How does an organism search? This is a question that has triggered an enormous research effort in the past few decades. From an animal searching for food, to a rescue team looking for a crashed plane in the ocean, to an algorithm searching for information in a database, all these cases demand an optimal strategy to efficiently home in an initially unlocated target. Identifying optimal search strategies is very relevant for humans too. It would help us to understand patterns of gene flow, large-scale migrations, the spread of disease and cultural traits, as well as many other aspects of the life of traveling individuals. Technological applications are also emerging, such as the correct allocation of massive information resources for mobile individuals using smart phones, wearable computers, and so on.
As a consequence of solving a problem known to statistical physicists as the “trapping problem", theoreticians back in the 70s suggested that living organisms optimally search their environment by moving in patterns called a fractal pattern, or power law, in mathematical terms. The first biological example advanced to support this idea was the Wandering Albatross (Diomedea exulans
), a seabird that spectacularly crosses the southern skies by flying in long straight lines that span thousands of kilometers. By studying the statistics of their movements, researchers concluded that the wandering albatrosses flight is indeed power-law distributed in an optimal way known as Lévy flights (after Paul-Pierre Lévy the French mathematician who first studied this statistical distribution in the mid twentieth century). However, a study published in 2007 in the acclaimed journal Nature
questioned the strength of the empirical evidence for biological Lévy flights, a result that in turn prompted the science media to announce that the so called "Lévy paradigm" in biology had been overturned. This 2007 study claimed that Wandering Albatross movements were, in fact, more compatible with an exponentially-distributed random process, a conclusion that ignited a hot debate in the science community.
In a recent study published in the prestigious open access journal PLoS ONE, a team of scientists from the National Autonomous University of Mexico in Mexico City and the Blanes Center for Advanced Studies in Spain have revisited the 2007 albatross data and have come out with a different picture. The movement patterns of these seabirds are the result of the interactions of the animal with its prey field. By studying computer models where prey is fractally distributed in the ocean (a well known fact familiar to marine ecologists), the authors of this study conclude that model seabirds flying over large-scale heterogeneous environments reproduce the observed detection (or capture) times between prey without ruling out the fact that albatross may actually be performing Levy flights during search. These new findings are also useful for disentangling the current debate on how organism-environment interactions build up statistical patterns of movement, not only in seabirds but in other animals, humans and cyber-machines as well.
Complex Systems Department, Physics Institute and Center for Complexity Sciences at the National Autonomous University of Mexico (UNAM).
Blanes Centre for Advanced Studies, Spain