Temporal fractals in seabird foraging behaviour: Diving through the scales of time

Scientific Reports

Volumn 3, Issue , 2013, Pages

  Macintosh, Andrew J J ^a   Pelletier, Laure ^b,c   Chiaradia, Andre ^d   Kato, Akiko ^b,c   Ropert Coudert, Yan ^b,c  

^a KYOTO UNIVERSITY   (Japan)

^b UNIVERSITÉ DE STRASBOURG   (France)

^c CNRS   (France)

^d Phillip Island Nature Park   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ANIMAL BEHAVIOR; ARTICLE; DECISION MAKING; DIVING; ENVIRONMENT; FEMALE; FRACTAL ANALYSIS; MALE; PENGUIN; PHYSIOLOGY; STATISTICAL MODEL; TIME;

ANIMALS; BEHAVIOR, ANIMAL; CHOICE BEHAVIOR; DIVING; ENVIRONMENT; FEMALE; FRACTALS; LINEAR MODELS; MALE; SPHENISCIDAE; TIME FACTORS;

EID: 84878681334     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep01884     Document Type: Article

References (86)

1. Havlin, S. et al. Scaling in nature: from DNA through heartbeats to weather. Physica A-Statistical Mechanics and Its Applications 273, 46-69 (1999). (Pubitemid 129588276)
2. Peng, C. K. et al. Long-range correlations in nucleotide sequences. Nature 356, 168-170 (1992).
3. Stanley, H. E. et al. Scaling and universality in animate and inanimate systems. Physica A-Statistical Mechanics and Its Applications 231, 20-48 (1996). (Pubitemid 126394127)
4. Goldberger, A. L., Rigney, D. R. & West, B. J. Chaos and fractals in human physiology. Sci. Am. 262, 43-49 (1990).
5. Peng, C. K. et al. Quantifying fractal dynamics of human respiration: age and gender effects. Ann. Biomed. Eng. 30, 683-692 (2002).
6. West, B. J. & Goldberger, A. L. Physiology in fractal dimensions. Am. Sci. 75, 354-365 (1987).
7. Mandelbrot, B. B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156, 636-638 (1967).
8. Glenny, R. W., Robertson, H. T., Yamashiro, S. & Bassingthwaighte, J. B. Applications of fractal analysis to physiology. J. Appl. Physiol. 70, 2351-2367 (1991).
9. Peng, C. K., Havlin, S., Stanley, H. E. & Goldberger, A. L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time-series. Chaos 5, 82-87 (1995).
10. Nelson, T. R., West, B. J. & Goldberger, A. L. The fractal lung: universal and species-related scaling patterns. Experientia 46, 251-254 (1990).
11. Shlesinger, M. F. & West, B. J. Complex fractal dimension of the bronchial tree. Phys. Rev. Lett. 67, 2106-2108 (1991).
12. Viswanathan, G. M., Da Luz, M. G. E., Raposo, E. P. & Stanley, H. E. The physics of foraging. (Cambridge University Press, 2011).
13. Bartumeus, F. Levy processes in animal movement: an evolutionary hypothesis. Fractals 15, 151-162 (2007). (Pubitemid 46970247)
14. Viswanathan, G. M., Raposo, E. P. & da Luz, M. G. E. Levy flights and superdiffusion in the context of biological encounters and random searches. Physics of Life Reviews 5, 133-150 (2008).
15. Sims, D. W. et al. Scaling laws of marine predator search behaviour. Nature 451, 1098-1102 (2008). (Pubitemid 351317439)
16. MacIntosh, A. J., Alados, C. L. & Huffman, M. A. Fractal analysis of behaviour in a wild primate: behavioural complexity in health and disease. J. Royal Soc. Interface 8, 1497-1509 (2011).
17. Alados, C. L., Escos, J. M. & Emlen, J. M. Fractal structure of sequential behaviour patterns: an indicator of stress. Anim. Behav. 51, 437-443 (1996).
18. Alados, C. L. & Weber, D. N. Lead effects on the predictability of reproductive behavior in fathead minnows (Pimephales promelas): a mathematical model. Environ. Toxicol. Chem. 18, 2392-2399 (1999). (Pubitemid 29451402)
19. Motohashi, Y., Miyazaki, Y. & Takano, T. Assessment of behavioral effects of tetrachloroethylene using a set of time series analyses. Neurotoxicol. Teratol. 15, 3-10 (1993). (Pubitemid 23043227)
