I listened to a talk on reindeer genetics by a Russian lady last year. Can't remember all the details but the reindeer was domesticated at least twice and separately in Fennoscandia (by the Saami) and in Western Russia.I read somewhere that language to do with Reindeer was definatley non Saami.
its only recently that Tarandus has been studied seriously, -was it true they were domesticated twice?
I don't know if there have been more domestication events, but not impossible.
There is genetic evidence for wild reindeer being brought into the bloodlines, but I have no clue if that might have been accidental or on purpose.