Chaotic model for lévy walks in swarming bacteria

A - Papers appearing in refereed journals

Ariel, G., Be’er, A. and Reynolds, A. M. 2017. Chaotic model for lévy walks in swarming bacteria. Physical Review Letters. 118 (22), p. 228102. https://doi.org/10.1103/PhysRevLett.118.228102

Publication dates
Authors	Ariel, G., Be’er, A. and Reynolds, A. M.
Abstract	We describe a new mechanism for Lévy walks, explaining the recently observed superdiffusion of swarming bacteria. The model hinges on several key physical properties of bacteria, such as an elongated cell shape, self-propulsion, and a collectively generated regular vortexlike flow. In particular, chaos and Lévy walking are a consequence of group dynamics. The model explains how cells can fine-tune the geometric properties of their trajectories. Experiments confirm the spectrum of these patterns in fluorescently labeled swarming Bacillus subtilis.
Keywords	biological fluid dynamics; cell aggregation; locomotion; swarming
Year of Publication	2017
Journal	Physical Review Letters
Journal citation	118 (22), p. 228102
Digital Object Identifier (DOI)	https://doi.org/10.1103/PhysRevLett.118.228102
PubMed ID	28621992
Open access	Published as ‘gold’ (paid) open access
Funder	Biotechnology and Biological Sciences Research Council
Funder project or code	Delivering Sustainable Systems (SS) [ISPG]
	Space use by bees - radar tracking of spatial movements for key pollinators
	Movement and spatial ecology in agricultural landscapes
Publisher's version	PhysRevLett.118.228102.pdf Copyright license CC BY
Output status	Published
Online	02 Jun 2017
Publication process dates
Accepted	16 Jan 2017
Publisher	American Physical Society (APS)
Grant ID	BBS/E/C/00005195
Copyright license	CC BY
ISSN	0031-9007

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Effective leadership in animal groups where no individual has pertinent information about resource locations: how interactions between leaders and followers can result in Levy walk movement patterns

A - Papers appearing in refereed journals

Reynolds, A. M. 2013. Effective leadership in animal groups where no individual has pertinent information about resource locations: how interactions between leaders and followers can result in Levy walk movement patterns. EPL. 102, p. 18001. https://doi.org/10.1209/0295-5075/102/18001

Are Levy flight patterns derived from the Weber-Fechner law in distance estimation?

A - Papers appearing in refereed journals

Reynolds, A. M., Schultheiss, P. and Cheng, K. 2013. Are Levy flight patterns derived from the Weber-Fechner law in distance estimation? Behavioral Ecology and Sociobiology. 67, pp. 1219-1226. https://doi.org/10.1007/s00265-013-1549-y

Selection pressures give composite correlated random walks Levy walk characteristics

A - Papers appearing in refereed journals

Reynolds, A. M. 2013. Selection pressures give composite correlated random walks Levy walk characteristics. Journal of Theoretical Biology. 332, pp. 117-122. https://doi.org/10.1016/j.jtbi.2013.04.035

The ontogeny of bumblebee flight trajectories: from naive explorers to experienced foragers

A - Papers appearing in refereed journals

Osborne, J. L., Smith, A. D., Clark, S. J., Reynolds, D. R., Barron, M. C., Lim, K. S. and Reynolds, A. M. 2013. The ontogeny of bumblebee flight trajectories: from naive explorers to experienced foragers. PLOS ONE. 8 (11), p. e78681. https://doi.org/10.1371/journal.pone.0078681

A simple iterative model accurately captures complex trapline formation by bumblebees across spatial scales and flower arrangements

A - Papers appearing in refereed journals

Reynolds, A. M., Lihoreau, M. and Chittka, L. 2013. A simple iterative model accurately captures complex trapline formation by bumblebees across spatial scales and flower arrangements. PLOS Computational Biology. 9, p. e1002938 (10pp). https://doi.org/10.1371/journal.pcbi.1002938

Beating the odds in the aerial lottery: passive dispersers select conditions at takeoff that maximize their expected fitness on landing

