It's not dominance. Seriously, it's not. There is no dominant breed. You don't have a dominant dog. Your dog's behavior is not a "dominance thing."
Now, I realize those statements might be causing some hardcore cognitive dissonance right now. Because from the moment you even became aware of dogs, you have been told that dogs are pack animals and a bunch of dominance stuff based on that assumption.
From the Merck Veterinary Manual:
"The dog’s social structure has been referred to as a pack hierarchy, but this does not accurately or entirely describe the relationship of dogs with other dogs or with people."
"The term dominance...is a relative term established by the value of the resource to each individual and the cumulative effects of learning."
For example, Animal A might challenge Animal B for a mate. Animal B might defer. But does that make Animal A the dominant animal?
What if Animal B waits until Animal A is distracted and mates with that female at another time? Is dominance even relevant at this point? I would argue that learning is far more pertinent than hierarchy.
The problem is that people tend to think of hierarchies in dogs just like hierarchies in humans. Governments, militaries, churches, schools, corporations all have linear hierarchical structures.
However, when it comes to dogs, it's not that simple.
"Hierarchy in dogs is neither static nor linear, because the motivation to obtain and retain a specific resource, together with previous learning, defines the relationship between two individuals for each encounter."
In other words, if you push me out of the way to get the last chocolate truffle, and I walk away...but I don't actually like chocolate truffles (I don't), you're not actually establishing dominance. I didn't want the resource, anyway. Or maybe I learned that, by walking away, I will be given the key to the room full of caramels. Mmmmm. Caramels.
What about aggression?
"A 'dominant' animal is not the one engaged in the most fighting and combat. Most high-ranking animals seldom have to contest their right of access to a resource. Instead, high-ranking animals are usually better identified by the character and frequency of deferential behaviors exhibited by others in their social group and by their ability to respond appropriately to a variety of social and environmental circumstances."
So, it is not the "dominant" dog who growls over a bone or fights with other dogs at the dog park. When your dogs are fighting at home, identifying the alpha is about as productive as a snipe hunt.
Why does it matter? Because if you are told that your dog's behavior is the result of dominance, the solution is almost always some form of rank reduction. Everything from making the dog sit for every bit of affection to methods that are too disturbing to detail. And it's all called "leadership."
Trying to change a dog's rank in an imaginary hierarchy only serves to delay behavior modification. In many cases, it makes the situation much worse.
If we want to change behavior, we need to explore the dog's health, environment, and learning history, as well as identify triggers and consequences for the behavior. From there, we can develop a complete plan that addresses the needs of the individual dog, reducing their stress, increasing tolerance, and reinforcing desirable responses.
Next time someone tells you that if your dog jumps, pulls on the leash, leans on you, sits on your foot, sleeps on top of the couch, barks, mounts/humps, doesn't listen, or anything else that isn't obedience or cowering in the corner, it's dominance, what they're really saying is that they don't understand dog behavior and are probably not someone you want to take advice from....let alone pay for that advice!
Relax. It's not dominance. Now we've got that out of the way, let's focus on changing behavior!
"But what about mounting/humping?" Here's a very good summary on the topic.