Abstract
The principles and methods of fractal analysis of the species structure of freshwater phytoplankton, zooplankton, and macrozoobenthos communities of plain water reservoirs and urban waterbodies are discussed. The theoretical foundation and experimental verification are provided for the authors’ concept of self-similar (quasi-fractal) nature of the species structure of communities. According to this concept, the adequate mathematical image of species richness accumulation with growing sampling effort is quasi-monofractals, while the generalized geometric image of the species structure of the community is a multifractal spectrum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Azovsky, A.I., Chertoprood, M.V., Kucheruk, N.V., et al., Fractal Properties of Spatial Distribution of Intertidal Benthic Communities, Marine Biol., 2000, vol. 136, pp. 581–590.
Azovsky, A.I., Species-Area and Species-Sampling Effort Relationships: Disentangling the Effects, Ecography, 2011, vol. 34, no. 1, pp. 18–30.
Borda-de-Agua, L., Hubbell, S.P., and McAllister, M., Species-Area Curves, Diversity Indices, and Species Abundance Distributions: A Multifractal Analysis, Am. Natur., 2002, vol. 159, pp. 138–155.
Jiller, P., Struktura soobshchestv i ekologicheskaya nisha (Structure of Communities and an Ecological Niche), Moscow: Mir, 1988.
Feder, E., Fraktaly (Fractals), Moscow: Mir, 1991.
Gelashvili, D.B., Dmitriev, A.I., Iudin, D.I., et al., Multifractal Analysis of the Species Structure of Small-Mammal Communities of the Volga-Ural Paleobiocenosis, Dokl. Biol. Sci., 2008a, vol. 421, no. 4, pp. 257–261.
Gelashvili, D.B., Iudin, D.I., Rozenberg, G.S., and Yakimov, V.N., Power-Law Patterns of Accumulation of Species Richness as a Fractal Structure Manifestation, Zh. Obshch. Biol., 2007b, vol. 68, no. 3, pp. 170–179.
Gelashvili, D.B., Iudin, D.I., Rozenberg, G.S., et al., Fractal Characteristics of the Species Structure of Ichneumon Wasp Communities in the Middle Urals, Dokl. Biol. Sci., 2010a, vol. 434, no. 6, pp. 351–354.
Gelashvili, D.B., Iudin, D.I., Rozenberg, G.S., et al., The Basiss of Multifractal Analysis of the Species Structure of Communities, Usp. Sovrem. Biol., 2008b, vol. 128, no. 1, pp. 21–34.
Gelashvili, D.B., Iudin, D.I., Rozenberg, G.S., et al., The Power Law and the Principle of Self-Similarity in the Description of the Species Structure of Communities, Povolzh. Ekol. Zh., 2004, no. 3, pp. 227–245.
Gelashvili, D.B., Iudin, D.I., Solntsev, L.A., et al., Multifractal Analysis of the Species Structure of Helminthic Communities of Small Mammals in the Samarskaya Luka, Dokl. Biol. Sci., 2009, vol. 427, no. 5, pp. 374–377.
Gelashvili, D.B., Pukhnarevich, D.A., and Iudin, D.I., Structural Organization and Fractal Nature of Macrozoobenthos of Small Urban Water Bodies, Povolzh. Ekol. Zh., 2007a, no. 1, pp. 3–15.
Gelashvili, D.B., Yakimov, V.N., Iudin, D.I., et al., Fractal Aspects of Taxonomic Diversity, Zh. Obshch. Biol., 2010b, vol. 71, no. 2, pp. 115–130.
Gelashvili, D.B., Yakimov, V.N., Iudin, D.I., et al., Multi-fractal Analysis of the Species Structure of Small Mammal Communities in the Volga Region (Nizhni Novgorod Area), Russ. J. Ecol., 2008c, vol. 39, no. 6, pp. 456–461.
Gilyarov, A.M., In Search for Universal Patterns of Community Organization: Progress toward Neutralism, Zh. Obshch. Biol., 2010, vol. 71, no. 5, pp. 386–401.
Harte, J., Kinzig, A.P., and Green, J., Self-Similarity in the Distribution and Abundance of Species, Science, 1999, vol. 284, pp. 334–336.
Hartley, S., Kunin, W.E., Lennon, J.J., and Pocock, M.J.O., Coherence and Discontinuity in the Scaling of Species’ Distribution Patterns, Proc. R. Soc. L. B., 2004, vol. 271, pp. 81–88.
Isaeva, V.V., Fractal and Chaotic Patterns in the Morphology of Animals, Tr. Zool. Inst. Ros. Akad. Nauk, 2009, vol. 313, no. 1, pp. 199–218.
Iudin, D.I., Gelashvili, D.B., and Rozenberg, G.S., Multi-fractal Analysis of the Species Structure of Biotic Communities, Dokl. Biol. Sci., 2003, vol. 389, no. 2, pp. 143–146.
