Genghis Khan's sons and heirs ruled over the various khanates in his empire, and may well have used their position to establish large harems, especially if they followed their father's example. David Morgan, a historian of Mongol history at the University of Wisconsin, said Genghis's eldest son, Tushi, had 40 sons.

As for Genghis himself, Dr. Morgan cited a passage from 'Ata-Malik Juvaini, a Persian historian who wrote a long treatise on the Mongols in 1260.

Juvaini said: ''Of the issue of the race and lineage of Chingiz Khan, there are now living in the comfort of wealth and affluence more than 20,000. More than this I will not say . . . lest the readers of this history should accuse the writer of exaggeration and hyperbole and ask how from the loins of one man there could spring in so short a time so great a progeny.''

Dr. Morgan said that since Mongol rulers controlled a large area, it was ''perfectly plausible'' that they should have fathered many children. ''It's pretty clear what they were doing when they were not fighting,'' he said.

The Mongol rulers' apparent assiduity in propagating their genes has surprised even human behavioral ecologists, researchers who seek to explain many aspects of human society in terms of the pursuit of reproductive advantage.

''I think it's astonishing,'' said Dr. Robin Dunbar of the University of Liverpool, co-author of a leading textbook of human behavioral ecology. ''This is a staggering example of how a very small lineage can have a hugely disproportionate share of the descendant population.''

Dr. Dunbar said it was known that in tribes like the Yanomamo of Brazil, men of high status tended to have more children. But the Mongol study was the first to his knowledge to document this on a genetic level. ''It's exactly equivalent to elephant seals slogging it out on the beach -- a handful of males get all the matings,'' he said.