Dynamical Robustness of Lévy Search Strategies

Raposo, Ernesto P.; Buldyrev, Sergey V.; Luz, M. G. E. da; Santos, M. C.; Stanley, H. Eugene; Viswanathan, G. M.

doi:10.1103/physrevlett.91.240601

Cited by 108 publications

(111 citation statements)

References 17 publications

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“…This model receives support from recent theoretical and empirical ecological research (34,35), which shows that across species, optimal search strategies, and hence patch residence times, are influenced heavily not only by environmental productivity, but also by the regeneration rates of key prey species. In patches where prey regeneration rates are fast, foragers can reuse habitats regularly because of the rapid restocking of prey, whereas in patches where prey regeneration rates are long to infinite (i.e., where foraging causes local extirpation of prey) optimal search strategies become linear (34,35), leading to high levels of mobility and the utilization of large foraging areas.…”

Section: Discussionmentioning

confidence: 97%

“…In patches where prey regeneration rates are fast, foragers can reuse habitats regularly because of the rapid restocking of prey, whereas in patches where prey regeneration rates are long to infinite (i.e., where foraging causes local extirpation of prey) optimal search strategies become linear (34,35), leading to high levels of mobility and the utilization of large foraging areas. Another, although not necessarily mutually exclusive, hypothesis suggests that colonizing populations followed least-cost pathways into the lower continent, where movement occurred rapidly either through favorable corridors, such as river drainages, or across areas of relatively homogenous topography (4,27).…”

Section: Discussionmentioning

confidence: 99%

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Spatial gradients in Clovis-age radiocarbon dates across North America suggest rapid colonization from the north

Hamilton

Buchanan

2007

Proc. Natl. Acad. Sci. U.S.A.

119

132

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A key issue in the debate over the initial colonization of North America is whether there are spatial gradients in the distribution of the Clovis-age occupations across the continent. Such gradients would help indicate the timing, speed, and direction of the colonization process. In their recent reanalysis of Clovis-age radiocarbon dates, Waters and Stafford [Waters MR, Stafford TW, Jr (2007) Science 315:1122-1126] report that they find no spatial patterning. Furthermore, they suggest that the brevity of the Clovis time period indicates that the Clovis culture represents the diffusion of a technology across a preexisting pre-Clovis population rather than a population expansion. In this article, we focus on two questions. First, we ask whether there is spatial patterning to the timing of Clovis-age occupations and, second, whether the observed speed of colonization is consistent with demic processes. With timedelayed wave-of-advance models, we use the radiocarbon record to test several alternative colonization hypotheses. We find clear spatial gradients in the distribution of these dates across North America, which indicate a rapid wave of advance originating from the north. We show that the high velocity of this wave can be accounted for by a combination of demographic processes, habitat preferences, and mobility biases across complex landscapes. Our results suggest that the Clovis-age archaeological record represents a rapid demic colonization event originating from the north.Early Paleoindian ͉ wave of advance ͉ landscape complexity ͉ hunter-gatherers ͉ Late Pleistocene

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Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Spatial gradients in Clovis-age radiocarbon dates across North America suggest rapid colonization from the north

Hamilton

Buchanan

2007

Proc. Natl. Acad. Sci. U.S.A.

119

132

View full text Add to dashboard Cite

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“…Importantly, Lévy searches with μ ∼2 are optimal for a very broad range of target densities and distributions (9). In the very low-density regime, Lévy strategies remain the optimal solution with the optimal exponent 1 < μ opt ≤ 2 dependent on specific environmental properties, such as the degree of spatial landscape heterogeneity or temporal target revisitability (10,11). Consequently, optimal Lévy searches result in more predictable target encounters during foraging in otherwise unpredictable environments (9).…”

mentioning

confidence: 99%

Hierarchical random walks in trace fossils and the origin of optimal search behavior

Sims

Reynolds

Humphries

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

102

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Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show that randomly introduced strophotaxis (U-turns)-initiated by obstructions such as self-trail avoidance or innate cueing-leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa.Brownian motion | superdiffusion | scale invariance | climate change

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“…Benhamou, 2007;Oshanin et al, 2009;Plank and James, 2008;Plank and Codling, 2009;Raposo et al, 2003;Reynolds and Bartumeus, 2009;Reynolds and Rhodes, 2009), yet burgeoning empirical evidence of Lévy patterns in recorded animal movements (de Jager et al, 2011;Humphries et al, 2012;Humphries et al, 2010;López-López et al, 2013;Sims et al, 2012;Sims et al, 2008). Consequently, it seems appropriate to present a thorough exploration of Lévy walks as a foraging strategy with the aim of clarifying the conditions under which a Lévy walk provides an advantageous search pattern and gaining a better understanding of when such patterns might be observed in free-ranging animals.…”

Section: Introductionmentioning

confidence: 99%

Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

Humphries

Sims

2014

Journal of Theoretical Biology

100

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Highlights Lévy walk foragers are optimal under a broader set of conditions than previously thought  The importance of prey-targeting has been largely overlooked  Lévy foragers outperform other strategies when prey is sparse and searching is required  Composite Brownian walk foragers outperform at some high levels of prey abundance, when searching is not required  Optimal Lévy foragers experience significantly fewer long periods of starvation Keywords: Simulation; Composite Brownian; Predator; Movement; Power-law Abstract While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24 x 10 6 simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

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Dynamical Robustness of Lévy Search Strategies

Cited by 108 publications

References 17 publications

Spatial gradients in Clovis-age radiocarbon dates across North America suggest rapid colonization from the north

Spatial gradients in Clovis-age radiocarbon dates across North America suggest rapid colonization from the north

Hierarchical random walks in trace fossils and the origin of optimal search behavior

Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

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