Abstract
The paper responds to the question: How should one go about designing the statistical analysis of biodiversity if it had to be done across scales in time and space? The conceptual basis of the design is the definition of biodiversity as a convolution of two community components. One of the components is richness, the product of species evolution, and the other structure, the consequence of environmental sorting (biotic, physical). The method of choice takes information in the manner of frequency distributions, and decomposes the associated total diversity into additive components specific to the deemed sorting factors. Diversity quantities are supplied by the analysis by which the relative importance of sorting factors can be measured and the dynamic oscillations which they generate in diversity can be traced. Examples support the a priori idea that the velocity of compositional change in the community during the late quaternary period has co-varied closely with the specific components of Kolmogorov-type complexity, Anand’s structural complexity and Rényi’s entropy of order one. The paper explains what is involved and why is it important.
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Abe, T., S.A. Levin, and M. Higashi (eds.) 1997. Biodiversity. An Ecological Perspective. Springer-Verlag, New York.
Abramson, N. 1963. Information Theory and Coding. McGraw-Hill, New York.
Anand, M. 2000. The fundamentals of vegetation change: complexity rules. Acta Biotheoretica 48: 1–14.
Anand, M. and L. Orlóci. 1996. Complexity in plant communities: notion and quantification. J. theor. Biol. 101: 529–540.
Anand, M. and L. Orlóci. 1997. Chaotic dynamics in multispecies community. Env. Ecol. Stat. 4: 337–344.
Anand, M. and L. Orlóci. 2000. On hierarchical partitioning of an ecological complexity function. Ecological Modelling 132: 51–62.
Aszalós, R. and F. Horváth. 1987. Prediction of vegetation pattern on the regional scale. In: G. Fekete (ed.), The Forefronts of Community Ecology, pp. 161–170. (In Hungarian) Scientia, Budapest.
Baltzter, H. 2000. Markov chain models for vegetation dynamics. Ecological Modelling 126: 139–154.
Berry, Th. 1990. The Dream of the Earth. Nature and Natural Philosophy Library, Sierra Club Books, San Francisco.
Box, E. O. 1981. Macroclimate and Plant Forms: An Introduction to Predictive Modelling in Plantgeography. W. Junk bv, The Hague.
Braun, E. L. 1950. Deciduous Forests of Eastern North America. The Blakston Co., Toronto.
Brillouin, L. 1962. Science and Information Theory. 2nd ed. Academic Press, New York.
Dawkins, R. 1986. The Blind Watchmaker. Penguin Books, Suffolk.
Delcourt, P. A. and H. R. Delcourt. 1987. Long-term Forest Dynamics of the Temperate Zone. Ecological Studies 63, Springer–Verlag, New York.
Dybas C. L. 2001 From biodiversity to biocomplexity: a multidisciplinary step toward understanding our environment. Bioscience 51: 426–430.
Edgington, E. S. 1987. Randomization Tests. 2nd ed. Marcel Dekker, New York.
Edwards, A. W. F. and L. L. Cavalli-Sforza. 1965. A method for cluster analysis. Biometrics 2: 362–375.
Ehrlich, P. R. and A. H. Ehrlich. 1981. Extinction: The Causes and Consequences of the Disappearing Species. Random House, New York.
Fekete, G. (ed.) 1994. Fundamentals for developing a national strategy of biodiversity conservation. Acta Zoologica Scientiarum Hungaricae 40: 289–327.
Fekete, G. and J. S. Lacza. 1970. A Survey of Plant Life-form Systems and Respective Research Approaches. II. Annales Hist.-Natur. Musei Nation. Hungarici, Pars Botanica 62: 115–127.
Feller, W. 1957. An Introduction to Probability Theory and its Applications. Vol. I, Wiley and Sons, London.
Fosberg, F. R. 1965. The entropy concept in ecology. In: Symposium on Ecological Research in Humid Tropics Vegetation, pp. 157–163. UNESCO and Government of Sarawak, Kuching, Sarawak.
Fox, L. and I. B. Parker. 1968. Chebyshev Polynomials in Numerical Analysis. Oxford University Press, London.
He, X. S. and L. Orlóci. 1998. Anderson Pond revisited: the late-Quaternary vegetation process. Abstracta Botanica 22: 81–93.
