Selfsimilarity of pedotaxa distributions at the planetary scale: A multifractal approach

Geoderma

Volumn 134, Issue 3-4, 2006, Pages 306-317

  Caniego, J ^a   Ibanez J J ^b   San Jose Martinez F ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b CDIS UV Generalitat Valenciana)   (Spain)

Author keywords

Multifractal analysis; Pedodiversity; Pedotaxa abundance distributions; R nyi dimensions; Singularity exponents

Indexed keywords

CHAOS THEORY; CLASSIFICATION (OF INFORMATION); COMPUTATIONAL GEOMETRY; DATABASE SYSTEMS; FRACTALS; INDICATORS (CHEMICAL); SPECTRUM ANALYSIS;

MULTIFRACTAL ANALYSIS; PEDODIVERSITY; PEDOTAXA-ABUNDANCE DISTRIBUTIONS; SINGULARITY EXPONENTS;

SOILS;

FRACTAL ANALYSIS; PEDOLOGY; PEDON;

EID: 33746354616     PISSN: 00167061     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geoderma.2006.03.007     Document Type: Article

References (62)

1. Amundson R., Guo Y., and Gong P. Soil diversity and land use in the United States. Ecosystems 6 (2003) 470-482
2. Beck C., and Schlögl F. Thermodynamics of Chaotic Systems. An Introduction (1995), Cambridge University Press, New York 286
3. Borda-de-Agua L., Hubbell S.P., and McAllister M. Species-area curves, diversity indices, and species abundances distributions: a multifractal analysis. The American Naturalist 159 (2002) 138-155
4. Caniego F.J., Martín M.A., and San José F. Singularity features of pore-size soil distribution: singularity strength analysis and entropy spectrum. Fractals 9 (2001) 305-316
5. Caniego F.J., Martín M.A., and San Jose F. Rényi dimensions of soil pore size distribution. Geoderma 112 (2003) 205-216
6. Caniego F.J., Espejo R., Martín M.A., and San José F. Multifractal scaling of soil spatial variability. Ecol. Mod. 182 (2005) 291-303
7. Cawley R., and Mauldin R.D. Multifractal decompositions of Moran fractals. Adv. Math. 92 (1992) 196-236
8. Chhabra A., and Jensen R.V. Direct determination of the f(α) singularity spectrum. Phys. Rev. Lett. 62 (1989) 1327-1330
9. Cheng O., Agterberg F.P., and Ballantine S.B. The separation of geochemical anomalies from background by fractal models. J. Geochem. Explor. 51 (1994) 109-130
10. Culling W.E.H. Dimension and entropy in the soil-covered landscape. Earth Surf. Process. Landf. 13 (1988) 619-648
11. Everstz C.J.G., and Mandelbrot B.B. Multifractal measures. In: Peitgen H., Jürgens H., and Saupe D. (Eds). Chaos and Fractals (1992), Springer, Berlin 921-953
12. FAO, 1974. FAO-UNESCO Soil Map of the World: Vol. I. Legend. UNESCO, Paris.
13. FAO. World reference base for soil resources. 84 World Soil Resources Reports (1998), FAO-UN, Rome. http://www.fao.org/docrep/W8594E/W8594E00.HTM http://www.fao.org/docrep/W8594E/W8594E00.HTM
14. Forte B., and Vrscay E.R. Solving the inverse problem for function/image approximation using iterated function systems: I. Theoretical basis. Fractals 2 (1994) 325-334
15. Forte B., and Vrscay E.R. Solving the inverse problem for function/image approximation using iterated function systems: II. Algorithms and computations. Fractals 2 (1994) 335-346
16. Frisch U., and Parisi G. Fully developed turbulence and intermittency. In: Ghil M., Benzi R., and Parisi G. (Eds). Turbulence and Predictability of Geophysical Flows and Climate Dynamics (1985), Amsterdam, North Holland 84-88
17. Gaston K.J. Rarity (1994), Chapman and Hall, London 220 pp.
18. Grassberger P. Generalization of Hausdorff dimensions for fractal measures. Phys. Lett., A 107 (1985) 101-105
19. Guo Y., Gong P., and Amundson R. Pedodiversity in the United States of America. Geoderma 117 (2003) 99-115
20. Guo Y., Amundson R., Gong P., and Ahrens R. Taxonomic structure, distribution, and abundance of soils in the USA. Soil Sci. Soc. Am. J. 67 (2003) 1507-1516
21. Halsey T.C., Jensen M.H., Kadanoff L.P., Procaccia I., and Shraiman B.J. Fractal measures and their singularities: the characterization of strange sets. Phys. Rev., A 33 (1986) 1141-1151
22. Harte D. Multifractals: Theory and Applications (2001), Chapman & Hall/CRC 248 pp.
23. Harte J., Kinzig A.P., and Green J. Self-similarity in the distribution and abundance of species. Science 284 (1999) 334-336
24. Hastings H.M., and Sugihara G. Fractals. A User's Guide for Natural Science (1993), Oxford University Press 235 pp.
25. Hirata T., and Imoto M. Multifractal analysis of spatial distribution of microearthquakes in the Kantano region. Geophys. J. Int. 107 (1991) 155-162
26. Huggett R.J. Climate, Earth Processes and Earth History (1991), Springer, Berlin
27. Hutchinson J.E. Fractals and self similarity. Indiana Univ. Math. J. 30 (1981) 713-747
28. Ibáñez J.J., and De Alba S. Pedodiversity and scaling laws: sharing Martín and Rey's opinion on the role of the Shannon index as a measure of diversity. Geoderma 98 (2000) 5-9 (Discussion Paper)
