*Science says:

"... misinterpretation and total misinformation like Kelley's has plagued me for years now. I do not in any way reject the notion of dominance." -Dr. L.David Mech

"Dominance is among the most pervasive and important behaviors of wolves in a pack."-Dr. L.David Mech

"It is absurd to argue that dominance (as an attribute, a property) does not exist when there are so many words for it, depending on context and nuance. If it didnít exist, neither would these terms. The numerous synonyms and connotations suggest, not only that the term is hard to define, but also that a property of behavior has been observed whose features are sufficiently dissimilar to other properties to make it worth classifying and naming." -Roger Abrantes, author of "How to Speak Dog".

"The concept of social dominance is not a myth. A myth is an invented story. The concept of dominance has been, and remains, a very important one that has been misunderstood and misused, often by those who haven't spent much time conducting detailed studies of other animals, including those living in the wild.
Dominance is a fact. Nonhuman (and human) animals dominate one another in a number of ways...."
-Dr. Mark Bekoff

"I discuss and explore dominance in canids because dominance can be a valuable AND COMPASSIONATE tool for capturing and handling feral or fearful dogs, which is the theme of this blog." -Veterinarian Mark Johnson, foremost authority on capture and handling of feral dogs.

"And why are so many people stating emphatically that feral dogs do not form packs? Please, I have captured and handled feral dogs around the world and feral dogs can run in packs and often do. " -Veterinarian Mark Johnson, "Is Dominance Always Bad?"

"Fighting and physical dominance rarely come into play during the maintenance of hierarchical harmony. On the contrary, the major function of hierarchical structure is to lessen the amount of fighting. Once established, the hierarchy provides most of the solutions before problems arise. For example, when there are two dogs but only one bone, the ownership of the bone is pre-decided and therefore, there is nothing to fight about." -Dr. Ian Dunbar

(Who do you think gets the bone?)

(Wolves and dogs have identical body language, and communicate freely. The books on dog communication, still in use today, were all based on the "wolf model". Are dogs = wolves, for purposes of communication? You decide.)

-->The data on wolves not showing a lot of dominance displays in the wild, comes from the fact that in the wild, most wolves live in *families*--where pups are automatically submissive to adults. This often carries over for their whole lives, or until they leave the pack, or the alpha gets weak and is overthrown. In mixed groups (such as anything in captivity), dominance displays are more common, as the social hierarchy was not already pre-set by the parent/child relationship.

Positive reinforcement is also good science: operant conditioning. There are many different forces shaping animal behaviour, and they operate TOGETHER--they don't compete.
*To be fair, punishment is exactly as valid of a science as positive reinforcement--it's the "other half" of operant conditioning! However, unless you are 100% sure the dog understands what you're asking, and has no additional reason he can't comply [fear, injury, etc] it is not fair to consider punishment. And speaking of "fairness" in dog culture, you are also not socially appropriate to use corrections unless you have a properly aligned relationship with the dog. Corrections are taken in context, and punishing a stranger is NOT the same as admonishing your own subordinate. Punishment should be a last resort, even if "it works" and has valid science behind it.

Dominance is psychological. While dogs do practice some physical acts to get their point across, these are simply rituals to accent their social standing.
DO NOT HIT YOUR DOG. That's not "dominance", and it won't get you where you need to be. Dogs need leadership above all, and the hierarchy provides that--no violence necessary! Having a rank system conserves energy, and prevents the damages of actual fighting. It fills a functional need for any cooperative, group-living species--to settle disputes, and give direction. 'Follower dogs' are happier, more secure, and scientifically proven to have lower levels of stress hormone. By neglecting leadership, owners are HARMING their dogs, not pleasantly "spoiling" them...that's why it's so critically important to help people understand the concept of social dominance, and the proper application of it.

You have to try very hard to NOT see a social hierarchy--in dogs, humans, or other group/pack/herd animals. (In fact, dogs are a strange case, in that they're the only social, hierarchal species who have "social hierarchy Deniers"!) Some dogs clearly perform the classic behaviours associated with that framework--such as "correcting" (snapping at) their owners when they sit on "the dog's couch" or do other things the dog doesn't like--and the problems are resolved by using that framework's solution: usually, a No Free Lunch/rank reduction program, confident leadership, and managing the environment.
Yes, hierarchies are fluid. Yes, many behaviour problems have *nothing* to do with dominance--they are training issues! Yes, dogs don't always want the bed, the biggest bone, or whatever you expect--they pick & choose what's valuable to them. I understand that the term has been misused, and misunderstood. (It's terrifying how misunderstood it is, even around "dog people"!) However, I find it better to explain how it really works, and what it ISN'T, than to pretend something that the average person witnesses all the time "does not exist". :-/