Dogs thrive on an ordered and established pack hierarchy; they need a stable pack order to feel secure. This is a natural pack behavior that enables dogs to maintain order. As uncomfortable as it can be to witness, it’s nearly always best to leave the dogs to it.
Dominant dogs use a variety of ritualized behaviors to assert their dominance. In a wild pack, the alpha dog -- typically a male -- will feed first, will have first rights with females and will lead the pack when they are on the move. In order to force submission on a subordinate, the alpha may mount less senior dogs, put his paws on their shoulders, stare them down and sometimes be directly aggressive by growling or flashing his teeth.
A subordinate dog has a variety of ways to show an alpha dog that he doesn’t pose a threat. In most cases, all that’s required is a little deference, typically in the form of moving out the alpha dog’s way, allowing him to feed first and not maintaining eye contact. Dogs who are very submissive will roll onto their backs to expose their tummies; some even urinate to display submissiveness. Typically these overt submissive gestures occur only when the alpha dog forces submission onto a subordinate.
Nature has programmed dogs to avoid physical conflict and has blessed them with a rich physical communication ability, so it’s rare that dominant behavior escalates into full-on violence. However, humans often muddy the waters by trying act as peacekeeper. In trying to give the weaker dog a little favor -- by feeding him first or by stopping the alpha dog from standing his ground, for instance -- an inexperienced dog owner may inadvertently encourage the alpha dog to become forceful in his dominance.
Monitor your dogs during play, but resist the urge to interfere unless a real threat of injury to one dog exists. If the play and roughhousing get out of hand, use noise to distract the dogs and separate them for a timeout. Respect the dominant dog’s position and act accordingly; feed him first, greet him first and put him on the leash first. It may feel unkind, but all you’re doing is assisting both dogs in establishing their order as quickly and painlessly as possible.