predecessor的含义是one that precedes; especially: a person who has previously occupied a position or office to which another has succeeded(from Merriam Webster)
因此any of their supposed Mediterranean predecessors,暗示了在用碳14做年代测量以前,人们原本认为(supposed)来自Mediterranean(地中海)的巨石碑的年代比Brittany(法国的一个半岛)的巨石碑更早。