Nature | Letter
Environmental context explains Lévy and Brownian movement patterns of marine predators
- Journal name:
- Nature
- Volume:
- 465,
- Pages:
- 1066–1069
- Date published:
- (24 June 2010)
- DOI:
- doi:10.1038/nature09116
- Received
- Accepted
- Published online
An optimal search theory, the so-called Lévy-flight foraging hypothesis1, 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 prey2, 3, 4. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned5, 6. Consequently, whether foragers exhibit Lévy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory’s central predictions. Here we use maximum-likelihood methods to test for Lévy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Lévy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Lévy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Lévy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Lévy-flight foraging hypothesis1, 7, supporting the contention8, 9 that organism search strategies naturally evolved in such a way that they exploit optimal Lévy patterns.
Subject terms:
Figures at a glance
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Figure 1: Examples of good fits to power-law and truncated power-law distributions. 
a, Synthetic power-law and truncated power-law (Pareto) distributions with upper truncations set to 50, 250, 5,000. b–f, Empirical power-law and truncated power-law fits to dive data from individual blue sharks (Prionace glauca; b, d) and an ocean sunfish (Mola mola, e), together with the diving time series for the individual in b (over ~8 d; c) and the individual in e (over ~4 d; f). The red line indicates a synthetic power law in a, a power law in b and truncated power-law MLE model fits to empirical data in d and e.
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Figure 2: Behavioural switching between Lévy and Brownian motion in relation to habitat type. 
a–e, Split moving-window analysis showing significant discontinuities in the dive time series of blue shark 10. Red lines indicate points where the time series was divided into sections (SEC1–SEC5). f–j, MLE analysis with μ values for sections best fitting a truncated power-law distribution: black circles, observed step lengths; red lines, best-fit truncated power law; blue lines, best-fit exponential distribution. k–o, Depth profiles of sea temperature recorded using electronic tags. p, q, Geo-referenced track sections of blue shark 10 overlaid on chlorophyll a concentrations (p) and bathymetry (q). Section numbers correspond to those in a–e and different data-point colours correspond to different sections: SEC1, black (higher latitude); SEC2, white (higher latitude); SEC3, grey; SEC4, black (lower latitude); SEC5, white (lower latitude).
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Figure 3: Spatial occurrence of Lévy and Brownian behaviour types. 
Frequencies of behaviour types in productive (frontal/shelf) and less productive (off-shelf) habitats in the northeast Atlantic (a), and in productive (frontal) and less productive (stratified) habitats in the central eastern Pacific (b). Tests of two predictions of the LFF hypothesis (Lévy behaviour where prey is sparse; Brownian movement where prey is abundant and not sparsely distributed) were performed on frequency data (not per cent frequency data). See main text for details of the statistical tests.
