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

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 43, 2009, Pages

  Reynolds, A M ^a  

^a ROTHAMSTED RESEARCH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72149131210     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/43/434006     Document Type: Article

References (33)

1. Atkinson R P D, Rhodes C J, MacDonald D W and Anderson R M 2002 Scale-free dynamics in the movement patterns of jackals Oikos 98 134-40
2. Bartumeus F 2007 Lévy processes in animal movement: an evolutionary hypothesis Fractals 15 151-62
3. Bartumeus F 2009 Behavioral intermittence, Lévy patterns, and randomness in animal movement Oikos 118 488-94
4. Bartumeus F, da Luz M G E, Viswanathan G M and Catalan J 2005 Animal search strategies: a quantitative random-walk analysis Ecology 86 3078-87
5. Bartumeus F, Peters F, Pueyo S, Marrasé C and Catalan J 2003 Helical Levy walks: adjusting searching statistics to resource availability in microzooplankton Proc. Natl Acad. Sci. 100 12771-5
6. Beggs J M and Plenz D 2003 Neuronal avalanches in neocortical circuits J. Neurosci. 23 11167-77
7. Boyer D, Ramos-Fernandez G, Miramontes O, Mateos J L, Cocho G, Larralde H, Ramos H and Rojas F 2006 Scale-free foraging by primates emerges from their interaction with a complex environment Proc. R. Soc. B 273 1743-50
8. Buchanan M 2008 The mathematical mirror to animal nature Nature 453 714-6
9. Dieker A B 2004 Simulation of fractional Brownian motion Master's thesis Vrije Universiteit Amsterdam, The Netherlands
10. Eckmann J P, Feinerman O, Gruendlinger L, Moses E, Soriano J and Tiusty T 2007 The physics of living neural networks Phys. Rep. 449 54-76
11. Edwards A M et al 2007 Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer Nature 449 1044-8
12. Frontier S 1987 Applications of fractal theory to ecology Developments in Numerical Ecology ed P Legendre and L Legendre (Berlin: Springer) 335-78
13. Kotulska M 2007 Natural fluctuations of an electropore show fractional Levy stable motion Biophys. J. 92 2412-21
14. Levin S A 1992 The problem of scale in ecology Ecology 73 113-31
15. Levina A, Herrmann J M and Geisel T 2007 Dynamical synapses causing self-organised criticality in neural networks Nature Phys. 3 857-60
16. Mandelbrot B B and Van Ness J W 1968 Fractional Brownian motions, fractional noises and applications SIAM Rev. 10 422-37
17. Mazzoni A, Broccard F D, Garcia-Perez E, Bonifazi P, Ruaro M E and Torre V 2007 On the dynamics of the spontaneous activity in neuronal networks PloS One 5 e439
18. Peng C K, Hausdorff J M, Mietus J E, Havlin S, Stanley H E and Goldberger A L 1993 Long-range anticorrelations and non-Gaussian behaviour in the heartbeat Phys. Rev. Lett. 70 1343-6
19. Qian H, Raymond G M and Bassingthwaighte J B 1998 On two-dimensional fractional Brownian motion and fractional Brownian random field J. Phys. A 31 L527-L535
20. Ramos-Fernandez G, Mateos J L, Miramontes O, Cocho G, Larralde H and Ayala-Orozco B 2004 Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi) Behav. Ecol. Sociobiol. 55 223-30
21. Reynolds A M 2007 Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy Europhys. Lett. 79 article 30006
22. Reynolds A M 2008a How many animals really do the Lévy walk? Ecology 89 2347-51
23. Reynolds A M 2008b Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey Phys. Rev. E 78 article 011906
24. Reynolds A M and Bartumeus F 2009 Optimizing the success of random destructive searches: Lévy walks can outperform ballistic motions J. Theor. Biol. submitted
25. Reynolds A M and Frye M A 2007 Free-flight odour tracking in Drosophila is consistent with an optimal intermittent scale-free search PLoS One 2 e354
26. Reynolds A M, Smith A D, Menzel R, Greggers U, Reynolds D R and Riley J R 2007a Displaced honeybees perform optimal scale-free search flights Ecology 88 1955-61
27. Reynolds A M, Smith A D, Reynolds D R, Carreck N L and Osborne J L 2007b Honeybees perform optimal scale-free searching flights when attempting to locate a food source J. Exp. Biol. 210 3763-70
28. Segev R, Benveniste M, Hulata E, Cohen N, Palesvki A, Kapon E, Shapira K and Ben-Jacob E 2002 Long term behaviour of lithographically prepared in vitro neuronal networks Phys. Rev. Lett. 88 article 118102
29. Sims D W et al 2008 Scaling laws of marine predator search behaviour Nature 451 1098-102
30. Turchin P 1998 Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants (Sunderland, MA: Sinauer)
31. Viswanathan G M, Afanasyev V, Buldyrev S V, Havlin S, da Luz M G E, Raposo E P and Stanley H E 2001 Lévy flight search patterns of biological organisms Physica A 295 85-8
32. Viswanathan G M, Afanasyev V, Buldyrev S V, Murphy E J, Prince P A and Stanley H E 1996 Lévy flight search patterns of wandering albatrosses Nature 381 413-5
33. Viswanathan G M, Buldyrev S V, Havlin S, da Luz M G E, Raposo E P and Stanley H E 1999 Optimizing the success of random searches Nature 401 911-4