The latest study to posit this result looked at 344 men from Europe and the Near East. Analyzing their Y chromosomes, the researchers found that more than 70% of them descend from six lineages that underwent very rapid expansion in the Bronze and Iron Ages. In the table above, TMRCA is Time to Most Recent Common Ancestor, estimated by two different methods.
Now this is not a very large study, and the estimates have a large margin of error. It actually does not match up in detail with some other studies I have read. But it agrees with many recent studies in finding these male lineages that underwent explosive expansion at some time in the past.
If these studies are right, most men who lived 5,000 years ago have no living descendants; most of us descend from a comparative handful of "super fathers." Of course the Bronze Age is the period when Europe first came to be dominated by sword-wielding warrior aristocrats; when Indo-European languages spread across the continent; and when, it seems, warrior tribes conquered and subjugated everyone else. But note that these successful recent lineages are found within both the R-1 clades that may be associated with the Indo-Europeans and within the J clade, which almost certainly came to Europe with the first Neolithic farmers; not all of the warrior dynasties were among the invaders.
There comparable evidence for women is much weaker. We study the genetic history of women using mitochondrial DNA, which we all get from our mothers, and mitochondrial DNA is something quite different from the rest of our genomes. Still, the evidence we have does not show the same pattern of just a few founding mothers in recent times. Genetic competition among women has been much less intense than among men.
The gendering of this pattern argues that it relates to male success in warfare. How that relates to the other great pressure on human populations, infectious disease, remains mysterious, as do many other things. But our knowledge is expanding so fast that we really may someday know.