A - Papers appearing in refereed journals

Reynolds, A. M. 2013. Beating the odds in the aerial lottery: passive dispersers select conditions at takeoff that maximize their expected fitness on landing. The American Naturalist. 181, pp. 555-561. https://doi.org/10.1086/669677

Incorporating sweeps and ejections into Lagrangian stochastic models of spore trajectories within plant canopy turbulence: modeled contact distributions are heavy-tailed

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Incorporating sweeps and ejections into Lagrangian stochastic models of spore trajectories within plant canopy turbulence: modeled contact distributions are heavy-tailed. Phytopathology. 102, pp. 1026-1033. https://doi.org/10.1094/PHYTO-01-12-0002

Gusts within plant canopies are extreme value processes

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Gusts within plant canopies are extreme value processes. Physica A: Statistical Mechanics and its Applications. 391 (21), pp. 5059-5063. https://doi.org/10.1016/j.physa.2012.05.062

Radar tracking and motion-sensitive cameras on flowers reveal the development of pollinator multi-destination routes over large spatial scales

A - Papers appearing in refereed journals

Lihoreau, M., Raine, N. E., Reynolds, A. M., Stelzer, R. J., Lim, K. S., Smith, A. D., Osborne, J. L. and Chittka, L. 2012. Radar tracking and motion-sensitive cameras on flowers reveal the development of pollinator multi-destination routes over large spatial scales. PLOS Biology. 10, p. e1001392. https://doi.org/10.1371/journal.pbio.1001392

Distinguishing between Levy walks and strong alternative models

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Distinguishing between Levy walks and strong alternative models. Ecology. 93 (5), pp. 1228-1233. https://doi.org/10.1890/11-1815.1

Fitness-maximizing foragers can use information about patch quality to decide how to search for and within patches: optimal Levy walk searching patterns from optimal foraging theory

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Fitness-maximizing foragers can use information about patch quality to decide how to search for and within patches: optimal Levy walk searching patterns from optimal foraging theory. Journal of the Royal Society Interface. 9, pp. 1568-1575. https://doi.org/10.1098/rsif.2011.0815

Olfactory search behaviour in the wandering albatross is predicted to give rise to Levy flight movement patterns

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Olfactory search behaviour in the wandering albatross is predicted to give rise to Levy flight movement patterns. Animal Behaviour. 83, pp. 1225-1229. https://doi.org/10.1016/j.anbehav.2012.02.014

Truncated Levy walks are expected beyond the scale of data collection when correlated random walks embody observed movement patterns

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Truncated Levy walks are expected beyond the scale of data collection when correlated random walks embody observed movement patterns. Journal of the Royal Society Interface. 9, pp. 528-534. https://doi.org/10.1098/rsif.2011.0363

Development and validation of a Lagrangian probability density function model of horizontally-homogeneous turbulence within and above plant canopies

A - Papers appearing in refereed journals

Reynolds, A. M. 2012. Development and validation of a Lagrangian probability density function model of horizontally-homogeneous turbulence within and above plant canopies. Boundary-Layer Meteorology. 142, pp. 193-205. https://doi.org/10.1007/s10546-011-9666-5

Exponential and power-law contact distributions represent different atmospheric conditions

A - Papers appearing in refereed journals

Reynolds, A. M. 2011. Exponential and power-law contact distributions represent different atmospheric conditions. Phytopathology. 101, pp. 1465-1470. https://doi.org/10.1094/PHYTO-01-11-0001

Animal orientation strategies for movement in flows

A - Papers appearing in refereed journals

Chapman, J. W., Klaassen, R. H. G., Drake, V. A., Fossette, S., Hays, G. C., Metcalfe, J. D., Reynolds, A. M., Reynolds, D. R. and Alerstam, T. 2011. Animal orientation strategies for movement in flows. Current Biology. 21, pp. R861-R870. https://doi.org/10.1016/j.cub.2011.08.014

Flight altitude selection increases orientation performance in high-flying nocturnal insect migrants