20. Rutherford, K. M. D., Haskell, M. J., Glasbey, C. & Lawrence, A. B. The responses of growing pigs to a chronic-intermittent stress treatment. Physiol. Behav. 89, 670-680 (2006). (Pubitemid 44895310)
21. Seuront, L. & Cribb, N. Fractal analysis reveals pernicious stress levels related to boat presence and type in the Indo-Pacific bottlenose dolphin, Tursiops aduncus. Physica A-Statistical Mechanics and Its Applications 390, 2333-2339 (2011).
22. West, B. J. Physiology in fractal dimensions: error tolerance. Ann. Biomed. Eng. 18, 135-149 (1990). (Pubitemid 20268794)
23. Goldberger, A. L. Fractal variability versus pathologic periodicity: complexity loss and stereotypy in disease. Perspect. Biol. Med. 40, 543-561 (1997). (Pubitemid 27500346)
24. Shimada, I., Kawazoe, Y. & Hara, H. A temporal model of animal behavior based on a fractality in the feeding of Drosophila melanogaster. Biol. Cybern. 68, 477-481 (1993).
25. Shimada, I., Minesaki, Y. & Hara, H. Temporal fractal in the feeding behavior of Drosophila melanogaster. J. Ethol. 13, 153-158 (1995). (Pubitemid 3024411)
26. Cole, B. J. Fractal time in animal behavior: the movement activity of Drosophila. Anim. Behav. 50, 1317-1324 (1995). (Pubitemid 26450232)
27. Alados, C. L. & Huffman, M. A. Fractal long-range correlations in behavioural sequences of wild chimpanzees: a non-invasive analytical tool for the evaluation of health. Ethology 106, 105-116 (2000). (Pubitemid 30144351)
28. Delignieres, D. et al. Fractal analyses for 'short' time series: A re-assessment of classical methods. J. Math. Psychol. 50, 525-544 (2006). (Pubitemid 44752644)
29. Weron, R. Estimating long-range dependence: finite sample properties and confidence intervals. Physica A-Statistical Mechanics and Its Applications 312, 285-299 (2002).
30. Cannon, M. J., Percival, D. B., Caccia, D. C., Raymond, G. M. & Bassingthwaighte, J. B. Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series. Physica A: Statistical Mechanics and its Applications 241, 606-626 (1997). (Pubitemid 127392898)
31. Eke, A. et al. Physiological time series: distinguishing fractal noises from motions. Pflugers Archiv-European Journal of Physiology 439, 403-415 (2000). (Pubitemid 30058830)
32. Maraun, D., Rust, H. W. & Timmer, J. Tempting long-memory-on the interpretation of DFA results. Nonlinear Processes in Geophysics 11, 495-503 (2004). (Pubitemid 39660861)
33. Beran, J. Statistics for long-memory processes. (Chapman and Hall/CRC, 1994).
34. Seuront, L., Brewer, M. & Strickler, J. R. in Handbook of scaling methods in aquatic ecology (eds Seuront, L. & Strutton, P. G.) 333-359 (CRC Press, 2004).
35. Seuront, L. Fractals and multifractals in ecology and aquatic science. 344 (Taylor and Francis, LLC, 2010).
36. Wiens, J. A., Crist, T. O., With, K. A. & Milne, B. T. Fractal patterns of insect movement in microlandscape mosaics. Ecology 76, 663-666 (1995).
37. Nams, V. O. Using animal movement paths to measure response to spatial scale. Oecologia 143, 179-188 (2005).
38. Nams, V. O. & Bourgeois, M. Fractal analysis measures habitat use at different spatial scales: an example with American marten. Can. J. Zool. 82, 1738-1747 (2005). (Pubitemid 40483037)
39. Garcia, F., Carrere, P., Soussana, J. F. & Baumont, R. Characterisation by fractal analysis of foraging paths of ewes grazing heterogeneous swards. Appl. Anim. Behav. Sci. 93, 19-37 (2005). (Pubitemid 41127960)
40. Clauset, A., Shalizi, C. & Newman, M. Power-Law Distributions in Empirical Data. SIAM Review 51, 661-703 (2009).
