Random walks with preferential relocations to places visited in the past and their application to biology

Physical Review Letters

Volumn 112, Issue 24, 2014, Pages

  Boyer, Denis ^a   Solis Salas, Citlali ^a  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; PHYSICS;

ANALYTICAL RESULTS; CENTRAL LIMIT THEOREM; LONG-RANGE MEMORY; MODEL FRAMEWORK; PROBABILITY DENSITIES; RANDOM WALKERS; SCALE-FREE STRUCTURE; SLOW DIFFUSION;

RANDOM PROCESSES;

ALGORITHM; ANIMAL; ARTICLE; BEHAVIOR; BIOLOGICAL MODEL; CEBUS; HUMAN; MEMORY; MOVEMENT (PHYSIOLOGY); PHYSIOLOGY;

ALGORITHMS; ANIMALS; BEHAVIOR; CEBUS; HUMANS; MEMORY; MODELS, BIOLOGICAL; MOVEMENT;

EID: 84902811496     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.240601     Document Type: Article

References (52)

1. P. Turchin, Quantitative Analysis of Movement. (Sinauer Associates Inc., Sunderland, MA, 1998).
2. E.A. Codling, M.J. Plank, and S. Benhamou, J. R. Soc. Interface 5, 813 (2008). 1742-5689 10.1098/rsif.2008.0014
3. G.M. Viswanathan, M.G.E. da Luz, E.P. Raposo, and H.E. Stanley, The Physics of Foraging (Cambridge University Press, Cambridge, England, 2011).
4. J.M. Morales, D.T. Haydon, J. Frair, K.E. Holsinger, and J.M. Fryxell, Ecology 85, 2436 (2004). ECGYAQ 0012-9658 10.1890/03-0269
5. R. Nathan, W.M. Getz, E. Revilla, M. Holyoak, R. Kadmon, D. Saltz, and P.E. Smouse, Proc. Natl. Acad. Sci. U.S.A. 105, 19052 (2008). PNASA6 0027-8424 10.1073/pnas.0800375105
6. D.W. Sims, Nature (London) 451, 1098 (2008). NATUAS 0028-0836 10.1038/nature06518
7. N.E. Humphries, H. Weimerskirch, N. Queiroz, E.J. Southall, and D.W. Sims, Proc. Natl. Acad. Sci. U.S.A. 109, 7169 (2012). PNASA6 0027-8424 10.1073/pnas.1121201109
8. D. Brockmann, L. Hufnagel, and T. Geisel, Nature (London) 439, 462 (2006). NATUAS 0028-0836 10.1038/nature04292
9. M.C. González, C.A. Hidalgo, and A.-L. Barabási, Nature (London) 453, 779 (2008). NATUAS 0028-0836 10.1038/nature06958
10. C. Song, Z. Qu, N. Blumm, and A.-L. Barabási, Science 327, 1018 (2010). SCIEAS 0036-8075 10.1126/science.1177170
11. C. Song, T. Koren, P. Wang, and A.-L. Barabási, Nat. Phys. 6, 818 (2010). NPAHAX 1745-2473 10.1038/nphys1760
12. G.M. Viswanathan, E.P. Raposo, and M.G.E. da Luz, Phys. Life Rev. 5, 133 (2008). 1571-0645 10.1016/j.plrev.2008.03.002
13. F. Bartumeus, M.G.E. da Luz, G.M. Viswanathan, and J. Catalan, Ecology 86, 3078 (2005). ECGYAQ 0012-9658 10.1890/04-1806
14. O. Bénichou, M. Coppey, M. Moreau, P.-H. Suet, and R. Voituriez, Phys. Rev. Lett. 94, 198101 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94. 198101
15. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Rev. Mod. Phys. 83, 81 (2011). RMPHAT 0034-6861 10.1103/RevModPhys.83.81
16. F. Bartumeus, Oikos 118, 488 (2009). OIKSAA 0030-1299 10.1111/j.1600-0706.2009.17313.x
17. X.-W. Wang, X.-P. Han, and B.-H. Wang, PLoS One 9, e84954 (2014). POLNCL 1932-6203 10.1371/journal.pone.0084954
18. D. Boyer, M.C. Crofoot, and P.D. Walsh, J. R. Soc. Interface 9, 842 (2012). 1742-5689 10.1098/rsif.2011.0582
19. C.H. Janson and R. Byrne, Anim. Cogn. 10, 357 (2007). 1435-9448 10.1007/s10071-007-0080-9
20. W.F. Fagan, Ecol. Lett. 16, 1316 (2013). ECLEFU 1461-023X 10.1111/ele.12165
21. A.O. Gautestad and I. Mysterud, Am. Nat. 165, 44 (2005). AMNTA4 0003-0147 10.1086/426673
22. A.O. Gautestad and I. Mysterud, Ecol. Complex. 3, 44 (2006) 10.1016/j.ecocom.2005.05.007.
