This seems to come up a lot, so...here are the basics of pack behaviour and social dominance in canines.
Dogs came from wolves, which are pack animals. Exactly how long ago and by what method the split occurred is still unknown. Stray and feral dogs today still gravitate towards packs. In places where prey is small, dogs are more likely to hunt solo, but they still have social needs. Feral dogs, dingoes, and coyotes are flexible enough to pack up to hunt larger prey, or split up to more efficiently hunt small prey, as dictated by the environment. Adding to this, some breeds of domesticated dog are becoming further and further removed from their roots, and some breeds have less 'pack drive' than others, and/or are more willing to substitute human companionship for that of their own kind. Regardless, all dogs still have a deep-seated need to belong to a group.
In wild canids, the social hierarchy is largely determined by birth order. Pups come hard-wired to defer to adults, and adults (the parents) lead the pack. This "early brainwashing" for deference to one's elders tends to last until the elders become old and weak. Canids often despise weakness, and at this point will often challenge the old (or injured) for higher status. In fact, both dogs and wolves have been known to kill a sickly or injured canine outright! Dogs may be more likely to enforce a less flexible hierarchy, overall, due to their behaviours and skill set being a more watered-down version of wolf behavior (most don't have the amazingly fine-tuned social skills of a wolf). Dogs rarely get to live together as family packs, but even when they do, the WORST infighting often comes from sister-sister or mother-daughter pairings--too evenly matched, and the hierarchy becomes unclear.
When unrelated adult wolves or dogs are mixed together in a 'forced pack', each wants to know his place in the pack, and here you will see a lot more of the overt dominant and submissive posturing. This is why Zimen documented numerous conflicts due to hierarchy, whereas Dr. Mech explains that a biological wolf family has far less conflict. The hierarchy is pre-set by the parent-child relationship. Once the animal understands how he fits into the group, any status interactions are normally more subtle. Dominance hierarchies exist to REDUCE violence within the pack, and most dogs do not care about being "top dog", so much as they simply want to know their place.
Humans factor into the social hierarchy for multiple reasons. Dogs absolutely know we are not dogs (!) but they are simpler animals than humans. They know their own language, and they interpret the world in terms of their own perspective--as do many humans, for that matter. If you lean over a dog, it sends the same signal to him as if another dog were leaning over him, and his emotions or instincts react accordingly. This is why so many children are bitten for hugging a dominant dog. (Even more children are bitten for hugging a *fearful* dog. "Fight-or-flight" minus "flight option" = defensive bite.) It's why a dominant dog attacks the front or face--where a fearful dog would sneak up from behind. When a resource guarder is eating, he sends the same signals--stop eating, freeze, stare, growl, lip raise, etc-- out to any animal, be it other dogs, people, even the cat...and he expects you to understand those signals. Their programming does, to some degree, apply to everyone around them. Add to that, dogs can recognize human emotions and they watch our faces for information. They are interacting with us as surrogate packmates and they really, really appreciate an effort to meet them partway.
Dogs NEED to be part of a group, and they need the security of a strong leader within that group. Confident dogs who see a leadership vacuum feel the need to fill it, however uncomfortable and inappropriate that is for them, and insecure dogs fall apart without it. Dogs who are forced to take a leadership role test higher for levels of the stress hormone cortisol than dogs who are safe and secure in their proper place as a follower. People are NOT doing dogs any favors by failing to provide leadership. Being the boss is stressful, and dogs make poor decisions within our modern world.
Social dominance as Nature intended does not involve abusive violence of any sort--only psychological "hacks" to establish yourself as the role model your dog needs.
It is worth noting that dogs come pre-programmed to follow a strong, calm leader who provides for their needs. This is part of their culture, and they have social needs related to the submissive and affiliative rituals that all canids practice. They enjoy their appeasement rituals the same way humans enjoy shaking hands, or saying "Good Morning, how are you today?" Dogs also expect to be held accountable for their behaviour, and they don't take offence to being swiftly and fairly corrected by their packmates when they transgress. They forgive immediately...as does the one who corrected them. We could learn a LOT by watching how dogs operate in their own society.
Many of these concepts are usually--unknowingly--fulfilled by people who don't even "believe in" dominance! The normal give & take relationship of a dog within a structured household, who is regularly trained in manners and obedience commands, can often provide enough leadership for an easygoing, stable dog with a moderate to low pack drive. However, for those who enjoy knowing "Why" a dog does what he does, the underlying principles above explain how his needs are being fulfilled.
It's also worth mentioning here that a dog can't be a "pack animal" without a pack to act in cooperation with! If he is the only dog, and his humans don't speak the language, then there's no one to "speak Dog" with...and that dimension of his life goes unfulfilled. Pack behaviour can't happen in a social vacuum. How social do humans appear, when they are kept all by themselves? And how much do their social abilities degrade, over time? Yet, we humans ARE a social species. In order to be socially savvy, one must be allowed to learn the social framework, and have frequent opportunities to rehearse it.
While dogs do correct each other for infractions, physical punishment and social status are two different things. Unpredictable aggression has nothing to do with increasing status, and will actually undermine it by removing the trust that the pack structure is built upon. Scruff pulls, "alpha rolls" (which are requested by the alpha through posturing, and OFFERED by the subordinate), muzzle grabs, and pinning are methods used by dogs to correct one another--mainly by the mother dog or wolf, towards her pups. Dogs do understand these things when practiced by humans, but the situations in which they would be appropriate are few & far between. However, just like leash pops and sharp "Ahhh!"s, these are *corrections*, not "dominance". Striking someone with the hands is a primate (monkey) reflex, and has nothing to do with dogs on any level, let alone socially. A leader has the right to fairly correct an underling for infractions, without recourse.A disrespected bully, on the other hand, who holds his rank by force, is likely to be displaced by his own method of choice: aggression.
Dogs are emotional creatures, not machines, and they live in the real world, not in the lab. Simplified mechanistic routines like operant conditioning (positive reinforcement &/or punishment) are not enough. Dogs have rich inner lives and deserve to be treated as sentient fellow beings, and to me that means making some attempt to understand their language and social customs, and to meet them partway in navigating this complicated world that we all share.
Further reading: Dogs know we are not dogs...
Follower's Boot Camp, aka How dominance REALLY works
Information from field scientists
Here are some studies discussing feral dogs in packs. Most hands-on people who work with ferals (not free-running owned dogs out on a lark, but actual ferals and pariahs) are well aware of their tendency to run in packs. Dogs are very flexible and, like coyotes or dingoes, will pack or not-pack depending on food source and other needs.
As field scientists will tell you, including the #1 expert on feral dogs listed above (the Feral Dog Blog by Dr. Mark Johnson)...
"Many people want to rid themselves of dominance so much that scientific studies are being interpreted to support their beliefs (which is always the weakness of science) and people are coming up with new interpretations of what wolves have always been doing."
Always be wary of agendas. Watch the canids themselves, if you want uncorrupted data that never wavers with the latest bandwagons or human ideologies.