Lévy patterns in seabirds are multifaceted describing both spatial and temporal patterning

Andrew M. Reynolds, Vitor H. Paiva, Jacopo G. Cecere, Stefano Focardi

The flight patterns of albatrosses and shearwaters have become a touchstone for much of Lévy flight research, spawning an extensive field of enquiry. There is now compelling evidence that the flight patterns of these seabirds would have been appreciated by Paul Lévy, the mathematician after whom Lévy flights are named. Here we show that Lévy patterns (here taken to mean spatial or temporal patterns characterized by distributions with power-law tails) are, in fact, multifaceted in shearwaters being evident in both spatial and temporal patterns of activity. We tested for Lévy patterns in the at-sea behaviours of two species of shearwater breeding in the North Atlantic Ocean (Calonectris borealis) and the Mediterranean sea (C. diomedea) during their incubating and chick-provisioning periods. We found that distributions of flight durations, on/in water durations and inter-dive time-intervals have power-law tails and so bear the hallmarks of Lévy patterns. The occurrence of these statistical laws is remarkable given that bird behaviours are strongly shaped by an individual's motivational state and by complex environmental interactions. Our observations could take Lévy patterns as models of animal behaviour to a new level by going beyond the characterisation of spatial movements to characterise how different behaviours are interwoven throughout daily animal life.