Fluctuation scaling in complex systems: Taylor's law and beyond

Advances in Physics

Volumn 57, Issue 1, 2008, Pages 89-142

  Eisler, Zoltán ^a,b   Bartos, Imre ^c,d   Kertész, János ^b  

^a Science and Finance   (France)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^c EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^d Columbia University ^*  (United States)

Author keywords

Complex systems; Fluctuation scaling; Scaling; Taylor's law

Indexed keywords

DATA REDUCTION; INTERNET; POPULATION DYNAMICS;

FLUCTUATION SCALING; INTERACTING ELEMENTS; TAYLOR'S LAW;

LARGE SCALE SYSTEMS;

EID: 42949145468     PISSN: 00018732     EISSN: 14606976     Source Type: Journal    
DOI: 10.1080/00018730801893043     Document Type: Article

References (112)

1. T. Vicsek, Fractal Growth Phenomena, World Scientific Publishing, Singapore, 1992.
2. P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59 (1987), pp. 381-384.
3. V. Pareto, Cours d'economie politique, Droz, Geneva, Switzerland, 1896.
4. G.K. Zipf, Harv. Stud. Classic. Philol. 15 (1929), pp. 1-95.
5. L.R. Taylor, Nature 189 (1961), pp. 732-735.
6. H. Fairfield Smith, J. Agric. Sci. 28 (1938), pp. 1-23.
7. M.A. de Menezes and A.-L. Barabási, Phys. Rev. Lett. 92 (2004), Article no. 28701.
8. Z. Eisler and J. Kertész, Phys. Rev. E 73 (2006), Article no. 046109.
9. B.B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, New York, 1982.
10. B.A. Maurer and M.L. Taper, Ecol. Lett. 5 (2002), pp. 223-231.
11. B.T. Grenfell et al., Nature 394 (1998), pp. 674-677.
12. O.N. Bjornstad and B.T. Grenfell, Science 293 (2001), pp. 638-643.
13. B.-E. Saether et al., Science 287 (2000), pp. 854-856.
14. P.A. Moran, Aust. J. Zool. 1 (1953), pp. 291-298.
15. D.H. Reed and G.R. Hobbs, Anim. Conserv. 7 (2004), pp. 1-8.
16. R.M. Anderson et al., Nature 296 (1982), pp. 245-248.
17. W.S. Kendal, Ecol. Modell. 80 (1995), pp. 293-297.
18. W.S. Kendal, Ecol. Complex. 1 (2004), pp. 193-209.
19. P.A. Marquet et al., J. Exp. Biol. 208 (2005), pp. 1749-1769.
20. R.B.R. Azevedo and A.M. Leroi, Proc. Natl. Acad. Sci. U.S.A. 98 (2001), pp. 5699-5704.
21. W.S. Kendal, J. Theor. Biol. 217 (2002), pp. 203-218.
22. W.S. Kendal, Mol. Biol. Evol. 20 (2003), pp. 579-590.
23. The International SNP Map Working Group, Nature 409 (2001), pp. 928-933.
24. L.E. Reichl, A Modern Course in Statistical Physics, 2nd ed., Wiley, New York, 1998.
25. L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics Volume 5: Statistical Physics Part I, 3rd ed., Pergamon International Library, Oxford, 1980.
26. R. Botet et al., Phys. Rev. Lett. 86 (2001), pp. 3514-3517.
27. R. Botet and M. Ploszajczak, Phys. Rev. E 62 (2000), pp. 1825-1841.
28. R. Botet and M. Ploszajczak, Nucl. Phys. B (Proc. Suppl.) 92 (2001), pp. 101-113.
29. P. Uttley and I.M. McHardy, Mon. Not. R. Astron. Soc. 323 (2001), pp. L26-L30.
30. S. Vaughan and P. Uttley, Proc. SPIE 6603 (2007), Article no. 660314.
31. M.A. de Menezes and A.-L. Barabási, Phys. Rev. Lett. 93 (2004), p. 68701.
32. J. Duch and A. Arenas, Phys. Rev. Lett. 96 (2006), Article no. 218702.