A - Papers appearing in refereed journals

Aralimarad, P., Reynolds, A. M., Lim, K. S., Reynolds, D. R. and Chapman, J. W. 2011. Flight altitude selection increases orientation performance in high-flying nocturnal insect migrants. Animal Behaviour. 82, pp. 1221-1225. https://doi.org/10.1016/j.anbehav.2011.09.013

Chemotaxis can provide biological organisms with good solutions to the travelling salesman problem

A - Papers appearing in refereed journals

Reynolds, A. M. 2011. Chemotaxis can provide biological organisms with good solutions to the travelling salesman problem. Physical Review E. 83, p. 052901 (4 pp). https://doi.org/10.1103/PhysRevE.83.052901

Chemotaxis can take plant-parasitic nematodes to the source of a chemo-attractant via the shortest possible routes

A - Papers appearing in refereed journals

Reynolds, A. M., Dutta, T. K., Curtis, R. H. C., Powers, S. J., Gaur, H. S. and Kerry, B. R. 2011. Chemotaxis can take plant-parasitic nematodes to the source of a chemo-attractant via the shortest possible routes. Journal of the Royal Society Interface. 8, pp. 568-577. https://doi.org/10.1098/rsif.2010.0417

On the origin of bursts and heavy tails in animal dynamics

A - Papers appearing in refereed journals

Reynolds, A. M. 2011. On the origin of bursts and heavy tails in animal dynamics. Physica A: Statistical Mechanics and its Applications. 390, pp. 245-249. https://doi.org/10.1016/j.physa.2010.09.020

Orientation cues for high-flying nocturnal insect migrants: do turbulence-induced temperature and velocity fluctuations indicate the mean wind flow?

A - Papers appearing in refereed journals

Reynolds, A. M., Reynolds, D. R., Smith, A. D. and Chapman, J. W. 2010. Orientation cues for high-flying nocturnal insect migrants: do turbulence-induced temperature and velocity fluctuations indicate the mean wind flow? PLOS ONE. 5, p. e15758 (6pp). https://doi.org/10.1371/journal.pone.0015758

Bridging the gulf between correlated random walks and Levy walks: autocorrelation as a source of Levy walk movement patterns

A - Papers appearing in refereed journals

Reynolds, A. M. 2010. Bridging the gulf between correlated random walks and Levy walks: autocorrelation as a source of Levy walk movement patterns. Journal of the Royal Society Interface. 7, pp. 1753-1758. https://doi.org/10.1098/rsif.2010.0292

Balancing the competing demands of harvesting and safety from predation: Levy walk searches outperform composite Brownian walk searches but only when foraging under the risk of predation

A - Papers appearing in refereed journals

Reynolds, A. M. 2010. Balancing the competing demands of harvesting and safety from predation: Levy walk searches outperform composite Brownian walk searches but only when foraging under the risk of predation. Physica A: Statistical Mechanics and its Applications. 389, pp. 4740-4746. https://doi.org/10.1016/j.physa.2010.06.027

Maze-solving by chemotaxis

A - Papers appearing in refereed journals

Reynolds, A. M. 2010. Maze-solving by chemotaxis. Physical Review E. 81, p. 062901. https://doi.org/10.1103/PhysRevE.81.062901

Animals that randomly reorient at cues left by correlated random walkers do the Levy walk

A - Papers appearing in refereed journals

Reynolds, A. M. 2010. Animals that randomly reorient at cues left by correlated random walkers do the Levy walk. The American Naturalist. 175, pp. 607-613. https://doi.org/10.1086/651617

A single wind-mediated mechanism explains high-altitude 'non-goal oriented' headings and layering of nocturnally migrating insects

A - Papers appearing in refereed journals

Reynolds, A. M., Reynolds, D. R., Smith, A. D. and Chapman, J. W. 2010. A single wind-mediated mechanism explains high-altitude 'non-goal oriented' headings and layering of nocturnally migrating insects. Proceedings of the Royal Society of London Series B Biological Sciences. 277, pp. 765-772. https://doi.org/10.1098/rspb.2009.1221

Can spontaneous cell movements be modelled as Levy walks?

