Environmental context explains Lévy and Brownian movement patterns of marine predators

@article{Humphries2010EnvironmentalCE,
  title={Environmental context explains L{\'e}vy and Brownian movement patterns of marine predators},
  author={Nicolas E. Humphries and Nuno Queiroz and Jennifer R. M. Dyer and Nicolas G. Pade and Michael K. Musyl and Kurt M. Schaefer and Daniel W. Fuller and Juerg M. Brunnschweiler and Thomas K. Doyle and Jonathan D. R. Houghton and Graeme C. Hays and Catherine Sue Jones and Leslie Robert Noble and Victoria J. Wearmouth and Emily J. Southall and David W. Sims},
  journal={Nature},
  year={2010},
  volume={465},
  pages={1066-1069}
}
An optimal search theory, the so-called Lévy-flight foraging hypothesis, predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned. Consequently, whether foragers exhibit Lévy… 
Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics.
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That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed.
The Lévy flight foraging hypothesis in a pelagic seabird.
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TLDR
It is demonstrated that selection often results in Lévy-like behaviour, although conditional; smaller populations, longer searches, and low searching costs increase the fitness of Lévardian behaviour relative to Brownian behaviour, and the results also evidence a bet-hedging strategy.
Foraging success of biological Lévy flights recorded in situ
TLDR
High-temporal-resolution tracking of wandering and black-browed albatrosses with simultaneous recording of prey captures is used to show that both species exhibit Lévy and Brownian movement patterns, and adds support to the possibility that biological LÉvy flight may have naturally evolved as a search strategy in response to sparse resources and scant information.
The evolutionary maintenance of Lévy flight foraging
TLDR
Some of the first evidence for the evolutionary maintenance of Lévy flight foraging is provided, extending the current theoretical framework by including evolutionary ecological contexts and exploring ecological contexts such as population size, lifespan, carrying capacity, searching costs, reproductive strategies, and different distributions of food.
Adaptive Lévy Processes and Area-Restricted Search in Human Foraging
TLDR
The results suggest that though power-law distributions do not accurately reflect human search, Lévy processes may still describe movement in dispersed environments, but not in patchy environments–where search was area-restricted.
Scavengers on the Move: Behavioural Changes in Foraging Search Patterns during the Annual Cycle
TLDR
Egyptian vultures followed a Brownian search strategy in their wintering sojourn in Africa, whereas they exhibited a more complex foraging search pattern at breeding grounds in Europe, including Lévy motion, which support the growing awareness about the role of behavioural flexibility at the individual level.
Lévy Walks Suboptimal under Predation Risk
TLDR
The findings indicate that animals may not perform Lévy walks often, and it is suggested that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.
Lévy flight movement patterns in marine predators may derive from turbulence cues
  • A. Reynolds
  • Environmental Science
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2014
TLDR
It is shown that the programming for these Lévy movement patterns does not need to be very sophisticated or clever on the predator's part, as these movement patterns would arise naturally if the predators change their direction of travel only after encountering patches of relatively strong turbulence (a seemingly natural response to buffeting).
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Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes, consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape.
Minimizing errors in identifying Lévy flight behaviour of organisms.
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Empirical reanalysis of data in published studies indicates that simple log transformation results in significant errors in estimating micro, which in turn affects reliability of the biological interpretation, and it is shown that using a large number of steps in movement analysis such as this will also increase the accuracy with which optimal Lévy flight behaviour can be detected.
Lévy flight search patterns of wandering albatrosses
LéVY flights are a special class of random walks whose step lengths are not constant but rather are chosen from a probability distribution with a power-law tail. Realizations of Lévy flights in
Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer
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This work analyzes a new, high-resolution data set of wandering albatross flights, and finds no evidence for Lévy flight behaviour, and proposes a widely applicable method to test for power-law distributions using likelihood and Akaike weights.
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The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems, fractal patterns show up in many subtle ways and have been interpreted as emer- gent phenomena
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Experimental evidence of predicted optimal changes in the flight-time distribution of a predator's walk in response to gradual density changes of its moving prey is presented and the idea of universality of the statistical laws in optimal searching processes despite variations in the biological details of the organisms is supported.
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How dynamic prey landscapes enable active habitat selection in large predators to be investigated from a trophic perspective is highlighted, an approach that may inform conservation by identifying critical habitat of vulnerable species.
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The need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching, is stressed.
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Lévy walks are superdiffusive and scale-free random walks that have recently emerged as a new conceptual tool for modeling animal search paths and may be confounded with them because they present apparent move-length-heavy tail distributions and superdiffusivity.
Optimizing the success of random searches
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It is shown that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Lévy flight motion, is an optimal strategy.
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