And yet it optimizes

Luz, M. G. E. da; Raposo, Ernesto P.; Viswanathan, G. M.

doi:10.1016/j.plrev.2015.07.007

Cited by 16 publications

(17 citation statements)

References 30 publications

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“…The earliest suggestions that Lévy processes could be related to the movement of organisms, based on empirical studies, date back to the late 1980’s [ 46 – 48 ]. In the 1990’s the first theoretical framework to explain this evidence appeared in the form of the so-called Lévy flight foraging hypothesis [ 1 , 49 ]: Organisms must have evolved via natural selection to exploit search strategies that optimize the search efficiency provided by Lévy distributions of move lengths under scarce information and sparse targets conditions (for a detailed discussion, see, e.g., [ 50 ]).…”

Section: Introductionmentioning

confidence: 99%

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The evolutionary origins of Lévy walk foraging

et al. 2017

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We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

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Section: Introductionmentioning

confidence: 99%

“…Since in several contexts the existence of Lévy foraging has ceased to be a matter of debate, other fundamental questions have progressively come into the spotlight [ 50 – 60 ] (but see [ 61 ]). For example, under precisely which circumstances is Lévy flight foraging advantageous over Brownian searches (e.g.…”

Section: Introductionmentioning

confidence: 99%

The evolutionary origins of Lévy walk foraging

et al. 2017

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“…So, given the lack of information, RSs are usually associated to optimization techniques, whose aim is to determine the best way of finding the maximum possible number of targets. Although in many instances it can be reduced to a single-and thus simple to characterize-objective (say, minimizing the distance covered upon the detection of a fixed number of targets [8]), eventually the most general solution implies the optimization of multiple demands, leading to conflictive tasks to account simultaneously [9,10]. Therefore, efficiency functions suitably designed for specific, nevertheless relevant, contexts should arise as a proper figure of merit (or metric) to compare between distinct search strategies.…”

Section: Introductionmentioning

confidence: 99%

Efficient search of multiple types of targets

et al. 2015

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Random searches often take place in fragmented landscapes. Also, in many instances like animal foraging, significant benefits to the searcher arise from visits to a large diversity of patches with a well-balanced distribution of targets found. Up to date, such aspects have been widely ignored in the usual single-objective analysis of search efficiency, in which one seeks to maximize just the number of targets found per distance traversed. Here we address the problem of determining the best strategies for the random search when these multiple-objective factors play a key role in the process. We consider a figure of merit (efficiency function), which properly "scores" the mentioned tasks. By considering random walk searchers with a power-law asymptotic Lévy distribution of step lengths, p(ℓ)∼ℓ(-μ), with 1<μ≤3, we show that the standard optimal strategy with μ(opt)≈2 no longer holds universally. Instead, optimal searches with enhanced superdiffusivity emerge, including values as low as μ(opt)≈1.3 (i.e., tending to the ballistic limit). For the general theory of random search optimization, our findings emphasize the necessity to correctly characterize the multitude of aims in any concrete metric to compare among possible candidates to efficient strategies. In the context of animal foraging, our results might explain some empirical data pointing to stronger superdiffusion (μ<2) in the search behavior of different animal species, conceivably associated to multiple goals to be achieved in fragmented landscapes.

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“…While diffusive strategies rely on distributions with finite (generally small) number of length scales, Lévy-like power-law models are scale free (or, alternatively, present infinite scales[5]). The scenario that maximizes the search efficiency in depleted landscapes is still an unsettled question in the context of animal motion[68][69][70].…”

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confidence: 99%

A Langevin dynamics approach to the distribution of animal move lengths

Santana-Filho¹,

Raposo²,

Macêdo³

et al. 2020

J. Stat. Mech.

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Movement is fundamental to the animals ecology, determining how, when, and where an individual interacts with the environment. The animal dynamics is usually inferred from trajectory data described as a combination of moves and turns, which are generally influenced by the vast range of complex stochastic stimuli received by the individual as it moves. Here we consider a statistical physics approach to study the probability distribution of animal move lengths based on stochastic differential Langevin equations and the superstatistics formalism. We address the stochastic influence on the move lengths as a Wiener process. Two main cases are considered: one in which the statistical properties of the noise do not change along the animal's path and another with heterogeneous noise statistics. The latter is treated in a compounding statistics framework and may be related to heterogeneous landscapes. We study Langevin dynamics processes with different types of nonlinearity in the deterministic component of movement and both linear and nonlinear multiplicative stochastic processes. The move length distributions derived here comprise the possibility of movement multiscales, diffusive and superdiffusive (Lévy-like) dynamics, and include most of the distributions currently considered in the literature of animal movement, as well as some new proposals.

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And yet it optimizes

Cited by 16 publications

References 30 publications

The evolutionary origins of Lévy walk foraging

The evolutionary origins of Lévy walk foraging

Efficient search of multiple types of targets

A Langevin dynamics approach to the distribution of animal move lengths

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