41. Delignieres, D., Torre, K. & Lemoine, L. Methodological issues in the application of monofractal analyses in psychological and behavioral research. Nonlinera Dynamics, Psychology, and Life Sciences 9, 451-477 (2005).
42. Boyd, I. L., Kato, A. & Ropert-Coudert, Y. Bio-logging science: sensing beyond the boundaries. Memoirs of the National Institute of Polar Research 58, 1-14 (2004).
43. Ropert-Coudert, Y. & Wilson, R. P. Trends and perspectives in animal-attached remote sensing. Frontiers in Ecology and the Environment 3, 437-444 (2005). (Pubitemid 41407518)
44. Ropert-Coudert, Y., Kato, A., Gremillet, D. & Crenner, F. in Sensors for Ecology: Towards integrated knowledge of ecosystems (eds Le Galliard, J. F., Guarini, J. M. & Gaill, F.) 17-41 (Centre National de la Recherche Scientifique (CNRS), Institut Écologie et Environnement (INEE) 2012).
45. Kembro, J. M., Marin, R. H., Zygaldo, J. A. & Gleiser, R. M. Effects of the essential oils of Lippia turbinata and Lippia polystacha (Verbenaceae) on the temporal pattern of locomotion of the mosquito Culex quinquefasciatus (Diptera: Culicidae) larvae. Parasitol. Res. 104, 1119-1127 (2009).
46. Kembro, J. M., Perillo, M. A., Pury, P. A., Satterlee, D. G. & Marin, R. H. Fractal analysis of the ambulation pattern of Japanese quail. Br. Poult. Sci. 50, 161-170 (2009).
47. Rutherford, K. M. D., Haskell, M. J., Glasbey, C., Jones, R. B. & Lawrence, A. B. Fractal analysis of animal behaviour as an indicator of animal welfare. Anim. Welf. 13, S99-S103 (2004). (Pubitemid 38351500)
48. Gao, J. B. et al. Assessment of long-range correlation in time series: How to avoid pitfalls. Physical Review E 73, (2006).
49. Stroe-Kunold, E., Stadnytska, T., Werner, J. & Braun, S. Estimating long-range dependence in time series: An evaluation of estimators implemented in R. Behav. Res. Methods 41, 909-923 (2009).
50. Humphries, N. E. et al. Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature 465, 1066-1069 (2010).
51. Sims, D. W., Humphries, N. E., Bradford, R. W. & Bruce, B. D. Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics. J. Anim. Ecol. 81, 432-442 (2012).
52. Rutherford, K. M. D., Haskell, M. J., Glasbey, C., Jones, R. B. & Lawrence, A. B. Detrended fluctuation analysis of behavioural responses to mild acute stressors in domestic hens. Appl. Anim. Behav. Sci. 83, 125-139 (2003). (Pubitemid 37078112)
53. Houston, A. I. & Carbone, C. The optimal llocation of time during the dive cycle. Behav. Ecol. 3, 233-262 (1992).
54. Kooyman, G. L. Diverse divers: physiology and behavior. (Springer-Verlag, 1989).
55. Reynolds, A. M. On the origin of bursts and heavy tails in animal dynamics. Physica A-Statistical Mechanics and Its Applications 390, 245-249 (2011).
56. Bartumeus, F. Behavioral intermittence, Levy patterns, and randomness in animal movement. Oikos 118, 488-494 (2009).
57. Kramer, D. L. Thebehavioral ecology of air breathing by aquatic animals. Can. J. Zool. 66, 89-94 (1988).
58. Seuront, L. & Leterme, S. Increased zooplankton behavioral stress in response to short-term exposure to hydrocarbon contamination. The Open Oceanography Journal 1, 1-7 (2007).
59. Turchin, P. Fractal analyses of animal movement: A Critique. Ecology 77, 2086-2090 (1996).
60. Benhamou, S. How to reliably estimate the tortuosity of an animal's path:: straightness, sinuosity, or fractal dimension? J. Theor. Biol. 229, 209-220 (2004). (Pubitemid 38780942)
61. Fritz, H., Said, S. & Weimerskirch, H. Scale-dependent hierarchical adjustments of movement patterns in a long-range foraging seabird. Proc. R. Soc. Lond. B Biol. Sci. 270, (2003).
62. Mori, Y. Dive bout organization in the chinstrap penguin at seal island, Antarctica. J. Ethol. 15, 9-15 (1997). (Pubitemid 27398673)
