Abstract
BackgroundThe 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.ResultsWe 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.ConclusionsThe 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.
Highlights
The flight patterns of albatrosses and shearwaters have become a touchstone for much of Lévy flight research, spawning an extensive field of enquiry
The exponentiallytruncated power-law fits typically reduce to truncated power-laws because the maximum likelihood estimates for the exponential decay rate, λ2, are usually zero and for this reason are not displayed
We found that Lévy patterns do, proliferate in shearwaters, a species closely related to the wandering albatross, describing their flight patterns [24] and flight durations, on/in water durations and inter-dive time-intervals
Summary
The flight patterns of albatrosses and shearwaters have become a touchstone for much of Lévy flight research, spawning an extensive field of enquiry. Given the long standing assumption of scale-dependency of ecological patterns [2], it is perhaps natural to presuppose that animal activity patterns will be Poisson – one of the most important, most studied and frequently encountered random process. Wearmouth et al [3] reported that the waiting times of marine sit-and-wait ambush predators are power-law distributed across a broad set of scales Such behaviours have been observed in more mobile little penguins (Eudyptula minor) [4]. Reynolds et al [5] subsequently reported that the pause and movement durations of a variety of invertebrates are power-law distributed across a broad set of scales when individuals are exposed
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