Lévy flight movement patterns in marine predators may derive from turbulence cues

Reynolds, Anne

doi:10.1098/rspa.2014.0408

Cited by 12 publications

(12 citation statements)

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“…By looking with fresh eyes we can make unexpected discoveries and connections that others have missed. Surprising connections have already been made: between Zipf's law for city sizes and the occurrence of Lévy searching patterns in honeybees [98]; between turbulence theory and Lévy flights in marine predators [97]; between the Movement Ecology Framework and Lévy flights in atomic vapours, even in interstellar space [179]; between passive aerial dispersal and analyses of on-line gaming strategies [79]; between effective searching for and within patches [121]; between percolation and Lévy walking. More surprises are likely to be in store as we make further advances.…”

Section: Discussionmentioning

confidence: 98%

“…This apparent discrepancy between observations and expectations puts strain on the Lévy flight foraging hypothesis. This is resolved by invoking the new hypothesis because, under this scenario, Lévy flights are an emergent property of a natural response to turbulence [97].…”

Section: Discussionmentioning

confidence: 99%

“…Research in this direction has shown that the programming for Lévy movement does not need to be very sophisticated and can be derived from simple, seemingly innocuous behaviours [42,65,79,97,99,102,103,[119][120][121]126,159,179,180]. Underlying all of the progress made has been Feynman's edict: "Probably the most powerful single assumption that contributes most to the progress of biology is the assumption that everything animals do the atoms can do, that the things that are seen in the biological world are the results of the behaviour of physical and chemical phenomena, with no 'extra something"' [181].…”

Section: Discussionmentioning

confidence: 99%

“…These seminal studies left open the question of what the underlying mechanisms were. Reynolds [97] addressed the issue by showing that the observations were consistent with marine predators changing their direction of travel upon encountering patches of relatively strong turbulence, but otherwise moving in straight-lines. According to the Lévy flight foraging hypothesis, marine predators do this because there is selection for Lévy flight behaviours.…”

Section: Lévy Walks In Marine Predators Honeybees Fruit Flies Bactmentioning

confidence: 91%

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Liberating Lévy walk research from the shackles of optimal foraging

Reynolds

2015

Physics of Life Reviews

154

205

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Section: Discussionmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Lévy Walks In Marine Predators Honeybees Fruit Flies Bactmentioning

confidence: 91%

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Liberating Lévy walk research from the shackles of optimal foraging

Reynolds

2015

Physics of Life Reviews

154

205

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“…Indeed, a number of studies have shown that characteristics of LFs and LWs may emerge naturally on large scales from more realistic case specific models of movement [45], including simple deterministic and semideterministic walks in complex environments [35,[46][47][48][49][50], self-avoiding random walks [51][52][53], diffusion with a timevarying diffusion constant [54][55][56], and a multiplicative, selfaccelerating process [9,57,58]. It has also been suggested that in some species a power-law distribution of lengths of straight line segments of their movement patterns, a hallmark of LWs and LFs, is a consequence of either the Weber-Fechner law in odometry [59], a power-law distribution of switching times between competing activities [60][61][62][63][64][65], or a so-called aerial lottery [66][67][68].…”

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confidence: 99%

Emergence of Lévy Walks from Second-Order Stochastic Optimization

Kuśmierz

Toyoizumi

2017

Phys. Rev. Lett.

