Bases of attachment of Archimedes colonies are very rare, but many colonies show evidence of origination from a pre-existing set of branches. The evidence consists of spiralled supports originating from fragments branches, proximal taper of colonies or axial screws to a diameter smaller than that of bases of attachment, early stages of new colonies originating from the whorl margins of older colonies, and sets of laterally fused colonies. In favorable environments Archimedes populations were dominated by a few genets that consisted of hundreds of genetically identical colonies. The ability to reproduce by colony fragmentation was probably an important cause of Archimedes' abundance in the Chesterian seas of eastern North American, especially where it occurred in dense populations in the lee of submarine carbonate shoals.--Modified journal abstract.