In each successive generation, the average size of the chunks becomes smaller because when DNA is swapped between the parents’ genomes in making the eggs or sperm, the cuts needed to generate the swapped sections are made in different places. Therefore, from the average size of the chunks in a person’s genome, the geneticists can calculate the number of generations since the mixing event.

“We are among the first to try to date ancestry events, and we have more ability to determine the source populations,” Dr. Myers said.

One of the most widespread events his group has detected is the injection of Mongol ancestry into populations within the Mongol empire, such as the Hazara of Afghanistan and the Uighur Turks of Central Asia. The event occurred 22 generations ago, according to genetic dating, which corresponds to the beginning of the 14th century, fitting well with the period of the Mongol empire.

In another example, the European colonization of America is recorded in the genomes of the Maya and Pima Indians. And Cambodian genomes mark the fall of the Khmer empire in the form of ancestral DNA from the invading Tai people.

Dr. Myers and his colleagues have detected European ancestry that entered the Tu people of central China between the 11th and 14th centuries; this, they surmise, could be from traders traveling the Silk Road. They find among Northern Italians an insertion of Middle Eastern DNA that occurred between 776 B.C. and A.D. 550, and may represent the Etruscans, a mysterious people said by the ancient Greek historian Herodotus to have emigrated from Lydia in Turkey.

The Myers group has posted its results on a web page that records the degree of admixture in each population. The English, however, known to be a rich medley of Celts with invaders such as the Angles, Saxons, Jutes, Danes and Norwegians, carry the notation “No strong evidence of admixture.” Dr. Myers said his method cannot yet detect genetic mixing between very similar populations, as was the case with the English and their invaders from Scandinavia and Northern Germany. He said he hoped to distinguish all these groups in a separate project on British ancestry.