[nostrademons]

Note that the observed genetic variance can be explained without any substantial drop in population (male or total):

Assume that humans are living in patrilineal clans of roughly 20 males and an equivalent number of females. All males are genetic descendants of the clan patriarch and share the same Y-chromosome markers. All females are born outside the clan and marry into it.

Now assume that 95% of clans are wiped out through a couple millenia of warfare. That Y-chromosome is now extinct; all male-line descendants of the patriarch are dead. However, genetic markers carried by the female are not extinct, because the 20 daughters born into the clan have married into 20 different clans, and at least one of them has survived.

Note that the population doesn't actually have to drop in this scenario! 95% extinction of clans over 2000 years implies only 0.15% extinction annually, assuming an exponential decay. If warfare is continuous and resources go to the victor, then one clan is exterminated, but the victorious clan quickly doubles in size as it takes the dead clan's resources (and oftentimes, womenfolk). Total population remains roughly constant, but all living descendants come from a tiny percentage of male ancestors.

Other articles about this study have made this distinction explicitly (or at least hinted about it), but it's totally missing from the headline.

[solidsnack9000]

So assuming that clans tend to get wiped out all of a piece, and males cross clans much less frequently than clans get wiped out, many of the Y-chromosome lines will go extinct, but few of the mitochondrial DNA lines will go extinct?

There are a very few matrilocal human societies; perhaps they show the obverse pattern.