Horn, H. S. 1981. Some causes of variety in patterns of secondary succession. In: D. C. West., H. H. Shugart and D. B. Botkin (eds.), Forest Succession: Concepts and Application, pp. 24–35. Springer-Verlag, New York.
Horváth, F. and P. Csontos. 1992. Thirty-years-change in some forest communities of Visegrád Mts., Hungary. In: A. Teller, P. Mathy and J. N. R. Jeffers (eds.), Responses of Forest Ecosystems to Environmental Changes, pp. 481–488. Elsevier Applied Science, London.
Horváth, F., Z. Korsós, E. Kovácsné Láng and I. Matskási. 1997. Handbooks of the Magyar National Biodiversity Monitoring System. (In Hungarian) Hungarian Natural History Museum, Budapest.
Hulst, R. van. 1992. From population dynamics to community dynamics: modelling succession as a species replacement process. In: D. C. Glenn-Lewin, R. K. Peet and T. T. Veblen (eds.), Plant Succession: Theory and Prediction, pp. 188–214. Chapman and Hall, London.
Izsák, J. and L. Papp. 1994. Numerical properties of jack knifed diversity indices tested on loose sets coenological samples (Diptera, Drosophilidae). Coenoses 9: 59–67.
Juhász-Nagy, P. and J. Podani. 1983. Information theory methods for the study of spatial processes and succession. Vegetatio 51: 129–140.
Kenkel, N. C. and D. J. Walker. 1993. Fractals in ecology. Abstracta Botanica 17: 53–70.
Krajina, V. J. 1963. Biogeoclimatic zones on the Hawaiian Islands. Newsletter of the Hawaiian Botanical Society 7: 93–98.
Küchler, A.W. 1990. Natural vegetation. In: E. B. Espenshade and J. L. Morrison (eds.), Goode’s World Atlas, pp. 16–17. 18th ed., Rand McNally, Chicago.
Kullback, S. 1959. Information Theory and Statistics. Wiley, N.Y.
Legendre, P. and M. J. Anderson. 1999. Distance based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecol. Monogr. 69: 1–24.
Levin, S. A. 1997. Biodiversity: Interfacing Populations and Ecosystems. In: T. Abe, S. A. Levin, and M. Higashi (eds.), Biodiversity: an Ecological Perspective, pp. 277–288. Springer-Verlag, New York.
Levin, S. A. (ed.) 2001. Encyclopaedia of Biodiversity. Academic Press, San Diego.
Li, Jingwen. 1993. The Forests of Heilongjiang. Northeast Forestry University Press, Harbin.
Lippe, E., De Smidt, J. T. and D. C. Glen-Lewin. 1985. Markov models and succession: a test from a heathland in the Netherlands. J. Ecol. 73: 775–791.
Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atm. Sci. 20: 130–141.
Magurran, A. E. 1988. Ecological Diversity and its Measurement. Croom Helm, London.
Manabe, S., K. Bryan, M.J. Spelman. 1990. Transient response of a global ocean-atmosphere model to a doubling of atmospheric carbon dioxide. J. Phys. Oceanogr. 20: 722–749.
Mandelbrot, B. B. 1967. How long is the coast line of Britain? Statistical self similarity and fractional dimension. Science 156: 636–638.
Mandelbrot, B. B. 1972. Fractals: Form, Chance and Dimension. Freeman, San Francisco.
Manion, P. D. and D. Lachance (eds.) 1992. Forest Decline Concepts. APS Press, St Paul, Minnesota.
Margalef, R. 1989. On diversity and connectivity, as historical expressions of ecosystems. Coenoses 4: 121–126.
Mason, J. 1990. The greenhouse effect and global warming. Information Office, British Coal, C.R.E. Stoke Orchard, Cheltenham, Gloucestershire, U.K. GL52 4RZ.
McArdle, B. H. and M. J. Anderson. 2001. Fitting multivariate models to community data: a comment on distance based community analysis. Ecology 82: 290–297.
McIntosh, R.P. 1967. An index of diversity and the relation of certain concepts to diversity. Ecology 48: 392–404.
