"More than half" is a very poor measure unless you define "more than half" of what. I think it's a fair point to make that Neanderthals are not entirely extinct - a good portion of their genes just are.
I guess one way to look at it is, assume that there are some genetic markers that make someone look asian. Now genocide everyone who's "pure" asian, i.e. has more than 50% of those markers. Would you consider "asian people" to be "extinct" then, even though most if not all of their genetic markers are sill in circulation in the human gene pool?
[*] http://genecuisine.blogspot.co.uk/2011/03/human-dna-similari...
Literature I'm seeing suggests humans and neanderthal were related subspecies. I suspect one measure of "not existing" is when there's no clearly distinguishable neanderthal clan or trait cluster. Though there are people who have features which look strongly neanderthalic.
I've been reading bits and pieces of various aspects of anthropology and human evolution. It seems that cro-magnon man were likely an early sub-species or tribe which settled across northern Africa, as far out as the Azores, and along what's now the Spanish-France border region. All of which now show similar linguistic roots. And suggest that the Basque language, unrelated to others in Europe, is derived from cro-magnon.
The Roma people migrated from India toward southeastern Europe.
And there's solid anthropological evidence of settlements in what is now the Black Sea, living on what was then dry land, prior to it being flooded and inundated about 5600 BC. Now if only there were a flood myth in human tradition ....
If the notion of "extinct" is as fuzzy as you propose, that implies Homo erectus is not extinct, as we descend directly from them.
