Each dog has his own way of behaving in certain situations. Some dogs greet other dogs enthusiastically, with a "let's be friends" attitude, while others barely tolerate the presence of other dogs. Then there are those dog-bullies who want to scare everyone with their ferocity, feigned or for real.
Here's an easy little clue on how to remember which animals are social and which are loners: if there is a group name for the animal, they're social, if not, they're loners. For example, you might hear of a "troop" of monkeys because monkeys are highly social animals. You never hear of a league of lizards or a society of snakes. That's because those animals are loners. Dogs, descended from wolves, are pack animals and probably the most highly sociable of all animals. With some exceptions, most dogs love to meet other dogs and do so enthusiastically. So, the way a dog should act when meeting another dog is with enthusiasm, curiosity and in a friendly manner.
In addition to being highly sociable, dogs are highly reliant on olfactory senses. Dogs can pick up all kinds of information just by sniffing around. When a dog sniffs the ground, he can tell if there have been other dogs in the area, when they were there, their approximate age, gender and relative health. This information helps the dog know if his territory is really his own or if he is sharing it with other dogs. When dogs meet one another, they sniff each other's anal area as a form of greeting, just like when people shake hands. It's a social convention in which all dogs partake instinctively. The anal region houses two scent glands that hold the key to all the information a dog needs to know about another dog, hence the butt sniffing and not, say, ear sniffing.
Have you ever seen two dogs stand side by side, head to tail? They seem to be staring off into the distance, but what they are doing is gauging the other dog's heft. Many times, one dog will actually lean against the other dog to get a better fix on just how strong and muscular the other dog is. Incidentally, if you've ever been around a dog who is a "leaner" you have seen this behavior first hand.
Dogs rely on body language much more than people do. This makes sense since their vocabulary skills are, well, non-existent. As pack animals, dogs live in a world of alphas and non-alphas. This means they choose a leader and everyone respects that leadership. When with people, most dogs happily step back and let the human take over. But when dogs meet other dogs, they need to determine who is the more dominant of the group. In addition to sniffing and leaning, some dogs will attempt to put their front paws on top of the other dog's back to make himself seem larger and to see what the other dog will do. If the other dog tolerates that act, the order has been established. If he does not, they may move on to other things such as humping -- an act of dominance, not sex. When one dog submits by rolling over and exposing his belly, the contest is over. Once a dog does that, the little dance is complete and play will commence.
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