Mueller-Dombois, D. 1992. A natural dieback theory, cohort senescence as an alternative to the decline disease theory. In: P. D. Manion and D. Lachance (eds.), Forest Decline Concepts, pp. 26–37. APS Press, St Paul, Minnesota.
Mueller-Dombois, D. and H. Ellenberg. 1974. Aims and Methods of Vegetation Ecology. Wiley, New York.
O’Neill, R. V. 2001. Is it time to bury the ecosystem concept? Ecology 82: 3275–3284.
Orlóci. L. 1978. Multivariate Analysis in Vegetation Research. W. Junk bv, The Hague.
Orlóci, L. 1991a. On character-based community analysis: choice, arrangement, comparison Coenoses 6: 103–107.
Orlóci, L. 1991b. Entropy and information. Ecological Computations Series, Vol. 3, SPB Academic Publishing bv. The Hague
Orlóci, L. 1993. The complexities and scenarios of ecosystem analysis. In: G. P. Patil and C. R. Rao (eds.), Multivariate Environ- mental Statistics, pp. 421–430, North Holland/Elsevier, New York.
Orlóci, L. 1994. Global warming: the process and its phytoclimatic consequences in temperate and cold zone. Coenoses 9: 69–74.
Orlóci, L. 2000. From Order to Causes. A personal view, concerning the principles of syndynamics. Published at the internet address: http://sites.netscape.netlorloci
Orlóci, L. 2001a. Prospects and expectations: reflections on a science in change Community Ecol. 2: 187–196.
Orlóci, L. 2001b. Pattern dynamics: an essay concerning principles, techniques, and applications Community Ecol. 2: 1–15.
Orlóci L., M. Anand and X. S. He. 1993. Markov chain: a realistic model for temporal coenosere? Biometrie-Praximetrie 33: 7–26.
Orlóci, L. and X. S. He. 1996. The entropy structure of biodiversity. Bull. Bot. Res. (NFU, Harbin, China) 16: 146–154.
Palmer, M. W. 1988. Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75: 91–102.
Palmer M. W. 1992. The coexistence of species in fractal landscapes. Am. Nat. 139: 375–397.
Patil, G. P. and C. Taillie. 1979. An overview of diversity. In: J. F. Grassle, G. P. Patil, W. Smith and C. Taillie (eds.), Ecological Diversity in Theory and Practice, pp. 3–27. International Co-operative Publishing House, Fairland, Maryland.
Peet, R. K. 1974. The measurement of species diversity. Ann. Rev. Ecol. Syst. 5: 285–307.
Petit, J.R., Jouzel, J. Raynaud, D., Barkov, N.I, Barnola, J.M., Basile, I., Bender, M., Chappellaz, J., Davis, J., Delaygue, G., Delmotte, M., Kotlyakov, V.M., Legrand, M., Lipenkov, V., Lorius, C., Pepin, L., Ritz, C., Saltzmann, E., and M. Stievenard. 1999. Climate and atmospheric history of the past 420,000 years from the Vostok Ice Core, Antarctica. Nature 300: 429–436.
Petit, J.R., Jouzel, J. Raynaud, D., Barkov, N.I, Barnola, J.M., Basile, I., Bender, M., Chappellaz, J., Davis, J., Delaygue, G., Delmotte, M., Kotlyakov, V.M., Legrand, M., Lipenkov, V., Lorius, C., Pepin, L., Ritz, C., Saltzmann, E., and M. Stievenard. 2001. Vostok Ice Core Data for 420,000 years, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2001–076. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.
Pielou, E. C. 1975. Ecological Diversity. Wiley, New York.
Pillar, V. D. and L. Orlóci. 1993. Character-based Community Analysis: the Theory and an Application Program. Ecological Computations Series, Vol. 6, SPB Academic Publishing bv, The Hague.
Pillar, V. D. and L. Orlóci. 1996. On randomisation testing in vegetation science: multifactor comparisons of relevé groups. J. Veg. Sci. 7: 585–592.
Podani, J. 2000. Introduction to the Exploration of Multivariate Data. Backhuys, Leiden.
Podani, J., T. Czárán and S. Bartha. 1993. Pattern, area and diversity: the importance of spatial scale in species assemblages. Abstracta Botanica 17: 37–51.
Poore, M. E. D. 1955. The use of phytosociological methods in ecological investigations. J. Ecol. 43: 245–69, 606–51.
