In this type of aggression the dogs don't have to be brothers or same breed or age or sex . I have found cases where the aggression is directed to the children of the family , remember for their minds , dogs don't understand equality with other dogs or with us for that matter they will seek their position in the pecking order , democracy is a misplaced ideology in the dog world .their minds work differently but we humans find this concept difficult to accept . Kind owners who elevate the submissive dogs and diminish the dominant ones are creating not only confusion but the dog will think is unnatural .
Rivalry occurs in two dogs when they are to similar hormonal or genetically makeup or one of them is ageing and the young one feels is his turn to take his place .this can happen indistinct of sex , breed or age . as a rule we shouldn't interfere in their hierarchy but we don't live in the wild so we have to stop in very subtle to not alter the natural order but keeping the harmony and peace at every instance.
The most delicate type is when is the aggression is directed to the children of the household in the dog's mind is as simple as who is who in the pecking order and the parents may be the leaders but they can think of the children as weak compared to their own status.