Keitt, T.H., Spectral Representation of Neutral Landscapes, Landscape Ecol., 2000, vol. 1, pp. 479–493.
Kunin, W.E., Extrapolating Species Abundance across Spatial Scales, Science, 1998, vol. 281, pp. 1513–1515.
Lawton, J.H., Are There General Laws in Ecology, Oikos, 1999, vol. 84, pp. 177–192.
Levich, A.P., Struktura ekologicheskikh soobshchestv (The Structure of Ecological Communities), Moscow: Izd. Mosk. Gos. Univ., 1980.
Mandelbrot, B., The Fractal Geometry of Nature, New York: Freeman, 1982.
Mandelbrot, B., Fraktal’naya geometriya prirody (The Fractal Geometry of Nature), Izhevsk: Inst. Komp. Issled., 2002.
Mandelbrot, B.B. and Wallis, J.R., Some Long-Run Properties of Geophysical Records, Water Resour. Res., 1969, vol. 5, pp. 321–340.
Margalef, R., Oblik biosfery (The Appearance of the Biosphere), Moscow: Nauka, 1992.
McGill, B.J., Etienne, R.S., Gray, J.S., et al., Species Abundance Distributions: Moving Beyond Single Prediction Theories to Integration within an Ecological Framework, Ecol. Let., 2007, vol. 10, pp. 995–1015.
Odum, E.P., Diversity as a Function of Energy Flow, in Unifying Concepts in Ecology, Van Dobben, Wh. and Lowe-Mcconnell, Rh., Eds., the Netherlands: Dr. W. Junk B.V. Publ., 1975, pp. 11–14.
Odum, Yu., Ekologiya (Ecology), Moscow: Mir, 1986, vol. 2.
Pesenko, Yu.A., Printsipy i metody kolichestvennogo analiza v faunisticheskikh issledovaniyakh (Principles and Methods of Quantitative Analysis of Faunal Studies), Moscow: Nauka, 1982.
Rozenberg, G.S., Methods to Construct Theoretical Ecology, Usp. Sovrem. Biol., 2005, vol. 125, no. 1, pp. 14–27.
Shitikov, V.K., Zinchenko, T.D., and Abrosimova, E.V., Nonparametric Methods for Comparative Assessment of Species Diversity of Macrozoobenthic River Communities, Zh. Obshch. Biol., 2010, vol. 71, no. 3, pp. 256–267.
Schroeder, M., Fraktaly, khaos, stepennye zakony. Miniatyury iz beskonechnogo raya (Fractals, Chaos, and Power Laws. Minuatures from an Infinite Paradise), NITs “Regular and Chaotic Dynamics,” Moscow: Inst. Komp. Issled., 2001.
Shurganova, G.V., Iudin, D.I., Gelashvili, D.B., and Yakimov, V.N., Multifractal Analysis of Species Diversity of Zooplanktonic Cenoses of the Cheboksary Reservoir, in Aktual’nye problemy ratsional’nogo ispol’zovaniya biologicheskikh resursov vodokhranilishch (Topical Problems of Sustainable Use of Biological Resources of Reservoirs, Rybinsk: Rybinsk. Dom Pechati, 2005, pp. 294–309.
Taylor, L.R., Aggregation, Variance and the Mean, Nature, 1961, vol. 189, pp. 732–735.
Uitteker, R., Soobshchestva i ekosistemy (Communities and Ecosystems), Moscow: Progress, 1980.
Urmantsev, Yu.A., The General Theory of Systems: State, Applications, and Prospects of Development, in Sistema. Simmetriya. Garmoniya (System. Symmetry. Harmony), Moscow: Mysl’, 1988, pp. 38–124.
Yakimov, B.N., Bossuyt, B., Iudin, D.I., and Gelashviliy, D.B., Multifractal Diversity-Area Relationship at Small Scales in Dune Slack Plant Communities, Oikos, 2008, vol. 117, pp. 33–39.
Zhang, Y., Ma, K., Anand, M., and Fu, B., Do Generalized Scaling Laws Exist for Species Abundance Distribution in Mountains?, Oikos, 2006, vol. 115, pp. 81–88.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © D.B. Gelashvili, D.I. Iudin, V.N. Yakimov, L.A. Solntsev, G.S. Rozenberg, G.V. Shurganova, A.G. Okhapkin, N.A. Startseva, D.A. Pukhnarevich, M.S. Snegireva, 2012, published in Izvestiya Akademii Nauk, Seriya Biologicheskaya, 2012, No. 3, pp. 327–335.
Rights and permissions
About this article
Cite this article
Gelashvili, D.B., Iudin, D.I., Yakimov, V.N. et al. Multifractal analysis of the species structure of freshwater hydrobiocenoses. Biol Bull Russ Acad Sci 39, 271–278 (2012). https://doi.org/10.1134/S1062359012010037
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1062359012010037