There are a number of ethnic groups (not species or subspecies, I realize) that are less than 3% of the gene pool today (and happened over a much shorter timespan I would suppose) such as Irish, Jewish, Armenian, etc. Would they be considered having been outcompeted at this point?
No. There are still 100% individuals of all those groups, and the timescale of recorded history is too small for the same kind of competition as between neanderthals and sapiens anyway.
