Public service announcement! :-)
Dominance has nothing to do with physical violence.
Scientists and dog/wolf experts do not deny that dominance exists.
The "debunking" of dominance has, itself, been thoroughly debunked.
An awful lot of people don't even know what this term means any more. It refers to the social hierarchy that all of Canis follows. However, some "positive reinforcement only" trainers are sick and tired of people hitting their dogs, in the (misguided) name of "dominance", so there is a modern movement to throw off the bad habit by denying that there is a social structure at all, including its leader (or "alpha") who has the right to make demands. This "boss", which dogs are naturally hardwired to accept, is a role perfect for the human owners--yet sadly too often filled by the dog itself, causing stress and problems for both.
Both social dominance/leadership AND positive reinforcement have their place, and when combined, make for a nicely balanced companion.
~This little girl shows lovely submissive behaviour towards her elders. She was readily accepted by the pack, and is responsive to human wishes as well.
Here are three additional links explaining what dominance actually is (and why it can cause problems) : Vet link 1 Vet link 2 SPCA link For further reading, you might try books by Roger Abrantes or other highly experienced ethologists.
p.s. The "alpha roll" is not forced by the alpha! It is volunteered by the subordinate. This is an important distinction, and a lack of understanding of how this mechanism works is likely to get you bitten, especially with a truly dominant dog.