Rothamsted Research

where knowledge grows


Andy Reynolds

Principal Investigator
Computational and Analytical Sciences

I am responsible for developing predictive, validated mechanistic models of insect movement patterns over landscape and regional scales. This research underpins Rothamsted Research strategic goal of understanding the impact of insects in agriculture, as pests, vectors of disease and pollinators.  It supports the BBSRC's 'A Ten Year Vision' of a drive 'towards predictive biology'. The work is arousing considerable interest amongst biologists, physicists and the general public because it is showing how advances made in the novel physics and mathematics of optimal searching, random walks and turbulence can illuminate the evolved, innate ways in which insects search across multiple scales. The research has been reported on by Nature, Science, BBC News, BBC Radio, ITV Anglia News, The New York Times, Der Speigel and others.


+44 (0) 1582 763 133 ext: +44 1582 938229
Rothamsted Research, West Common, Harpenden, Hertfordshire, AL5 2JQ
Past Projects
Project Leader
  • Mathematical modelling of invertebrate movement patterns
  • Movement and spatial ecology in agricultural landscapes
  • Determining navigational mechanisms in migratory insect pests: a feasibility study

Some Recent Publications


Reynolds A.M. 2006. Co-operative random Levy flight searches and the flight patterns of honeybees. Physics Letters A 354, 384-388, 2006.

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, 371-373.

Reynolds A.M. 2006. On the intermittent behaviour of foraging animals. Europhysics Letters 75, 517-520. 

Reynolds A.M. 2006. Optimal scale-free searching strategies for the location of moving targets: new insights into visually cued mate location behaviour in insects. Physics Letters A 360, 224-227.

Reynolds A.M., Reynolds D. R., Smith, A. D., Svensson G.P. and Lofstedf C. 2007. Appetitive flight patterns of Agrotis segetum over landscape scales. J. Theoretical Biology 245, 141-14.

Reynolds A.M. Bohan D.A. and Bell J.R. 2007. Ballooning dispersal in arthropod taxa: conditions at take-off. Biology Letters 3, 237-240.

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 4, e354.

Reynolds A. M., Smith A. D., Menzel R., Greggers U., Reynolds D.R. and Riley J.R. 2007. Displaced honeybees perform optimal scale-free search flights. Ecology 88, 1955-1961.

Reynolds A.M. 2007. Dissipation conditioned stochastic modelling of scalar fluctuations in turbulent flows. Physics of fluids, 19, 075101.

Reynolds A.M. 2007. Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy. Europhysics Letters 79, 30006.

Reynolds A.M. Smith A.D., Reynolds D.R., Carreck N.L. and Osborne J.L. 2007. Honeybees perform optimal scale-free searching when attempting to locate a food source. Journal of Experimental Biology 210, 3763-3770.

Reynolds A.M. 2008. Optimal Random Levy-loop searching: New insights into the searching behaviours of central-place foragers. Europhysics Letters 82, article 20001.

Reynolds A.M. 2008. How many animals do the Levy walk? Ecology 89, 2347-2351.

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 article 011906.

Guy A.G., Bohan D.A., Powers S.J. and Reynolds A.M. 2008. Avoidance of conspecific odour by predatory carabid beetles and the emergence of scale-free searching patterns. Animal Behaviour 76, 585-591.

Reynolds A.M. and Rhodes C.J. 2009. The Levy flight paradigm. Random search patterns and mechanisms. Ecology 90, 877-887.

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 B 276, 137-143.

Reynolds A.M. Sword G.A., Simpson S.J. and Reynolds, D.R. 2009. Predator percolation, insect outbreaks and phase polyphenism. Current Biology 19, 1-5. 

Reynolds A.M. 2009. Adaptive Levy walks can outperform composite Brownian walks in non-destructive random walk scenarios. Physica A 388, 561-564.

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, 87-95.

Reynolds A.M. and Bartumeus, F. 2009. Optimising the success of random destructive searches: Levy walks can outperform ballistic motion. Journal of Theoretical Biology 260, 98-103.

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 42 article 434006.

