I love this topic and here is how we feel.
We live with a large pack of dogs and are constantly introducing new dogs for days or weeks at a time. This gives us a consistent opportunity to observe the dynamics of an ever changing pack.
We are not fans of speaking about 'dominance' or 'alpha' because it tweaks the human brain too much. It does exist but not in every environment or within every animal. Most families have parents who call the shots and set the rules and boundaries for that family, but kids should not be in charge and teenagers shouldn't be telling the parents what to do. But all families have different ways of implementing the rules of the houses: some are militant, some are more low key in how they maintain balance in their homes, some homes have no rules what so ever and typically might suffer for it as their children grow and test their world.
Dogs are very similar. Young dogs need guidance, discipline, rules and boundaries in order to learn their place in the world and how to get along. Remember that a pack should strive for balance and harmony in order to live as stress free a life as possible. The more clear the structure of the pack is the easier it is for every member to know the rules. The less clear the rules and boundaries are the more likely the members are to constantly test each other = less harmony. Structure is determined by the leaders of the group.
Alpha (dont like that word) roles can change in a heart beat and change within each environment. Think of your own home, you might be in charge of your hobby room in the house but your spouse is in charge of the kitchen. One dog might be in charge of the other dogs behavior in the house but not outside, when another dog takes over. So 'who' is in charge can change with the environment.
We tend to describe the whole situation as this... there is a ball in the home with the word LEADER on it. The person needs to be carrying this ball at all times. But because people are so easily distracted they drop the ball all of the time. The dog is always watching who is holding the ball, and if it gets forgotten then they are ready to pick it up at anytime. There are different kinds of dogs who will respond to the ball in different ways. There are dogs who are ready to steal the ball at any chance, in fact they will try to get you to give it up - sometimes with aggression. There are other dogs who are happy to take the ball from you but not willing to get aggressive for it. There are dogs who simply pick up the ball because the person stinks at carrying it. There are dogs who take the ball because no one else is wiling to, and there are dogs who really don't want the ball but understand that someone must carry it so they do so reluctantly. Each dog will carry the ball in their own way, some are good at it and others are not. Few dogs are born to be great leaders and few dogs really want the job. Leadership comes with lots of responsibility and not many dogs are good at it. Thats when bad behaviors show up. A truly good leader is calm and benign, and their very presence exudes leadership - thats what a good human leader needs to emulate.
The rule that does hold true in all situations is someone needs to be in charge and that someone should be a human. Heck, we have the bigger brains (not always the smarter ones though
). The dogs need to be in the habit of looking to the human for the answers and the human needs to be ready with an answer or the dogs will stop checking in.
I figure everyone talks about dominance and alphas because they want to understand their dogs better, but the simple answer is if your dog looks to you for advice before making a decision then most of your problems are solved ahead of time. Be a confident leader and you will have a confident pack.