Monthly Archives: April 2012

Lévy flights of wandering albatrosses: fact or fiction?

A very recent and remarkable study appears to overturn the conventional wisdom about how wandering albatrosses move when they search for food. A new paper published in the Proceedings of the National Academy of Sciences USA (PNAS) by Nicolas E. Humphries et al. looks at whether or not the idea of Lévy flight foraging is supported by empirical data for two species of albatrosses: the wandering albatross and the black-browed albatross. A Lévy flight is a type of random walk in which the zig-zag patterns contain rare but extra long jumps.  In mathematical terms, Lévy flights contain a power law tailed probability density function of jump lengths. The latest results add a new twist to the controversy surrounding wandering albatrosses.

A little background: More than a decade ago in 1994, as a graduate student of Professor Gene Stanley at Boston University, I analyzed flight data of wandering albatrosses.  Our motivation was to try to gain insight into nebulous concepts such as the “free will” of animals.  If  free will really exists and confers real advantages, then it ought to operate in complex and sophisticated behaviors such as foraging.  At least, that was our thinking.  The research progressed rapidly and, in 1996, we published in Nature a paper titled Lévy flight search patterns of wandering albatrosses in which we reported what we thought was evidence of Lévy flights.  A year later, in 1997, I returned to Brazil.  In Natal and later in Maceió, I continued to investigate this phenomenon.  In 1998, my collaborators and I made some unexpected discoveries about previously unknown properties of Lévy flights.  In 1999, Sergey Buldyrev, Shlomo Havlin, Marcos da Luz, Ernesto Raposo, Gene Stanley and I published these results in another paper in Nature.  We showed analytically  that Lévy flights can optimize random searches under conditions of scarcity when the targets are revisitable and randomly located.  (Actually we also assumed some other simplifying conditions, such as negligible learning and memory, but it turns out that these issues do not significantly alter the main findings of the 1999 paper.)

The main reason why Lévy flights increase efficiency is that they can
reduce the expensive habit (known as “oversampling”) of Brownian random walkers to revisit previously visited sites.  They also increase, relative to ballistic motion, the chance of reaching nearby targets at the cost of reaching far away targets, thereby reducing overall traveled distances.  These and many other issues are discussed in our new book, The Physics of Foraging.

Over the next 5 years or so, a growing number of studies added weight to the Lévy flight foraging hypothesis.  Naturally, so did attempts to overturn or falsify the hypothesis.  As Karl Popper explained, scientists do not just verify hypotheses, rather they work to falsify them. This is in large part how science advances.   Supplanting old theories with new and better theories is how our understanding grows and improves.

The Lévy flight foraging hypothesis exploded into controversy in 2007, when another  paper published in Nature by A. M. Edwards et al.  questioned the validity of the hypothesis.  The hypothesis holds that animals should have evolved to move in a superdiffusive Lévy flight type of behavior under conditions of scarcity, because such behavior improves search efficiencies and encounter rates according to mathematical predictions.  Early papers from the 1980s and early 1990s looked at Lévy walks and similar behavior of microorganisms. But it was only in 1996 that the idea of Lévy flight foraging became a hot topic, when we reported evidence  (apparently) showing that Diomedea exulans, the wandering albatross, performs Lévy flight search patterns.   But there was a problem with the data. In 2007, in a paper authored by A. M. Edwards and many others,  we reported evidence which corrected the 1996 results.

Journalists had a field day.  For example, it was claimed by a journalist (Alexandra Witze of Science News) that the 1996 albatross results had been ‘debunked.’   After 2007  few people thought that albatrosses used Lévy flight patterns to forage.

It is in this context that the results reported in this new PNAS paper are simply extraordinary.  The crucial point is that this study directly contradicts the 2007 paper of Edwards et al.  How could this be?  The authors provide an explanation for the inconsistency: Whereas the 2007 study only looked at pooled data sets, the present paper looks at individual birds.  If I understood the paper correctly, the authors have re-tested the 2007 data and found that the behavior of individual birds can be strikingly different from the average behavior.  What I understood was that individual birds do not always use the Lévy behavior, so when you average the data for many birds, the signal-to-noise ratio degrades and the power law tail is less clear.  The authors also reconfirm what was suspected all along, viz., that the 2007 paper did not explicitly take into account power law truncation. But the bigger effect seems to be the pooling.

Maybe albatrosses do in fact use Lévy flight foraging patterns after all.