29. Ibáñez, J.J., Ruiz-Ramos, M., in press. A mathematical comparison of classification structures: the case of USDA Soil Taxonomy. Eurasian Soil Res.
30. Ibáñez J.J., Jiménez-Ballesta R., and García-Álvarez A. Soil landscapes and drainage basins in Mediterranean mountain areas. Catena 17 (1990) 573-583
31. Ibáñez J.J., De-Alba S., Bermúdez F.F., and García-Álvarez A. Pedodiversity concepts and tools. Catena 24 (1995) 215-232
32. Ibáñez J.J., De-Alba S., Lobo A., and Zucarello V. Pedodiversity and global soil patterns at coarser scales (with discussion). Geoderma 83 (1998) 199-201
33. Ibáñez J.J., Caniego J., and San José F. Pedodiversity and biodiversity-area relationships at the planetary scale: a power law, fractal and multifractal analysis. Pedofracta2004: International Workshop on Fractal Mathematics Applied to Soil and Heterogeneous Systems. Barco de Avila (Spain) July 2-6, 2004. Summaries of the Conferences (2004) 20-21 pp.
34. Ibáñez J.J., Caniego J., San José F., and Carrera C. Pedodiversity-area relationships for islands. Ecol. Mod. 182 (2005) 257-269
35. Ibáñez J.J., Caniego J., and García-Álvarez A. Nested subset analysis and taxa-range size distributions of pedological assemblages: implications for biodiversity studies. Ecol. Mol. 182 (2005) 239-256
36. Jenny H. Factors of Soil Formation: A System of Quantitative Pedology (1941), McGraw-Hill, New York
37. Kravchenko A.N., Boast C.W., and Bullock D.G. Multifractal analysis of soil spatial variability. Agron. J. 91 (1999) 1033-1041
38. Kunin W.E. Extrapolating species abundance across spatial scales. Science 281 (1998) 1513-1515
39. Lévy Véhel J., and Mignot P. Multifractal segmentation of images. Fractals 2 (1994) 371-377
40. Lévy Véhel J., and Riedi R.H. Fractional Brownian motion and data traffic modeling: the other end of the spectrum. In: Lévy Véhel J., Lutton E., and Tricot C. (Eds). Fractals in Engineering vol. 97 (1997), Springer 185-202
41. Magurran A.E. Ecological Diversity and its Measurement (1988), Croom Helm, London 179 pp.
42. Mandelbrot B. Intermittent turbulence in self-similar cascades: diverge of high moments and dimension of carrier. J. Fluid Mech. 62 (1974) 331-358
43. Mandelbrot B. Multifractals measures. Especially for the geophysicist. Pure Appl. Geophys. 131 (1989) 5-42
44. Mandelbrot B., and Everstz C.J.G. Multifractality of the harmonic measure on fractal aggregates and extended self-similarity. Physica A 177 (1991) 386-393
45. Martín M.A., and Montero E. Laser diffraction and multifractal analysis for the characterization of dry soil volume-size distributions. Soil Till. Res. 64 (2002) 113-123
46. Martín M.A., and Taguas F.J. Fractal modelling, characterization and simulation of particle-size distributions in soil. Proc. R. Soc. Lond., A 454 (1998) 1457-1468
47. May R.M. Patterns of species abundance and diversity. In: Cody M.L., and Diamond J.M. (Eds). Ecology and Evolution of Communities (1975), Harvard Univ. Press, Cambridge, MA 81-120
48. May R.M. Patterns in multispecies communities. In: May R.M. (Ed). Theoretical Ecology (1981), Blackwell Scientific Publications, Oxford 197-227
49. McBratney A.B. Pedodiversity. Pedometron 3 (1995) 1-3
50. McBratney A.B., Odeh I.O.A., Bishop T.F.A., Dunbar M.S., and Shatar T.M. An overview of pedometric techniques for use in soil survey. Geoderma 97 (2000) 293-327
51. Pascual M., Ascioto F.A., and Caswell H. Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability. J. Plankton Res. 17 (1995) 01209-01232
52. Phillips J.D. Stability implications of the state factor model of soils as a nonlinear dynamical system. Geoderma 58 (1993) 1-15
53. Phillips J.D. On the relations between complex systems and the factorial model of soil formation (with discussion and response). Geoderma 86 (1998) 1-43
54. Phillips J.D. Earth Surface Systems: Complexity, Order and Scale (1999), Blackwell, Massachusetts
55. Phillips J.D. Divergent evolution and the spatial structure of soil landscape variability. Catena 43 (2001) 101-113
56. Phillips J.D. Geogenesis, pedogenesis and multiple causality in the formation of texture-contrast soils. Catena 58 (2004) 275-295
57. Pielou E.C. Ecological Diversity (1975), John Wiley and Sons, New York 385 pp.
58. Rényi A. Probability Theory (1970), North-Holland, Amsterdam
59. Rosenzweig M.L. Species Diversity in Space and Time (1995), Cambridge Univ. Press, Cambridge 436 pp.
60. Scheuring I., and Riedi R. Applications of multifractals to the analysis of vegetation pattern. J. Veg. Sci. 5 (1994) 489-496
61. Sugihara G., and May R.M. Applications of fractal to ecology. Trends Ecol. Evol. 5 (1990) 79-86
62. Vrscay E.R. Moment and collage methods for the inverse problem of fractal construction with iterated function systems. In: Peitgen H.O., Henriques J.M., and Penedo L.F. (Eds). Fractals in Fundamentals and Applied Sciences (1991), North-Holland, The Netherlands 443-446