics.com)
It's important that you hold the «alpha dog behavior» position and that each family member are viewed as holding a higher position than your dog. (dog-health-guide.org)
That's a great write up on Alpha dogs and pack mentality. (chasingdogtales.com)