Reynolds A.M. 2009. Levy flight patterns are an emergent property of a bumblebees' foraging strategy. Behavioral Ecology and Sociobiology 64, 19-23.

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, 115-123.

Reynolds A.M. 2010. Can spontaneous cell movements be modelled as Levy walks? Physica A 389, 273-277.

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 B 277, 765-772.

Reynolds A.M.  2010. Animals that randomly reorientate at cues left by correlated random walkers do the Lévy walk. American Naturalist 175, 607-613.

Reynolds A.M.  2010. Maze-solving by chemotaxis. Physical Review E 81, article 062901.

Reynolds A.M. 2010. Balancing the competing demands of harvesting and safety from predation: Lévy walk searches outperform composite Brownian walk searches but only when foraging under the risk of predation. Physica A 389, 4740-4746.

Reynolds A.M. 2010. Bridging the gulf between correlated random walks and Lévy walks: Autocorrelation as a source of Lévy walk movement patterns. The Journal of the Royal Society Interface 7, 1753-1758.

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 e15758.

Reynolds A.M. 2011. On the origin of bursts and heavy tails in animal dynamics. Physica A 390, 245-249.

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. The Journal of the Royal Society Interface 8, 568-577. 

Reynolds A.M. 2011. Chemotaxis can provide biological organisms with good solutions to the travelling salesman problem. Physical Review E 83, article 052901.

Reynolds A.M. 2011. Exponential and power-law contact distributions represent different atmospheric conditions. Phytopathology 101, 1465-147 .

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, 1221-1225.

Reynolds A.M. 2012. Development and validation of a Lagrangian Probability Density Function model of turbulence within and above plant canopies. Boundary-Layer Meteorology 142, 193-205.

Reynolds A.M. 2012. Truncated Lévy walks are expected beyond the scale of data collection when correlated random walks embody observed movement patterns. Journal of the Royal Society Interface 9, 528-534.

Reynolds A.M. 2012. Fitness maximizing foragers can use information about patch quality to decide how to search for and within patches: optimal Lévy walk searching patterns from optimal foraging theory. Journal of the Royal Society: Interface 72, 1568-1575.

Reynolds A.M. 2012. Distinguishing between Lévy walks and strong alternative models. Ecology 93,1228-1233.

Reynolds A.M. 2012. Olfactory search behaviour in the wandering albatross is predicted to give rise to Lévy flight movement patterns. Animal Behaviour 83, 1225-1229.

Reynolds A.M. 2012. Gusts within plant canopies are extreme value processes. Physica A 391, 5059-5063.

Reynolds A.M. 2012. Incorporating sweeps and ejections into Lagrangian stochastic models of spore trajectories within plant canopy turbulence: modelled contact distributions are heavy-tailed. Phytopathology 102, 1026-1033.

Lihoreau M., Raine N.E, Reynolds A.M., Stelzer R.J., Lim K.S., Smith A.D., OsborneJ.L. and Chittka L. 2012. Harmonic Radar Tracking and Motion Sensitive Cameras on Flowers Reveal How Bumblebees Optimise Multi-Destination Routes. PloS Biology 10 e1001392.

Reynolds A.M. 2013. Beating the odds in the aerial lottery: passive dispersers select conditions at take-off that maximise their expected fitness on landing. The American Naturalist 181, 555-561.

Reynolds A.M., LihoreauM. 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 e1002938.

Reynolds A.M. 2013. Effective leadership in animal groups when no individual has pertinent information about resource locations: How interactions between leaders and followers can result in Lévy walk movement patterns.  Europhysics Letters 102, 18001.

Reynolds A.M., Schultheiss P, and ChengK. 2013. Are Lévy flight patterns derived from the Weber-Fechner law in distance estimation? Behavioral Ecology and Sociobiology 67, 1219-1226.

Reynolds A.M. 2013. Selection pressures give composite correlated random walks Lévy walk characteristics. Journal of Theoretical Biology 332, 117-122.

