I was going to try to trick you and ask you to guess which dog is the “alpha” dog. Tigerlily is 12, a curly barbet, and Bee is a 7 year old mixed breed. Both are spayed females. And the answer to my silly question is “it depends.”
Dogs change roles, they trade places and behave differently in different contexts. The term “alpha dog” really doesn’t mean much if it means anything at all.
What matters is that Bee has great social skills around dogs, and she is most eager for human contact (which is really evident when Albert leaves the room, as she will stare after him and bounce around with excitement when he comes back). Tigerlily is most driven to sniff and hunt, which is obvious by the way she might scream with excitement if a kitty approaches her.
Bee is more dependable off leash around prey, whereas Tiger performs best doing water retrieves and tricks that involve retrieving games.
Bee dominates (babysits) Tiger in many situations. She tells her what to do and helps me keep her out of trouble. But Bee also grovels, she used to submissive urinate, she is sensitive and emotional, while Tigerlily is tough as nails and doesn’t need attention but knows how to get the things she does want.
Labels , such as alpha dog, can make it difficult to see behavior objectively. There are many reasons why one dog might behave aggressively, or why another might seem like such a wuss. It’s not because one dog is alpha and the other dog is not.