Lévy Processes, Saltatory Foraging, and Superdiffusion

Burrow, J.F.; Baxter, Paul D.; Pitchford, Jonathan W.

doi:10.1051/mmnp:2008060

Cited by 14 publications

(28 citation statements)

References 32 publications

(42 reference statements)

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“…This assumption does not necessarily hold, especially when a forager moves with Lévy-like movements in a patchy environment (Burrow et al 2008); the distribution of sizes at a given time is characteristically heavy-tailed. Figure 3f uses all of the simulated hitting time results, rather than making an implicit diffusive assumption, to estimate the probability of recruitment as…”

Section: Evolutionary Optimality M D Preston Et Al 1303mentioning

confidence: 99%

Evolutionary optimality in stochastic search problems

Preston

Pitchford

Wood

2010

J. R. Soc. Interface.

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'Optimal' behaviour in a biological system is not simply that which maximizes a mean, or temporally and spatially averaged, fitness function. Rather, population dynamics and demographic and environmental stochasticity are fundamental evolutionary ingredients. Here, we revisit the problem of optimal foraging, where some recent studies claim that organisms should forage according to Lévy walks. We show that, in an ecological scenario dominated by uncertainty and high mortality, Lévy walks can indeed be evolutionarily favourable. However, this conclusion is dependent on the definition of efficiency and the details of the simulations. We analyse measures of efficiency that incorporate population-level characteristics, such as variance, superdiffusivity and heavy tails, and compare the results with those generated by simple maximizing of the average encounter rate. These results have implications on stochastic search problems in general, and also on computational models of evolutionary optima.

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Section: Evolutionary Optimality M D Preston Et Al 1303mentioning

confidence: 99%

Evolutionary optimality in stochastic search problems

Preston

Pitchford

Wood

2010

J. R. Soc. Interface.

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“…The jumps are modelled through a stochastic mean reverting jump diffusion process, which captures large deviations in turn rate in an otherwise well-behaved random process. Jump diffusion processes are commonly used to model sudden changes in stock prices and interest rates in finance [35,36], considerable deviations in particle kinematics in statistical physics [37][38][39], and the dispersal of microorganisms and foraging of animals in biology [40][41][42]. We evaluate the JPTW model on an experimental dataset [34] consisting of trajectories of single zebrafish in a shallow water tank.…”

Section: Introductionmentioning

confidence: 99%

A jump persistent turning walker to model zebrafish locomotion

Mwaffo

Anderson

Butail

et al. 2015

J. R. Soc. Interface.

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Zebrafish are gaining momentum as a laboratory animal species for the investigation of several functional and dysfunctional biological processes. Mathematical models of zebrafish behaviour are expected to considerably aid in the design of hypothesis-driven studies by enabling preliminary in silico tests that can be used to infer possible experimental outcomes without the use of zebrafish. This study is motivated by observations of sudden, drastic changes in zebrafish locomotion in the form of large deviations in turn rate. We demonstrate that such deviations can be captured through a stochastic mean reverting jump diffusion model, a process that is commonly used in financial engineering to describe large changes in the price of an asset. The jump process-based model is validated on trajectory data of adult subjects swimming in a shallow circular tank obtained from an overhead camera. Through statistical comparison of the empirical distribution of the turn rate against theoretical predictions, we demonstrate the feasibility of describing zebrafish as a jump persistent turning walker. The critical role of the jump term is assessed through comparison with a simplified mean reversion diffusion model, which does not allow for describing the heavy-tailed distributions observed in the fish turn rate.

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“…In the words of movement ecology occupied with the movement patterns of animals, this process is called blind search with saltatory motion. It is typical for predators hunting at spatial scales exceeding their sensory range [7][8][9][10]. For instance, blind search is observed for plankton-feeding basking sharks [11], jellyfish predators and leatherback turtles [12], and southern elephant seals [13].…”

Section: Introductionmentioning

confidence: 99%

Space-fractional Fokker–Planck equation and optimization of random search processes in the presence of an external bias

2014

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We study the efficiency of random search processes based on Lévy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher based on prior experience. While Lévy flights turn out to be efficient search processes when relative to the starting point the target is upstream, in the downstream scenario regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Lévy flights, due to which Lévy flights typically overshoot a point or small interval. Extending our recent work on biased LF search [V. V. Palyulin, A. V. Chechkin, and R. Metzler, Proc. Natl. Acad. Sci. USA, 111, 2931 (2014).] we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favors Lévy flights over regular Brownian search. Contrary to the common belief that Lévy flights with a Lévy index α = 1 (i.e., Cauchy flights) are optimal for sparse targets, we find that the optimal value for α may range in the entire interval (1, 2) and include Brownian motion as the overall most efficient search strategy.

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Lévy Processes, Saltatory Foraging, and Superdiffusion

Cited by 14 publications

References 32 publications

Evolutionary optimality in stochastic search problems

Evolutionary optimality in stochastic search problems

A jump persistent turning walker to model zebrafish locomotion

Space-fractional Fokker–Planck equation and optimization of random search processes in the presence of an external bias

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