Why? Dr. Reich speculated that growing populations of farmers began linking to one another via trade networks. People moved along those routes and began to intermarry and have children together. Genes did not just flow across the Fertile Crescent — they also rippled outward. The scientists have detected DNA from the first farmers in living people on three continents.

“There seem to be expansions out in all directions,” Dr. Lazaridis said.

Early farmers in Turkey moved across the western part of the country, crossed the Bosporus and traveled into Europe about 8,000 years ago. They encountered no farmers there. Europe had been home to groups of hunter-gatherers for more than 30,000 years. The farmers seized much of their territory and converted it to farmland, without interbreeding with them.

The hunter-gatherers clung to existence for centuries, and were eventually absorbed by bigger farming communities. Europeans today can trace much of their ancestry to both groups.

The early farmers in what is now Iran expanded eastward. Eventually, their descendants ended up in present-day India, and their DNA makes up a substantial portion of the genomes of Indians.

And the people of Ain Ghazal? Their population expanded into East Africa, bringing crops and animals with them. East Africans retain ancestry from the first farmers of the southern Levant — in Somalia, a third of people’s DNA comes from there.

Dr. Reich hopes to learn more about the early farmers by obtaining samples more systematically from across the Fertile Crescent. “It’s not easy to come by these unique and special specimens,” he said.

But he is pessimistic about filling in some of the most glaring gaps in the genetic map of the Fertile Crescent. No one has yet recovered DNA from the people who lived in the oldest known farming settlements. And it’s unlikely they’ll be trying again anytime soon. To do so, they would have to venture into the heart of Syria’s civil war.