In the future, as in the past, the height of a man's pants denotes rank. Thus, Barry is the leader, followed at a great distance by Robin, who is in turn just slightly above Maurice.
Robin would come to greatly resent Barry because of this, leading him to split off from the brothers Gibb and create his own faction, raising an army of mutated scavagers to rule the future wasteland.
Barry and Maurice were forced to fall back and fortify themselves against the Robin-led survivors, but the lack of electricity and working technology meant they had to rely on some outdated weaponry and equipment if they wanted to last against their brother's violent, oppresive reign.
I think it's pretty clear by now that the Bee Gees' initial story ideas for Saturday Night Fever were stolen for and recycled for
Doomsday.