A - Papers appearing in refereed journals

Reynolds, A. M. 2010. Can spontaneous cell movements be modelled as Levy walks? Physica A: Statistical Mechanics and its Applications. 389, pp. 273-277. https://doi.org/10.1016/j.physa.2009.09.027

Honeybees use a Levy flight search strategy and odour-mediated anemotaxis to relocate food sources

A - Papers appearing in refereed journals

Reynolds, A. M., Swain, J. L., Smith, A. D., Martin, A. P. and Osborne, J. L. 2009. Honeybees use a Levy flight search strategy and odour-mediated anemotaxis to relocate food sources. Behavioral Ecology and Sociobiology. 64, pp. 115-123. https://doi.org/10.1007/s00265-009-0826-2

Levy flight patterns are predicted to be an emergent property of a bumblebee's foraging strategy

A - Papers appearing in refereed journals

Reynolds, A. M. 2009. Levy flight patterns are predicted to be an emergent property of a bumblebee's foraging strategy. Behavioral Ecology and Sociobiology. 64, pp. 19-23. https://doi.org/10.1007/s00265-009-0813-7

Scale-free animal movement patterns: Levy walks outperform fractional Brownian motions and fractional Levy motions in random search scenarios

A - Papers appearing in refereed journals

Reynolds, A. M. 2009. Scale-free animal movement patterns: Levy walks outperform fractional Brownian motions and fractional Levy motions in random search scenarios. Journal of Physics A-Mathematical and Theoretical. 42, p. 434006 (11pp). https://doi.org/10.1088/1751-8113/42/43/434006

Optimising the success of random destructive searches: Levy walks can outperform ballistic motions

A - Papers appearing in refereed journals

Reynolds, A. M. and Bartumeus, F. 2009. Optimising the success of random destructive searches: Levy walks can outperform ballistic motions. Journal of Theoretical Biology. 260, pp. 98-103. https://doi.org/10.1016/j.jtbi.2009.05.033

The Levy flight paradigm - random search patterns and mechanisms

A - Papers appearing in refereed journals

Reynolds, A. M. and Rhodes, C. J. 2009. The Levy flight paradigm - random search patterns and mechanisms. Ecology. 90 (4), pp. 877-887. https://doi.org/10.1890/08-0153.1

Adaptive Levy walks can outperform composite Brownian walks in non-destructive random searching scenarios

A - Papers appearing in refereed journals

Reynolds, A. M. 2009. Adaptive Levy walks can outperform composite Brownian walks in non-destructive random searching scenarios. Physica A: Statistical Mechanics and its Applications. 388, pp. 561-564. https://doi.org/10.1016/j.physa.2008.11.007

Predator percolation, insect outbreaks and phase polyphenism

A - Papers appearing in refereed journals

Reynolds, A. M., Sword, G. A., Simpson, S. J. and Reynolds, D. R. 2009. Predator percolation, insect outbreaks and phase polyphenism. Current Biology. 19, pp. 20-24. https://doi.org/10.1016/j.cub.2008.10.070

Does a 'turbophoretic' effect account for layer concentrations of insects migrating in the stable night-time atmosphere?

A - Papers appearing in refereed journals

Reynolds, A. M., Reynolds, D. R. and Riley, J. R. 2009. Does a 'turbophoretic' effect account for layer concentrations of insects migrating in the stable night-time atmosphere? Journal of the Royal Society Interface. 6, pp. 87-95. https://doi.org/10.1098/rsif.2008.0173

Aphid aerial density profiles are consistent with turbulent advection amplifying flight behaviours: abandoning the epithet 'passive'

A - Papers appearing in refereed journals

Reynolds, A. M. and Reynolds, D. R. 2009. Aphid aerial density profiles are consistent with turbulent advection amplifying flight behaviours: abandoning the epithet 'passive'. Proceedings of the Royal Society of London Series B Biological Sciences. 276, pp. 137-143. https://doi.org/10.1098/rspb.2008.0880