Prigogine, I. 1968. Introduction to Thermodynamics of Irreversible Processes. 3rd ed. Wiley Interscience, New York.
Rajski, C. 1961. Entropy and metric spaces. In: C. Cherry (ed.), Information Theory, pp. 41–45. Butterworths, London.
Rao, C.R. 1982. Diversity and dissimilarity coefficients: a unified approach. Theor. Popul Biol. 21: 24–43.
Rayner, J. N. 1971. An Introduction to Spectral Analysis. Pion, London.
Rényi, A. 1961. On measures of entropy and information. In: J. Neyman (ed.), Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, pp. 547–561. University of California Press, Berkeley.
Routledge, R. D. 1977. On Whittaker’s components of diversity. Ecology 58: 1120–1127.
Scheuring, I. 1993. Multifractality: a new concept in vegetation science. Abstracta Botanica 17: 71–77.
Schneider, D. C. 1994. Quantitative Ecology: Spatial and Temporal Scaling. Academic Press, San Diego.
Schroeder, M. 1991. Fractals, Chaos, Power Laws. Freeman, New York.
Shannon, C. E. 1948. A Mathematical Theory of Communication. Bell Syst. Tech. J. 27: 379–423.
Simpson, E. H. 1949. Measurement of diversity. Nature 163: 688.
Tóthmérész, B. 1997. Diversity Orderings. (In Hungarian) Scientia, Budapest.
Tóthmérész, B. 1998a. On the characterisation of scale-dependent diversity Abstracta Botanica 22: 149–1956.
Tóthmérész, B. 1998b. Quantitative ecological methods for examination of scale dependences. In: G. Fekete (ed.), The Forefronts of Community Ecology, pp. 145–160. Scientia, Budapest. (In Hungarian).
Usher, M. B. 1981. Modelling ecological succession with particular reference to Markovian models. Vegetatio 46: 11–18.
Varga, Z. 1996. Speciation and biological diversity. Term észet Világa 127 (II): 11–15. (In Hungarian)
Waggoner P. E. and G. R. Stephens. 1970. Transition probabilities for a forest. Nature 225: 1160–1161.
Wagner, H. and O. Wildi, 1997. Markov chains and vegetation monitoring. Student 2: 13–26.
Walker, D. J. and N. C. Kenkel. 1998. Fractal analysis of spatio-temporal dynamics in boreal forest landscapes. Abstracta Botanica 22: 13–28.
Walter, H., E. Harnickell and D. Mueller-Dombois. 1975. Climate Diagram Maps. Springer-Verlag, New York.
Whittaker, R. H. 1960. Vegetation of the Siskiyou Mountains, Oregon and California. Ecol. Monogr. 30:279–338.
Wildi, O. and M. Schütz. 2000. Reconstruction of a long-term recovery process from pasture to forest. Community Ecol. 1: 25–32.
Wilson, E. O. 1992. The Diversity of Life. W. W. Norton, New York.
Wilson, E. O. 2001. Foreword. In: S.A. Levin (ed.), Encyclopaedia of Biodiversity, p. XXV. Academic Press, San Diego.
Wootton, J. T. 2001. Prediction in complex communities: analysis of empirically derived Markov models. Ecology 82: 580–598.
Acknowledgements
L.O. expresses his thanks to the representatives of the Brazilian Ecological Society, namely Professora Sandra Maria Hartz and Professor Valério DePillar at the Universidade Federal do Rio Grande do Sul in Porto Alegre, for the invitation to present a plenary lecture on this paper at the Society’s 2001 Congress. M.A. acknowledges funding from the Canada Foundation for Innovation and NSERC of Canada, and V.D.P. from the Brazilian CNPq and UFRGS, which facilitated the collaborative project. Special thanks are expressed to Eng. Márta Mihály for suggested revisions at different stages, and to Professor Michael W. Palmer for the constructive comments.
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Orlóci, L., Anand, M. & Pillar, V.D. Biodiversity analysis: issues, concepts, techniques. COMMUNITY ECOLOGY 3, 217–236 (2002). https://doi.org/10.1556/ComEc.3.2002.2.8
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DOI: https://doi.org/10.1556/ComEc.3.2002.2.8