Making matters worse, the hair had been cut with scissors. The best way to get genetic material from a strand of hair is to pull it out at its DNA-rich root.

Given these uncertainties, the scientists decided to increase the odds of success by searching for abundant mitochondrial DNA, which is situated outside the cell nucleus and is inherited solely from the mother. Eventually, the scientists managed to piece together all the mitochondrial genes in each of the hair samples.

By comparing the aboriginal sequences to DNA from other parts of the world, the scientists determined that they all belonged to a single human lineage, indicating that all aborigines descended from a single migration to the continent.

Mitochondrial DNA gradually accumulates mutations at a roughly regular rate, ticking like a molecular clock. By adding up the mutations in the hair samples, the scientists also estimated that their owners all descended from a common ancestor who lived around 50,000 years ago. That finding fits nicely with the estimated ages of the oldest archaeological sites in Australia.

The mitochondrial tree also provided clues to how people spread through the continent.

Fifty thousand years ago, sea levels were so low that Australia and New Guinea formed a single continent. Humans moved from Southeast Asia onto this landmass, some settling in what is now New Guinea, others traveling farther south into Australia.

They kept to the coastlines until they reached southern Australia 49,000 years ago. But once this great migration was finished, the new study suggests, the ancestors of today’s aborigines hunkered down in their new homes — for tens of thousands of years.

The mitochondrial DNA contains no evidence that these populations mixed in any significant way, surprising researchers. “We were fully expecting a fully diverse mix of people in all places at all times,” Dr. Cooper said.