In short, no they are not.
People get really passionate over the subject of dominance with regards to dog training, the idea has been around for a pretty long time.
It comes from a scientist called Rudolph Schenkel, he studied wolves in the 1930s and 1940s, and found that they fought to establish dominance. The winner was called the Alpha, and they were able to access resources before the others.
Over time people assumed that dogs must be the same, as they’re descended from wolves. This led to millions of books, articles, tv shows, documentaries, and textbooks, all telling us about the Alpha Dog.
The reason Rudolph Schenkel’s studies had the conclusion of the ‘Alpha’ is because the wolves he was studying were captured from different areas and different packs. They were then caged with each other as strangers in a small area. This led to protective behaviour and confusion. Wild wolves don’t act this way at all. In fact, they’re a family unit of two parents and their cubs, just like many human families. Sometimes the pack has older siblings that stay and grow the pack but the senior parents remain the leader till it’s time to step down. There is very rarely any inter pack aggression.
On top of the flaws in the study the problem is that dogs aren’t wolves anyway. There is 30,000 years separating the two animals. Dogs have grown and evolved with humans over this time.
Unfortunately for dogs, this myth just won’t die. Popular tv shows and books perpetuate the idea that you should be the ‘pack leader’, and if you don’t eat and go through doorways before your dog they might try to take over your household in the night whilst you sleep. Many people tell me, “I know I should probably be more firm with my dog so she knows I’m the Alpha…”. But that’s just not true!
In reality I t’s all down to the relationship you have with your dog. If you like playing rough and tumble with your pup, good stuff. If you want your dog to never get on the sofa, great! If you want your dog to sleep in your bed with you, no problem.
It’s up to you to decide what rules you put in place and how your relationship works. As long as you're not hurting or abusing your dog and ensuring they are happy and engaged to the best of your ability it’s all good.
Your dog is not trying to be the Alpha, so stop worrying about that and enjoy the relationship with them.