Bee searching strategies in the landscape

C2 - Non-edited contributions to conferences

Osborne, J. L., Smith, A. D. and Reynolds, A. M. 2008. Bee searching strategies in the landscape. Abstracts 3rd European Conference of Apidology (EurBee3), Belfast,8-11 September 2008 . pp. 79

How many animals really do the Levy walk? Comment

A - Papers appearing in refereed journals

Reynolds, A. M. 2008. How many animals really do the Levy walk? Comment. Ecology. 89 (8), pp. 2347-2351. https://doi.org/10.1890/07-1688.1

Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey

A - Papers appearing in refereed journals

Reynolds, A. M. 2008. Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey. Physical Review E. 78, p. 011906 (5 pages). https://doi.org/10.1103/PhysRevE.78.011906

Particle deposition onto rough surfaces

A - Papers appearing in refereed journals

Lo Iacono, G., Reynolds, A. M. and Tucker, P. G. 2008. Particle deposition onto rough surfaces. Journal of Fluids Engineering. 130, p. 074501 (5 pages). https://doi.org/10.1115/1.2948359

Avoidance of conspecific odour by carabid beetles: a mechanism for the emergence of scale-free searching patterns

A - Papers appearing in refereed journals

Guy, A. G., Bohan, D. A., Powers, S. J. and Reynolds, A. M. 2008. Avoidance of conspecific odour by carabid beetles: a mechanism for the emergence of scale-free searching patterns. Animal Behaviour. 76, pp. 585-591. https://doi.org/10.1016/j.anbehav.2008.04.004

Optimal random Levy-loop searching: new insights into the searching behaviours of central-place foragers

A - Papers appearing in refereed journals

Reynolds, A. M. 2008. Optimal random Levy-loop searching: new insights into the searching behaviours of central-place foragers. EPL-Europhysics Letters. 82, p. 20001 (6pp). https://doi.org/10.1209/0295-5075/82/20001

Modelling of concentrations along a moving observer in an inhomogeneous plume. Biological application: model of odour-mediated insect flights

A - Papers appearing in refereed journals

Lo Iacono, G. and Reynolds, A. M. 2008. Modelling of concentrations along a moving observer in an inhomogeneous plume. Biological application: model of odour-mediated insect flights. Environmental Fluid Mechanics. 8, pp. 147-168. https://doi.org/10.1007/s10652-008-9054-y

The influence of search strategies and homogeneous isotropic turbulence on planktonic contact rates

A - Papers appearing in refereed journals

Rhodes, C. J. and Reynolds, A. M. 2007. The influence of search strategies and homogeneous isotropic turbulence on planktonic contact rates. EPL-Europhysics Letters. 80, p. 60003 (5pp). https://doi.org/10.1209/0295-5075/80/60003

Honeybees perform optimal scale-free searching flights when attempting to locate a food source

A - Papers appearing in refereed journals

Reynolds, A. M., Smith, A. D., Reynolds, D. R., Carreck, N. L. and Osborne, J. L. 2007. Honeybees perform optimal scale-free searching flights when attempting to locate a food source. Journal Of Experimental Biology. 210, pp. 3763-3770. https://doi.org/10.1242/jeb.009563

Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy

A - Papers appearing in refereed journals

Reynolds, A. M. 2007. Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy. EPL-Europhysics Letters. 79, p. 30006 (5 pages). https://doi.org/10.1209/0295-5075/79/30006

Dissipation conditioned stochastic modeling of scalar concentration fluctuations in turbulent flows

A - Papers appearing in refereed journals

Reynolds, A. M. 2007. Dissipation conditioned stochastic modeling of scalar concentration fluctuations in turbulent flows. Physics Of Fluids. 19, p. 075101 (6pp). https://doi.org/10.1063/1.2747681

Displaced honey bees perform optimal scale-free search flights

A - Papers appearing in refereed journals

Reynolds, A. M., Smith, A. D., Menzel, R., Greggers, U., Reynolds, D. R. and Riley, J. R. 2007. Displaced honey bees perform optimal scale-free search flights. Ecology. 88 (8), pp. 1955-1961. https://doi.org/10.1890/06-1916.1

