Lévy flights do not always optimize random blind search for sparse targets

Proceedings of the National Academy of Sciences of the United States of America

Volumn 111, Issue 8, 2014, Pages 2931-2936

  Palyulin, Vladimir V ^a   Chechkin, Aleksei V ^b,c   Metzler, Ralf ^a,d  

^a UNIVERSITY OF POTSDAM   (Germany)

^b Kharkov Institute of Physics and Engineering   (Ukraine)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^d TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

L vy foraging hypothesis; Search optimization; Stochastic processes

Indexed keywords

ADAPTATION; ARTICLE; BROWNIAN MOTION; CONTROLLED STUDY; EXTERNAL BIAS; FLIGHT; FORAGING; HUMAN; LEVY FLIGHT; MOTION; NATURAL SELECTION; NONHUMAN; PREDATOR; PRIORITY JOURNAL; PROCESS OPTIMIZATION; RELIABILITY; SEARCH OPTIMIZATION; WALKER; WATER FLOW; WIND; AIR; ANIMAL; APPETITE; BIOLOGICAL MODEL; COMPUTER SIMULATION; GENETIC SELECTION; LÉVY FORAGING HYPOTHESIS; PHYSIOLOGY; SPECIES DIFFERENCE; STATISTICS;

LÉVY FORAGING HYPOTHESIS; SEARCH OPTIMIZATION; STOCHASTIC PROCESSES;

ADAPTATION, BIOLOGICAL; AIR MOVEMENTS; ANIMALS; APPETITIVE BEHAVIOR; COMPUTER SIMULATION; MODELS, BIOLOGICAL; SELECTION, GENETIC; SPECIES SPECIFICITY; STOCHASTIC PROCESSES; WATER MOVEMENTS;

EID: 84896875159     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1320424111     Document Type: Article

References (52)

