Rohde created a program that put an initial population on a map of the world at some date in the past, ranging from 7,000 to 20,000 years ago. Then the program allowed those initial inhabitants to go about their business. He allowed them to expand in number according to accepted estimates of past population growth, but had to cap the expansion at 55 million people due to computing limitations. Although unrealistic in some respects — 55 million is a lot less than the 6.5 billion people who actually live on Earth today — he found through trial and error that the limitation did not significantly change the outcome with regard to common ancestry.

The model also had to allow for migration based on what historians, anthropologists and archaeologists know about how frequently past populations moved both within and between continents. Rohde, Chang and Olson chose a range of migration rates, from a low level where almost nobody left their native home to a much higher one where up to 20 percent of the population reproduced in a town other than the one where they were born, and one person in 400 moved to a foreign country.

Allowing very little migration, Rohde's simulation produced a date of about 5,000 B.C. for humanity's most recent common ancestor. Assuming a higher, but still realistic, migration rate produced a shockingly recent date of around 1 A.D.

Some people even suspect that the most recent common ancestor could have lived later than that.

"A number of people have written to me making the argument that the simulations were too conservative," Rohde said.

Migration is the key. When a people have offspring far from their birthplaces, they essentially introduce their entire family lines into their adopted populations, giving their immediate offspring and all who come after them a set of ancestors from far away.

People tend to think of preindustrial societies as places where this sort of thing rarely happened, where virtually everyone lived and died within a few miles of the place where they were born. But history is full of examples that belie that notion.

Take Alexander the Great, who conquered every country between Greece and northern India, siring two sons along the way by Persian mothers. Consider Prince Abd Al-Rahman, son of a Syrian father and a Berber mother, who escaped Damascus after the overthrow of his family's dynasty and started a new one in Spain. The Vikings, the Mongols, and the Huns all traveled thousands of miles to burn, pillage and — most pertinent to genealogical considerations — rape more settled populations.

More peaceful people moved around as well. During the Middle Ages, the Gypsies traveled in stages from northern India to Europe. In the New World, the Navaho moved from western Canada to their current home in the American Southwest. People from East Asia fanned out into the South Pacific Islands, and Eskimos frequently traveled back and forth across the Bering Sea from Siberia to Alaska.

"These genealogical networks, as they start spreading out they really have the ability to get virtually everywhere," Olson said.

Though people like to think of culture, language and religion as barriers between groups, history is full of religious conversions, intermarriages, illegitimate births and adoptions across those lines. Some historical times and places were especially active melting pots — medieval Spain, ancient Rome and the Egypt of the pharaohs, for example.

"And the thing is, you only need one," said Mark Humphrys, an amateur anthropologist and professor of computer science at Dublin City University.

One ancestral link to another cultural group among your millions of forbears, and you share ancestors with everyone in that group. So everyone who reproduced with somebody who was born far from their own natal home — every sailor blown off course, every young man who set off to seek his fortune, every woman who left home with a trader from a foreign land — as long as they had children, they helped weave the tight web of brotherhood we all share.