The researchers analyzed the birds’ positions over seven minutes of flight, and compared those observations with theoretical predictions generated by aerodynamic models. The upward-moving swirls of air, called tip vortices, are a byproduct of winged flight, said Kenny Breuer, a professor in the school of engineering and a professor of ecology and evolutionary biology at Brown University, who with David Willis and other colleagues, developed the predictions. As wings push air down to generate lift, other air rises to the right and left of the wings, forming the vortices. Airplane wings also shed them; they are sometimes visible as vapor trails.

But a bird’s wake is more complicated than an airplane’s. “The strength of those tip vortices varies throughout the phase of the wing-beat,” Dr. Breuer said. “There’s a favored position you want to fly in and a favored phase you want to flap in to take advantage of the leading bird.”

An analysis of 24,000 flaps showed that the ibises on average adjusted their position and wing phase to optimize the lift from the vortices, and readjusted their phasing when they changed positions within the V. The new study does not say how much energy the ibises saved by these maneuvers, but small gains could be useful over long migrations, experts say.

Another open question is how the birds know to fly in these optimal spots. Dr. Usherwood said that they might have evolved “rules of thumb” for flying, or that “they have good sensors” and adjust to find spots that feel good.

“Splitting apart those possibilities would be possible with cunning experiments we have planned,” he said.

As for the ibises, they made it to Tuscany in September 2011. They are expected to spend a few years there and then, if all goes well, migrate back to Salzburg. “This spring would be the first they would think of returning,” Dr. Portugal said. “This will be a telling year.”