Obsorne, J.L., Smith A., Clark S.J., Reynolds D.R., Barron M.C., Lim K.S. and Reynolds A.M. 2013. The ontogeny of bumblebee flight trajectories: from naïve explorers to experienced foragers. PloS One 8, e78681.

Reynolds A.M., Leprêtre, L. and Bohan, D.A. 2013. Movement patterns of Tenebrio beetles demonstrate empirically that correlated-random-walks have similitude with a Lévy walk. Scientific Reports 3: 3158.

Reynolds A.M., SchultheissP. and ChengK. 2014 Does the Australian desert ant Melophorus bagoti approximate an optimal Lévy search pattern by an intrinsic bi-modal walk? Journal of Theoretical Biology 340, 17-22.

Reynolds D.R., Reynolds A.M. and Chapman J.W. 2014. Non-volant modes of migration in terrestrial arthropods. Animal Migration 1, 8-28.

Reynolds, A.M. 2014. Reply to Comment on ‘Distinguishing between Lévy walks and strong alternative models’. Ecology 95, 1109-1112.

Wearmouth V.J., McHugh M.J., Humphries, N.E., NaegelenA., Ahmed, M.Z., Southall, E.J., Reynolds, A.M. and Sims, D.W. 2014. Scaling laws of ambush predator ‘waiting’ behaviour are tuned to a common ecology. Proceedings of the Royal Society B 281, article 20132997.

Reynolds, A.M. 2014. Towards a mechanistic framework that explains correlated random walk behaviour: correlated random walkers can optimise their fitness when foraging under the risk of predation. Ecological Complexity 19, 18-22.

Reynolds, A.M. 2014. Mussels realize Weierstrassian Lévy walks as composite correlated random walks. Scientific Reports 4, article 4409.

Sims D.W., Reynolds A.M., WearmouthV.J., HumphriesN.E., SouthallE.J., MetcalfeB. and  Twitchett R.J. 2014.Hierarchical random walks in trace fossils and the origin of optimal search behaviour. Proceedings of the National Academy of Sciences USA 111, 11073-11078.

Reynolds A.M. 2014. Signatures of active and passive optimized Lévy searching in jellyfish. Journal of the Royal Society Interface  article 20140665.

Reynolds A.M. 2014. Lévy flight movement patterns in marine predators may derive from turbulence cues. Proceedings of the Royal Society A 470 article 20140408.

Reynolds A.M. 2014. Detecting Lévy walks without turn designation Behavioral Ecology and Sociobiology 68, 1893-1899.

Reynolds A.M. and S.A.H. Geritz 2015. Tsallis distributions, Lévy walks and correlated-type anomalous diffusion result from state-dependent diffusion. Physica A 424, 317-321.

Reynolds A.M. 2015. Liberating Lévy walk research from the shackles of optimal foraging. Physics of Life Reviews. 14, 59-83.

ReynoldsA.M., Jones H.B.C., Hill J.K., PearsonA.J., WilsonK., WolfS., LimK.S., ReynoldsD.R. and Chapman J.W. 2015.Evidence for a pervasive ‘idling-mode’ activity template in flying and pedestrian insects. Royal Society Open Science 2, 150085.

ReynoldsA.M. 2015 Extending Lévy search theory from one to higher dimensions: Lévy walking favours the blind. Proceedings of the Royal Society A.  471: 20150123.

Reynolds A.M., Cecere J.G., PaivaV.H., RamosJ.A. and FocardiS. 2015.  Pelagic seabird flight patterns are consistent with a reliance on olfactory maps for oceanic navigation. Royal Society Proceedings B. 282: 20150468.

Reynolds A.M., Ropert-CoudertY., KatoA., ChiaradiaA. and MacIntosh, A.J.J. 2015. A priority-based queuing process explanation for scale-free foraging behaviours. Animal Behaviour108, 67-71.

Reynolds A.M. 2015. Venturing beyond the Lévy flight foraging hypothesis: Reply to invited comments on “Liberating Lévy walk research from the shackles of optimal foraging.”  Physics of Life Reviews. 14, 115-119. 

