Bonnie visited us today. She is an older dog of unknown breed - well, she probably knows her breeding, but she isn't telling. She's been a regular visitor since Penny was very young.
When Penny was smaller than Bonnie it was logical that she would defer to the older and wiser visitor. However, to the human observer it seems odd that Penny still sees Bonnie as more important in the scheme of things.
Bonnie's arrival is the signal for Penny to follow her around the house and out into the backyard, energetically trotting around her in circles, getting twice the exercise that Bonnie gets. If Bonnie wants to sit on Penny's mat, that's quite okay. Penny will wait patiently for the visitor to initiate some activity.
It seems to relate to the concept of 'dominance', but not quite in the simplistic way that some references define it. I think the discussion at 'Showdogs' is one of the best explanations I have read of what may be going on. For instance the author says:
"Alpha" does not mean physically dominant. It means "in control of resources." Many, many alpha dogs are too small or too physically frail to physically dominate, but they have earned the right to control the valued resources. An individual dog determines which resources he considers important. Thus an alpha dog may give up a prime sleeping place because he simply couldn't care less.
I'm not sure whether this might mean that Penny doesn't care who lies on her mat - ie she is alpha; or whether Bonnie is alpha and Penny has to let her lie there.
I have always been interested in the work of the Coppingers, who believe that domestic dogs are not descended from wolves, and this particular site quotes from them in its discussion of dominance.