Perhaps each "Link" has been pre-determined and pre-destined by the gods. I dont think there is any long-lasting lineage that interconnect the green-clad heroes in each game, but a set of common moral principles and a common destiny that each of them shared. I.E. to be called upon to thwart a great evil when need arises. They aren't related at all, not by blood any way. But the Link in
OoT was the first Link, and the first to wield the master sword against Ganon. Thats why I named my quest logs in
TP and WW somthing besides "Link", because their completley different people seperated by hundred-year generation gaps.