Chapman JW, Nilsson C, Lim KS, BäckmanJ, Reynolds DR, AlerstamT, Reynolds AM. 2015. Detection of flow direction in high-flying insect and songbird migrants. Current Biology R751–R752.

Hu G., Lim K.S., Reynolds D., Reynolds A.M., Chapman, J.W. 2016. Wind-related orientation patterns in diurnal, crepuscular and nocturnal high-altitude insect migrants. Frontiers in Behavioral Neuroscience 10:32, 1-8.

Reynolds A.M., BartumeusF, KölzschA, van de Koppel J. 2016. Signatures of chaos in animal search patterns. Scientific Reports 6:23492.

SchultheissP., StannardT., PereiraS, Reynolds A.M., WehnerR., ChengK. 2016. Similarities and differences in path integration and search in two species of desert ants inhabiting a visually cluttered and a visually barren habitat. Behavioural Ecology and Sociobiology (In Press).

Reynolds A.M., Reynolds D., Sane S.P., Hu G., Chapman J.W. 2016. Orientation in migrating insects in relation to flows: mechanisms and strategies. Philosophical Transactions Royal Society B 371: 20150392.

Lihoreau M., Ings T.C., Chittka L., Reynolds A.M. 2016. Signatures of a globally optimal searching strategy in the three-dimensional foraging flights of bumbles. Scientific Reports 6:30401.

Reynolds A.M., Paiva V.H., Cecere  J.G., Focardi S. 2016. Lévy patterns in seabirds are multifaceted describing both spatial and temporal patterning. Frontiers in Zoology 13:29.

Reynolds, A.M. Ouellette N.T. 2016 Swarm dynamics may give rise to Lévy flights. Scientific Reports 6:30515.

Woodgate J.L., Makinson J.C., Lim K.S., Reynolds, A.M., Chittka, L. 2016. Life-long radar tracking of bumblebees. PLoS ONE 11:e0160333.

Wolf S., NichollsE., Reynolds A.M., Wells P., Lim K.S., Paxton R.J., Osborne, J.L. 2016. Optimal search patterns in honeybee orientation flights are robust against emergent diseases.  Scientific Reports 6:32612.

Reynolds, A.M. 2016. The Cahn-Hilliard phase separation principle maybe the tip of an iceberg: Comment on “Phase separation driven by density-dependent movement: a novel mechanism for ecological patterns” by Q-X Liu et al. Physics of Life Reviews 19, 135-136.

Reynolds A.M. , SinhuberM., Ouellette N.T. 2017 Are midge swarms bound together by an effective velocity-dependent gravity? European Physical Journal E 40:46.

Ariel, G., Be’er, A., Reynolds A.M. (2017) Chaotic model of Lévy walks in swarming bacteria. Physical Review Letters (Accepted).

Invited book chapters.

‘Beyond optimal searching: Recent developments in the modelling of individual movement patterns as Lévy walks’ in “Dispersal, individual movement and spatial ecology: A mathematical perspective” edited by Mark Lewis, Philip Maini and Sergei Petrovskii. Springer Lecture Notes in Mathematics Vol. 2071.



PhD in Theoretical Physics (University of Warwick)


BSc in Physics (University of Warwick)

Measures of esteem


  • Editorial Highlight, and Cover story: EPJE: Are midges swarms bound together by an effective velocity-dependent gravity?


  • Invited Lecture University of Toulouse


  • Invited Lecture University of Helsinki
  • Editorial Board Member of Nature Scientific Reports
  • Research Highlight in Nature: Foraging patterns found in fossils
  • Invited Lecture University of Florence


  • Invited Lecture University of Helsinki


  • Research Highlight in Nature: Sensible Swarms


  • External examiner for the University of London
  • Research Highlight in Nature: Aphids With Altitude


  • Outstanding paper prize: Journal of Experimental Biology
  • Editorial Highlight of 2007: Europhysics Letters
  • Invited Lecture ESA Annual Meeting


  • Editorial highlight of 2006: Europhysics Letters
  • BBSRC Business Cover Story


  • M.Inst.P
  • C.Phys
  • CSci