63. Hart, T., Coulson, T. & Trathan, P. N. Time series analysis of biologging data: autocorrelation reveals periodicity of diving behaviour in macaroni penguins. Anim. Behav. 79, 845-855 (2010).
64. Ropert-Coudert, Y., Kato, A., Naito, Y. & Cannell, B. L. Individual diving strategies in the Little Penguin. Waterbirds 26, 403-408 (2003). (Pubitemid 38265511)
65. Le Vaillant, M. et al. How age and sex drive the foraging behaviour in the king penguin. Marine Biology 160, 1147-1156 (2013).
66. Kato, A., Ropert-Coudert, Y. & Chiaradia, A. Regulation of trip duration by an inshore forager, the little penguin (Eudyptula Minor), during incubation. The Auk 125, 588-593 (2008).
67. Zimmer, I., Ropert-Coudert, Y., Poulin, N., Kato, A. & Chiaradia, A. Evaluating the relative importance of intrinsic and extrinsic factors on the foraging activity of top predators: a case study on female little penguins. Marine Biology 158, 715-722 (2011).
68. Chiaradia, A. & Kerry, K. R. Daily nest attendance and breeding performance in the Little Penguin Eudyptula minor at Phillip Island, Australia. Mar. Ornithol. 27, 13-20 (1999). (Pubitemid 30664625)
69. Arnould, J. P., Dann, P. & Cullen, J. M. Determining the sex of little penguins (Eudyptula minor) in northern Bass Strait using morphometric measurements. Emu 104, 261-265 (2004).
70. Bannasch, D. G., Wilson, R. P. & Culik, B. Hydrodynamic aspects of design and attachment of a back-mounted device in penguins. J. Theor. Biol. 194, 83-96 (1994).
71. Wilson, R. P. et al. Long term attachment of transmitting and recording devices to penguins and other seabirds. Wildl. Soc. Bull. 25, 101-106 (1997).
72. Bryce, R. M. & Sprague, K. B. Revisiting detrended fluctuation analysis. Sci. Rep. 2 (2012).
73. Taqqu, M. S., Teverovsky, V. & Willinger, W. Estimators for long-range dependence: an empirical study. Fractals 3, 785-788 (1995).
74. Mercik, S., Weron, K., Burnecki, K. & Weron, A. Enigma of self-similarity of fractional Levy stable motions. Acta Physica Polonica B 34, 3773-3791 (2003).
75. Liebovitch, L. S. & Toth, T. A fast algorithm to determine fractal dimensions by box counting. Phys. Lett. A 141, 386-390 (1989).
76. Constantine, W. & Percival, D. fractal: fractal time series modeling and analysis. R package version 1.1-1, http://CRAN.R-project.org/ package5fractal. (2011).
77. Sevcikova, H., Gneiting, T. & Percival, D. fractaldim: estimation of fractal dimensions. R package version 0.8-1, http://CRAN.R-project.org/ package5fractaldim. (2011).
78. R: a language and environment for statistical computing. v.2.15.0. (R Foundation for Statistical Computing, Vienna, Austria, 2012).
79. Hurst, H. E. Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers 116, 770-808 (1951).
80. Mandelbrot, B. B. & Van Ness, J. W. Fractional brownian motions, fractional noises and applications. SIAM Review 10, 422-437 (1968).
81. Mandelbrot, B. B. The fractal geometry of nature. (W. H. Freeman and Company, 1983).
82. Longley, P. A. & Batty, M. On the Fractal Measurement of Geographical Boundaries. Geographical Analysis 21, 47-67 (1989).
83. Rea, W., Oxley, L., Reale, M. & Brown, J. Estimators for long range dependence: an empirical study. (2009), http://arxiv.org/abs/0901.0762.
84. Gneiting, T. & Schlather, M. Stochastic models that separate fractal dimension and the Hurst effect. Society for Industrial and Applied Mathematics 46, 269-282 (2004).
85. Pinheiro, J., Bates, D., DebRoy, S. & Sarkar, D. nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-98, http://CRAN.R-project. org/package5nlme. (2011).
86. Fox, J. & Weisberg, S. An R companion to applied regression Second Edition edn, (Sage, 2011).