Appetitive flight patterns of male Agrotis segetum moths over landscape scales

A - Papers appearing in refereed journals

Reynolds, A. M., Reynolds, D. R., Smith, A. D., Svensson, G. P. and Lofstedt, C. 2007. Appetitive flight patterns of male Agrotis segetum moths over landscape scales. Journal of Theoretical Biology. 245, pp. 141-149. https://doi.org/10.1016/j.jtbi.2006.10.007

Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search

A - Papers appearing in refereed journals

Reynolds, A. M. and Frye, M. A. 2007. Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PLOS ONE. 2, p. e354. https://doi.org/10.1371/journal.pone.0000354

Optimal scale-free searching strategies for the location of moving targets: new insights on visually cued mate location behaviour in insects

A - Papers appearing in refereed journals

Reynolds, A. M. 2006. Optimal scale-free searching strategies for the location of moving targets: new insights on visually cued mate location behaviour in insects. Physics Letters A. 360, pp. 224-227. https://doi.org/10.1016/j.physleta.2006.08.047

Ballooning dispersal in arthropod taxa with convergent behaviours: dynamic properties of ballooning silk in turbulent flows

A - Papers appearing in refereed journals

Reynolds, A. M., Bohan, D. A. and Bell, J. R. 2006. Ballooning dispersal in arthropod taxa with convergent behaviours: dynamic properties of ballooning silk in turbulent flows. Biology Letters. 2, pp. 371-373. https://doi.org/10.1098/rsbl.2006.0486

Stochastic simulation of Lagrangian trajectories in near-wall turbulence

A - Papers appearing in refereed journals

Reynolds, A. M. 2006. Stochastic simulation of Lagrangian trajectories in near-wall turbulence. Physics Of Fluids. 18, p. Art no. 075107. https://doi.org/10.1063/1.2236303

On the intermittent behaviour of foraging animals

A - Papers appearing in refereed journals

Reynolds, A. M. 2006. On the intermittent behaviour of foraging animals. EPL-Europhysics Letters. 75, pp. 517-520. https://doi.org/10.1209/epl/i2006-10157-x

On chirality and turbulent dispersion

A - Papers appearing in refereed journals

Reynolds, A. M. 2006. On chirality and turbulent dispersion. Physica D-Nonlinear Phenomena. 218, pp. 185-190. https://doi.org/10.1016/j.physd.2006.05.008

Cooperative random Levy flight searches and the flight patterns of honeybees

A - Papers appearing in refereed journals

Reynolds, A. M. 2006. Cooperative random Levy flight searches and the flight patterns of honeybees. Physics Letters A. 354, pp. 384-388. https://doi.org/10.1016/j.physleta.2006.01.086

Parameterizations of Lagrangian spin statistics and particle dispersion in the presence of coherent vortices

A - Papers appearing in refereed journals

Veneziani, M., Griffa, A., Reynolds, A. M., Garraffo, Z. D. and Chassignet, E. P. 2005. Parameterizations of Lagrangian spin statistics and particle dispersion in the presence of coherent vortices. Journal Of Marine Research. 63, pp. 1057-1083. https://doi.org/10.1357/002224005775247571

Scale-free movement patterns arising from olfactory-driven foraging

A - Papers appearing in refereed journals

Reynolds, A. M. 2005. Scale-free movement patterns arising from olfactory-driven foraging. Physical Review E. 72, p. Art. no. 041928 (5 pages). https://doi.org/10.1103/PhysRevE.72.041928

A Lagrangian stochastic model for the dispersion and deposition of Brownian particles in the presence of a temperature gradient

A - Papers appearing in refereed journals

Lo Iacono, G. and Reynolds, A. M. 2005. A Lagrangian stochastic model for the dispersion and deposition of Brownian particles in the presence of a temperature gradient. Journal Of Aerosol Science. 36, pp. 1238-1250.

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