The new paper describes the more straightforward of the two experiments. Ron Fouchier of the Erasmus Medical Center in the Netherlands and colleagues started off with H5N1 isolated from an Indonesian patient and introduced mutations to the virus’s genes. They then transferred the virus from one ferret to another, allowing more mutations to accumulate. After five mutations, viral strains emerged that were able to spread from one ferret to the next through the air.

Acquiring a series of mutations is also probably how a bird flu gave rise to the 1918 pandemic. In another paper in Science, Derek Smith, an evolutionary biologist at the University of Cambridge, and his colleagues investigated how easy it would be for natural H5N1 to acquire the five mutations identified by Dr. Fouchier.

They found that two of the mutations have arisen numerous times in the wild. In one group of closely related H5N1 viruses, both mutations are present in their genes, so they would need to acquire only three more mutations to spread between mammals.

To judge the likelihood of that, they developed a mathematical model based on what is known about flu viruses.

A flu infection can produce 100 trillion new viruses in a matter of days. And because these viruses have a high mutation rate, just about every new virus will be slightly different from its ancestor. Dr. Smith and his colleagues found that under plausible conditions, there was a small chance that the flu viruses could gain the final three mutations in a single person during a single infection.

But figuring the exact odds is tricky.

“It’s possible that the chances are one in a thousand, and we’ve just gotten lucky,” Dr. Smith said. “Or it’s possible that the chance is one in a million and it might not happen for a long time.”

The Nature paper, by Yoshihiro Kawaoka of the University of Wisconsin and colleagues, offers a different path to a human form of H5N1 — a path based on a kind of viral sex.