33. Z. Eisler and J. Kertész, Phys. Rev. E 71 (2005), Article no. 057104.
34. S.H. Yook and M.A. de Menezes, Europhys. Lett. 72 (2005), pp. 541-547.
35. M. Šuvakova and B. Tadić, Physica A 372 (2006), pp. 354-361.
36. J. Duch and A. Arenas, Eur. Phys. J. ST 143 (2007), pp. 253-255.
37. A.M. Kilpatrick and A.R. Ives, Nature 422 (2003), pp. 65-68.
38. L.R. Taylor, J. Anim, Ecol. 55 (1986), pp. 1-38.
39. R. May, Stability and Complexity in Model Ecosystems, 2nd ed., Princeton University Press, Princeton, NJ, 1974.
40. A.J. Lotka, Elements of Physical Biology, Williams and Wilkins, Baltimore, MD, 1925.
41. V. Volterra, Variations and fluctuations of the number of individuals in animal species living together. Animal Ecology, McGraw-Hill, New York, 1925, pp. 409-448.
42. M.J. Keeling, Theor. Popul. Biol. 58 (2000), pp. 21-31.
43. J.N. Perry, Proc. R. Soc. Lond. B 257 (1994), pp. 221-226.
44. A. Satake and Y. Iwasa, J. Theor. Biol. 203 (2000), pp. 63-84.
45. F. Ballantyne IV and A.J. Kerkhoff, J. Theor. Biol. 235 (2005), pp. 373-380.
46. F. Ballantyne IV and A.J. Kerkhoff, Oikos 116 (2007), pp. 174-180.
47. A.J. Kerkhoff and F. Ballantyne IV, Ecol. Lett. 6 (2003), pp. 850-856.
48. W.D. Koenig and J.M.H. Knops, Am. Nat. 155 (2000), pp. 59-69.
49. K. Tallqvist, Folia Forestall 364 (1978), pp. 1-60.
50. J.F. Franklin, Cone production by upper slope conifers, Research Paper No. PNW-60, Pacific NW Forest Range Experiment Station, 1968.
51. M.J. Weaver and F. Forcella, Cone Production in Pinus albicaulis Forests, General Technical Report INT-203, USDA Forest Service, 1986.
52. M.J. Keeling and B.T. Grenfell, Philos. Trans. R. Soc. Lond., B, Biol. Sci. 354 (1999), pp. 769-776.
53. M.E.J. Woolhouse, L.H. Taylor and D.T. Haydon, Science 292 (2001), pp. 1109-1112.
54. A. Bar-Even et al, Nat. Genet. 38 (2006), pp. 636-643.
55. Z. Eisler et al., Europhys. Lett. 69 (2005), pp. 664-670.
56. Z. Eisler and J. Kertész, Eur. Phys. J. B 51 (2006), pp. 145-154.
57. Z. Eisler and J. Kertész, Europhys. Lett. 77 (2007), Article no. 28001.
58. New York Stock Exchange, Trades and Quotes Database for 2000-2002, New York Stock Exchange, New York, 2003.
59. Z.-Q. Jiang, L. Guo and W.-X. Zhou, Eur. Phys. J. B 57 (2007), pp. 347-355.
60. J.W. Kantelhardt et al., Physica A 316 (2002), pp. 87-114.
61. Y. Lee et al., Phys. Rev. Lett. 81 (1998), pp. 3275-3278.
62. L.A.N. Amaral et al., Phys. Rev. Lett. 80 (1998), pp. 1385-1388.
63. I.M. Jánosi and J.A.C. Gallas, Physica A 271 (1999), pp. 448-457.
64. K. Dahlstedt and H.J. Jensen, Physica A 348 (2005), pp. 596-610.
65. Z. Eisler, I. Bartos and I.M. Jánosi, in preparation.
66. T.H. Keitt and H.E. Stanley, Nature 393 (1998), pp. 257-260.
67. T.H. Keitt et al, Philos. Trans. R. Soc. Lond., B, Biol. Sci. 357 (2002), pp. 627-633.
68. W.S. Kendal, Proc. Natl. Acad. Sci. U.S.A. 98 (2001), pp. 837-841.
69. J.C. Nacher, T. Ochiai and T. Akutsu, Mod. Phys. Lett. B 19 (2005), pp. 1169-1177.
70. J. Zivković et al., Eur. Phys. J. B 50 (2006), pp. 255-258.
71. A. Mitninski and K. Rockwood, Mech. Ageing Dev. 437 (2005), pp. 699-706.