23. G.M. Schütz and S. Trimper, Phys. Rev. E 70, 045101(R) (2004). PLEEE8 1539-3755 10.1103/PhysRevE.70.045101
24. J.C. Cressoni, Marco Antonio Alves da Silva, and G.M. Viswanathan, Phys. Rev. Lett. 98, 070603 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.070603
25. M. Serva, Phys. Rev. E 88, 052141 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.88.052141
26. E. Bolthausen and U. Schmock, Ann. Probab. 25, 531 (1997). APBYAE 0091-1798 10.1214/aop/1024404411
27. B. Davis, Probab. Theory Relat. Fields 84, 203 (1990). PTRFEU 0178-8051 10.1007/BF01197845
28. H.G. Othmer and A. Stevens, SIAM J. Appl. Math. 57, 1044 (1997). SMJMAP 0036-1399 10.1137/S0036139995288976
29. J. Choi, J.I. Sohn, K.I. Goh, and I.M. Kim, Europhys. Lett. 99, 50001 (2012). EULEEJ 0295-5075 10.1209/0295-5075/99/50001
30. L. Peliti, J. Phys. France 46, 1469 (1985); 10.1051/jphys: 019850046090146900 0368-3400
31. L. Peliti and L. Pietronero, Riv. Nuovo Cimento 10, 1 (1987). RNUCAC 0393-697X 10.1007/BF02742985
32. M.R. Evans and S.N. Majumdar, Phys. Rev. Lett. 106, 160601 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.160601
33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.112.240601 for a derivation of the master equation.
34. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
35. P.R. Moorcroft and M.A. Lewis, Mechanistic Home Range Analysis (Princeton University Press, Princeton, NJ, 2006).
36. L. Börger, B.D. Dalziel, and J.M. Fryxell, Ecol. Lett. 11, 637 (2008). ECLEFU 1461-023X 10.1111/j.1461-0248.2008.01182.x
37. B. van Moorter, D. Visscher, S. Benhamou, L. Börger, M.S. Boyce, and J.-M. Gaillard, Oikos 118, 641 (2009). OIKSAA 0030-1299 10.1111/j.1600-0706. 2008.17003.x
38. M.C. Crofoot, I.C. Gilby, M.C. Wikelski, and R.W. Kays, Proc. Natl. Acad. Sci. U.S.A. 105, 577 (2008). PNASA6 0027-8424 10.1073/pnas.0707749105
39. A. Godec and R. Metzler, Phys. Rev. Lett. 110, 020603 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.020603
40. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.058101
41. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. 99, 210601 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601
42. G.U. Yule, Phil. Trans. R. Soc. B 213, 21 (1925). PTRBAE 0962-8436 10.1098/rstb.1925.0002
43. H.A. Simon, Biometrika 42, 425 (1955). BIOKAX 0006-3444 10.1093/biomet/42.3-4.425
44. A.-L. Barabási and R. Albert, Science 286, 509 (1999). SCIEAS 0036-8075 10.1126/science.286.5439.509
45. P.L. Krapivsky, S. Redner, and F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.4629
46. H. Kesten, Physica (Amsterdam) 138A, 299 (1986). PHYADX 0378-4371 10.1016/0378-4371(86)90186-X
47. A.O. Golosov, Russ. Math. Surv. 41, 199 (1986). 0036-0279 10.1070/RM1986v041n02ABEH003271
48. P. Le Doussal, C. Monthus, and D.S. Fisher, Phys. Rev. E 59, 4795 (1999). PLEEE8 1063-651X 10.1103/PhysRevE.59.4795
49. M.A.A. da Silva, J.C. Cressoni, G.M. Schütz, G.M. Viswanathan, and S. Trimper, Phys. Rev. E 88, 022115 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.88.022115
50. S.C. Lim and S.V. Muniandy, Phys. Rev. E 66, 021114 (2002). PLEEE8 1063-651X 10.1103/PhysRevE.66.021114
51. D. Boyer and P.D. Walsh, Phil. Trans. R. Soc. A 368, 5645 (2010). PTRMAD 1364-503X 10.1098/rsta.2010.0275
52. J. Nabe-Nielsen, J. Tougaard, J. Teilmann, K. Lucke, and M.C. Forchhammer, Oikos 122, 1307 (2013). OIKSAA 0030-1299 10.1111/j.1600-0706.2013. 00069.x