That is a dominance display, but that's not what dominance theory is.
Dominance theory is the belief that wolves live in packs that have a linear structure of hierarchy (alphas, betas, omegas) and that carries over to dogs, but that's wrong.
1) Wolves don't live in packs organized like that. That was based on a study of captive wolves in the 1940s and has since been disproven. Wolf packs have a breeding pair and puppies. THey don't fight for dominance. When the puppies are old enough they simply leave and start their own packs.
2) Some dogs are more dominant than others, and some may have a self perception of being more dominant than their owners, but in many instances this is not the case. Dogs don't understand humans and they don't understand what humans want from them- many times when they misbehave they are just being a dog. Severe behavior problems may be from fear or aggression, but that doesn't mean that the dog is trying to dominate you, it's just from early upbringing by its mother, littermates, breeder, and owner in the first 4 months or so of its life.
"The whole dominances thing is, once again, a case of leaping to a conclusion before ruling out more obvious explanations. Dogs chew furniture because what else could furniture possibly be for? They are disobedient because they have no idea what the command means, are undermotivated to comply or something else has won the behavioral gambit at that moment in time, like a fleeing squirrel. Rank is not on their minds." Jean Donaldson
Dogs are dogs. If one bites, it's not necessarily being dominant. It might have fear issues, it might be telling you something in dog language like "leave me alone," or it might just simply bite because that's what dogs do. Dogs are motivated by rewards. If a dog doesn't come when its called, that's because it's chasing a squirrel, eating poop, meeting another dog, etc. Not because it thinks that it's dominant but because it's having fun. Dogs simply don't think like that. Instead of bullying dogs around owners should concentrate on teaching them what they DO want. If a dog barks at the UPS truck, teach it to come when called instead of yelling at it.
For training I recommend "Don't Shoot the Dog" by Karen Pryor. I also really like "It's Me or the Dog." Victoria Stilwell is a great example of a modern trainer who uses positive reinforcement which is the accepted method in dog training today.
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