72. F. Lillo and R.N. Mantegna, Phys. Rev. E 62 (2000), pp. 6126-6134.
73. A.-L. Barabási, Nature 435 (2005), pp. 207-211.
74. J.G. Oliveira and A.-L. Barabási, Nature 437 (2005), p. 1251.
75. A. Vázquez et al., Phys. Rev. E 73 (2006), Article no. 036127.
76. U. Harder and M. Paczuski, Physica A 361 (2006), pp. 329-335.
77. B.H. McArdle, K.J. Gaston and J.H. Lawton, J. Anim. Ecol. 59 (1990), pp. 439-454.
78. S.J. Clark and J.N. Perry, Environ. Ecol. Stat. 1 (1994), pp. 287-302.
79. J. Paulsson, Nature 427 (2004), pp. 415-418.
80. S. Engen, O. Bakke and A. Islam, Biometrics 54 (1998), pp. 840-846.
81. H.E. Hurst, Trans. Am. Soc. Civil Eng. 116 (1951), pp. 770-808.
82. F. Mainardi et al., Physica A 287 (2000), pp. 468-481.
83. W. Feller, An Introduction to Probability Theory and its Applications, Vol. I and II, Wiley, New York, 1970.
84. L.R. Taylor and I.P. Woiwod, J. Anim. Ecol. 51 (1982), pp. 879-906.
85. R.J. Cho et al., Mol. Cell 2 (1998), pp. 65-73.
86. K.J. Gaston and J.H. Lawton, Nature 331 (1988), pp. 709-712.
87. K.J. Gaston, Trends Ecol. Evol. 11 (1996), pp. 197-201.
88. S.K. Bar-Lev and P. Enis, Ann. Stat. 14 (1986), pp. 1507-1522.
89. B.J. West, Chaos Solitons Fractals 20 (2004), pp. 33-44.
90. A. Colman-Lerner et al., Nature 437 (2005), pp. 699-706.
91. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74 (2002), pp. 47-97.
92. G.H. Weiss, Aspects and Applications of the Random Walk, North-Holland, Amsterdam, 1994.
93. S. Boccaletti et al., Phys. Rep. 424 (2006), pp. 175-308.
94. J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press, Cambridge, 1996.
95. R.S. Ellis and C.M. Newman, J. Stat. Phys. 19 (1978), pp. 149-161.
96. P. Bak, How Nature Works: The Science of Self-Organized Criticality, Copernicus, New York, 1996.
97. M. Paczuski, S. Boettcher and M. Baiesi, Phys. Rev. Lett. 95 (2005), Article no. 181102.
98. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Clarendon Press, Oxford, 1971.
99. J.R. Banavar et al., Phys. Rev. Lett. 98 (2007), Article no. 068104.
100. P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.
101. A.-L. Barabási and H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995.
102. C. Tebaldi, M. De Menech and A.L. Stella, Phys. Rev. Lett. 83 (1999), pp. 3952-3955.
103. D. Koutsoyiannis, Hydrol. Sci. J. 47 (2002), pp. 573-595.
104. S. Prakash et al., Phys. Rev. A 46 (1992), pp. R1724-R1727.
105. B.V. Gnedenko and V.Yu. Korolev, Random Summation: Limit Theorems and Applications, Chemical Rubber Company, Boca Raton, FL, 1996.
106. R.S. Ellis, C.M. Newman and Z. Wahrsch, Verw. Geb. 44 (1978), pp. 117-139.
107. R.S. Ellis, C.M. Newman and J.S. Rosen, Z. Wahrsch. Verw. Geb. 51 (1980), pp. 153-169.
108. F. Baldovin and A.L. Stella, Phys. Rev. E 75 (2007), Article no. 020101(R).
109. K.J. Gaston and B.H. McArdle, Philos. Trans. R. Soc. Lond., B, Biol. Sci. 345 (1994), pp. 335-358.
110. B. Jørgensen, The Theory of Dispersion Models, Chapman & Hall, London, 1997.
111. B. Jørgensen et al., Scand. J. Statist. 21 (1994), pp. 223-243.
112. P. Whittle, Biometrika 43 (1956), pp. 337-343.