Math in the News
Mathematical Model of Albatross Flight Crashes
November 21, 2007
A new report has apparently overturned a previously proposed mathematical model of how some animals search for food.
Wandering albatrosses, an endangered species, inhabit Bird Island, a 5-kilometer-long rocky island off South Georgia in the South Atlantic. With no food to be found on the island, the birds undertake long treks, sometimes for days, flying across the ocean surface to feed on squid. Ecologists use logging devices attached to the birds' legs to indicate how often the birds land on the water to feed.
In 1996, using data from such logging devices, a team of researchers proposed that wandering albatrosses forage for food using a strategy based on Lévy flights. The birds, they said, make clusters of short flights, connected by infrequent, longer ones.
Lévy flights are named after French mathematician Paul Lévy. In such random walks, increments are apportioned according to a probability distribution with a heavy power-law tail. In other words, this kind of random motion is marked by frequent short spurts and occasional longer jumps.
The Lévy flight strategy for foraging was subsequently applied to a wide range of organisms, including zooplankton, grey seals, and spider monkeys. It was even used as a mathematical model of how fishermen pursue schools of fish.
Now, an international team of scientists, basing their research on new analyses of high-resolution data collected by the logging devices, has overturned the theory. Earlier analyses had failed to take into account long periods when the birds were still at their nests. "It now seems the albatrosses come across food at simpler random intervals," said Andrew Edwards, formerly of the British Antarctic Survey and now at the Pacific Biological Station in Nanaimo, B.C.
"Our work also questions whether other animals thought to exhibit Lévy flights really do all forage in the same way," he added. Indeed, new analyses of existing data for deer and bumblebees using alternative statistical methods show that none of these animals exhibit evidence of Lévy flight foraging patterns.
The article called "Revisiting Lévy Flight Search Patterns of Wandering Albatrosses, Bumblebees and Deer," by Andrew M. Edwards and his colleagues, appeared in the Oct. 25 Nature.