1. Bénichou O, Loverdo C, Moreau M, Voituriez R (2011) Intermittent search strategies. Rev Mod Phys 83(1):81-129.
2. Bressloff PC, Newby JM (2013) Stochastic models of intracellular transport. Rev Mod Phys 85(1):135-196.
3. Shlesinger MF (2009) Random searching. J Phys A 42:434001.
4. Viswanathan GE, da Luz MGE, Raposo EP, Stanley HE (2011) The Physics of Foraging: An Introduction to Random Searches and Biological Encounters (Cambridge Univ Press, New York).
5. Shlesinger MF, Klafter J (1986) On Growth and Form, eds Stanley HE, Ostrowsky N (Martinus Nijhoff, Dordrecht, The Netherlands).
6. Nathan R, et al. (2008) A movement ecology paradigm for unifying organismal movement research. Proc Natl Acad Sci USA 105(49):19052-19059.
7. James A, Pitchford JW, Plank MJ (2010) Efficient or inaccurate? Analytical and numerical modelling of random search strategies. Bull Math Biol 72(4):896-913.
8. Sims DW, et al. (2008) Scaling laws of marine predator search behaviour. Nature 451(7182):1098-1102. (Pubitemid 351317439)
9. Humphries NE, et al. (2010) Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature 465(7301):1066-1069.
10. Burrow JF, Baxter PD, Pitchford JW (2008) Lévy processes, saltatory foraging, and superdiffusion. Math Model Nat Phenom 3(3):115-130.
11. Sims DW, Witt MJ, Richardson AJ, Southall EJ, Metcalfe JD (2006) Encounter success of free-ranging marine predator movements across a dynamic prey landscape. Proc Biol Sci 273(1591):1195-1201. (Pubitemid 47324453)
12. Houghton JD, Doyle TK, Wilson MW, Davenport J, Hays GC (2006) Jellyfish aggregations and leatherback turtle foraging patterns in a temperate coastal environment. Ecology 87(8):1967-1972. (Pubitemid 44215721)
13. Bradshaw CJA, Hindell MA, Sumner MD, Michael KJ (2004) Loyalty pays: Potential life history consequences of fidelity to marine foraging regions by southern elephant seals. Anim Behav 68:1349-1360. (Pubitemid 39588476)
14. Viswanathan GM, et al. (1999) Optimizing the success of random searches. Nature 401(6756):911-914.
15. Viswanathan GM, et al. (1996) Lévy flight search patterns of wandering albatrosses. Nature 381(6581):413-415.
16. de Jager M, Weissing FJ, Herman PMJ, Nolet BA, van de Koppel J (2011) Lévy walks evolve through interaction between movement and environmental complexity. Science 332(6037):1551-1553.
17. Ramos-Fernández G, et al. (2004) Lévy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi) . Behav Ecol Sociobiol 55(3):223-230. (Pubitemid 38162060)
18. Atkinson RPD, Rhodes CJ, MacDonald DW, Anderson RM (2002) Scale-free dynamics in the movement patterns of jackals. Oikos 98(1):134-140. (Pubitemid 34877847)
19. González MC, Hidalgo CA, Barabási A-L (2008) Understanding individual human mobility patterns. Nature 453(7196):779-782.
20. Brockmann D (2010) Following the money. Phys World 23(2):31-34.
21. Korobkova E, Emonet T, Vilar JMG, Shimizu TS, Cluzel P (2004) From molecular noise to behavioural variability in a single bacterium. Nature 428(6982):574-578. (Pubitemid 38480542)
22. Tu Y, Grinstein G (2005) How white noise generates power-law switching in bacterial flagellar motors. Phys Rev Lett 94(20):208101.
23. van Dartel M, Postma E, van den Herik J, de Croon G (2004) Macroscopic analysis of robot foraging behaviour. Connect Sci 16(3):169-181. (Pubitemid 39616838)
24. Boyer D, et al. (2006) Scale-free foraging by primates emerges from their interaction with a complex environment. Proc Biol Sci 273(1595):1743-1750. (Pubitemid 46931030)
25. Jansen VAA, Mashanova A, Petrovskii S (2012) Comment on "Lévy walks evolve through interaction between movement and environmental complexity". Science 335(6071):918, author reply 918.
26. Mashanova A, Oliver TH, Jansen VAA (2010) Evidence for intermittency and a truncated power law from highly resolved aphid movement data. J R Soc Interface 7(42):199-208.
27. Petrovskii S, Mashanova A, Jansen VAA (2011) Variation in individual walking behavior creates the impression of a Levy flight. Proc Natl Acad Sci USA 108(21):8704-8707.
28. Edwards AM, et al. (2007) Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449(7165):1044-1048. (Pubitemid 350017586)
29. Humphries NE, Weimerskirch H, Queiroz N, Southall EJ, Sims DW (2012) Foraging success of biological Lévy flights recorded in situ. Proc Natl Acad Sci USA 109(19):7169-7174.
30. Metzler R, Klafter J (2000) The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys Rep 339:1-77.
31. Metzler R, Klafter J (2004) The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J Phys A 37:R161-R208. (Pubitemid 39063557)
32. Chechkin AV, Metzler R, Gonchar VY, Klafter J, Tanatarov LV (2003) First passage time density for Lévy flight processes and the failure of the method of images. J Phys A 36:L537-L544. (Pubitemid 37331371)
33. Koren T, Lomholt MA, Chechkin AV, Klafter J, Metzler R (2007) Leapover lengths and first passage time statistics for Lévy flights. Phys Rev Lett 99(16):160602.
34. Koren T, Chechkin AV, Klafter J (2007) On the first passage time and leapover properties of Lévy motions. Physica A 379(1):10-22. (Pubitemid 46453054)
35. Sato K-I (1999) Lévy Processes and Infinitely Divisible Distributions (Cambridge Univ Press, Cambridge, UK).
36. Lomholt MA, Koren T, Metzler R, Klafter J (2008) Lévy strategies in intermittent search processes are advantageous. Proc Natl Acad Sci USA 105(32):1055-11059.
37. Lomholt MA, Ambjörnsson T, Metzler R (2005) Optimal target search on a fast-folding polymer chain with volume exchange. Phys Rev Lett 95(26):260603.
38. Bartumeus F, da Luz MGE, Viswanathan GM, Catalan J (2005) Animal search strategies: A quantitative random-walk analysis. Ecology 86(1):3078-3087. (Pubitemid 41677458)
39. Bartumeus F, Levin SA (2008) Fractal reorientation clocks: Linking animal behavior to statistical patterns of search. Proc Natl Acad Sci USA 105(49):19072-19077.
40. Reynolds AM (2008) Optimal random Lévy-loop searching: New insights into the searching behaviours of central-place foragers. EPL 82(2):20001.
41. Reynolds AM (2009) Scale-free animal movement patterns: Lévy walks outperform fractional Brownian motions and fractional Lévy motions in random search scenarios. J Phys A 42:434006.
42. Pavlyukevich I (2007) Lévy flights, non-local search and simulated annealing. J Comput Phys 226(2):1830-1844.
43. Klafter J, Blumen A, Shlesinger MF (1987) Stochastic pathway to anomalous diffusion. Phys Rev A 35(7):3081-3085.
44. Bénichou O, Coppey M, Moreau M, Suet PH, Voituriez R (2005) Optimal search strategies for hidden targets. Phys Rev Lett 94(19):198101.
45. Loverdo C, Bénichou O, Moreau M, Voiturierz R (2008) Enhanced reaction kinetics in biological cells. Nat Phys 4(2):134-137.
46. Benhamou S (2007) How many animals really do the Lévy walk? Ecology 88(8):1962-1969.
47. Reynolds A (2009) Adaptive Lévy walks can outperform composite Brownian walks in non-destructive random walk scenarios. Physica A 388(5):561-569.
48. Bovet P, Benhamou S (1988) Spatial analysis of animals' movements using a correlated random walk model. J Theor Biol 131(4):419-433.
49. Stanley HE (1988) Introduction to Phase Transitions and Critical Phenomena (Oxford Univ Press, New York).
50. Bartumeus F, Catalan J, Fulco UL, Lyra ML, Viswanathan GM (2002) Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys Rev Lett 88(9):097901.
51. Barabási A-L (2010) Bursts: The Hidden Patterns Behind Everything We Do, from Your E-mail to Bloody Crusades (Dutton, New York).
52. Vahabi M, Schulz JHP, Shokri B, Metzler R (2013) Area coverage of radial Lévy flights with periodic boundary conditions. Phys Rev E Stat Nonlin Soft Matter Phys 87(4):042136.