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In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter involves no apparent memory or information processing and can be mathematically modeled by random walks. We show that both types of search can be generated by a common mechanism in which Lévy flights or Lévy walks emerge from a second-order gradient-based search with noisy observations. No explicit switching mechanism is required -instead, continuous transitions between the directed and random motions emerge depending on the Hessian matrix of the cost function. For a wide range of scenarios the Lévy tail index is α = 1, consistent with previous observations in foraging organisms. These results suggest that adopting a second-order optimization method can be a useful strategy to combine efficient features of directed and random search.Many organisms must actively search for resources in order to survive and produce offspring. Foraging theory examines the various search strategies implemented by organisms depending on their abilities and the environments in which they live. In directed search, greater involvement of sensory and information processing abilities enable more complicated strategies. In contrast, in the boundary case of a memoryless and senseless forager, the only option is to wander randomly in the environment (random search). Even in this case, however, different strategies exist, depending on the character of the random motion. A natural candidate model for the random strategy is Brownian motion that describes a wide range of natural phenomena, including the movement of inanimate particles under thermal noise. A prominent feature of Brownian motion is the linear growth of the variance of the position with time. However, empirical data indicate that for organisms the observed growth is often faster. Lévy walks (LWs) [1][2][3] [22][23][24][25][26][27][28][29][30][31][32] and alternative superdiffusive models [33]. These observations have led to the so-called Lévy flight optimal foraging hypothesis, which states that LFs (or LWs) represent evolutionary adaptations due to their distinct advantages over other random search strategies [22,34,35].Recently this view has been disputed because none of the mentioned organisms is senseless and all of them are able to perform some forms of directed search (taxis), for example T cells and isolated bacteria perform chemotaxis [36][37][38][39][40], whereas fruit flies perform phototaxis [41], geotaxis [42], and chemotaxis [43,44]. Indeed, a number of studies have shown that characteristics of LFs and LWs may emerge naturally on large scales from more realistic case specific models of movement [45], including simple deterministic and semideterministic walks in complex environments [35,[46][47][48][49][50], self-avoiding random walks [51][52][53], diffusion with a timevarying diffusion constant [54][55][56], and a multiplicative, selfac...

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The elements and richness of particle diffusion during sediment transport at small timescales

Furbish

Fathel

Schmeeckle

et al. 2016

Earth Surf Processes Landf

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The ideas of advection and diffusion of sediment particles are probabilistic constructs that emerge when the Master equation, a precise, probabilistic description of particle conservation, is approximated as a Fokker–Planck equation. The diffusive term approximates nonlocal transport. It ‘looks’ upstream and downstream for variations in particle activity and velocities, whose effects modify the advective term. High‐resolution measurements of bedload particle motions indicate that the mean squared displacement of tracer particles, when treated as a virtual plume, primarily reflects a nonlinear increase in the variance in hop distances with increasing travel time, manifest as apparent anomalous diffusion. In contrast, an ensemble calculation of the mean squared displacement involving paired coordinate positions independent of starting time indicates a transition from correlated random walks to normal (Fickian) diffusion. This normal behavior also is reflected in the particle velocity autocorrelation function. Spatial variations in particle entrainment produce a flux from sites of high entrainment toward sites of low entrainment. In the case of rain splash transport, this leads to topographic roughening, where differential rain splash beneath the canopy of a desert shrub contributes to the growth of a soil mound beneath the shrub. With uniform entrainment, rain splash transport, often described as a diffusive process, actually represents an advective particle flux that is proportional to the land surface slope. Particle diffusion during both bedload and rain splash transport involves motions that mostly are patchy, intermittent and rarefied. The probabilistic framework of the Master equation reveals that continuous formulations of the flux and its divergence (the Exner equation) represent statistically expected behavior, analogous to Reynolds‐averaged conditions. Key topics meriting clarification include the mechanical basis of particle diffusion, effects of rarefied conditions involving patchy, intermittent motions, and effects of rest times on diffusion of tracer particles and particle‐borne substances. Copyright © 2016 John Wiley & Sons, Ltd.

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Lévy flight movement patterns in marine predators may derive from turbulence cues

Cited by 12 publications

References 33 publications

Liberating Lévy walk research from the shackles of optimal foraging

Liberating Lévy walk research from the shackles of optimal foraging

Emergence of Lévy Walks from Second-Order Stochastic Optimization

The elements and richness of particle diffusion during sediment transport at small timescales

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