Parametric scaling from species to growth-form diversity: an interesting analogy with multifractal functions.

We propose a measure of divergence from species to life-form diversity aimed at summarizing the ecological similarity among different plant communities without losing information on traditional taxonomic diversity. First, species and life-form relative abundances within a given plant community are determined. Next, using Rényi's generalized entropy, the diversity profiles of the analyzed community are computed both from species and life-form relative abundances. Finally, the speed of decrease from species to life-form diversity is obtained by combining the outcome of both profiles. Interestingly, the proposed measure shows some formal analogies with multifractal functions developed in statistical physics for the analysis of spatial patterns. As an application for demonstration, a small data set from a plant community sampled in the archaeological site of Paestum (southern Italy) is used.

[1]  N. Kenkel,et al.  Fractals in the Biological Sciences , 1996 .

[2]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[3]  L. Mucina,et al.  Variance in species richness and guild proportionality in two contrasting dry grassland communities , 1999 .

[4]  C. Loehle,et al.  Landscape habitat diversity: a multiscale information theory approach , 1994 .

[5]  Wolfgang Cramer,et al.  Plant functional types and climatic change: Introduction , 1996 .

[6]  Rudolf H. Riedi,et al.  Application of multifractals to the analysis of vegetation pattern , 1994 .

[7]  J. Brickmann B. Mandelbrot: The Fractal Geometry of Nature, Freeman and Co., San Francisco 1982. 460 Seiten, Preis: £ 22,75. , 1985 .

[8]  Béla Tóthmérész,et al.  Comparison of different methods for diversity ordering , 1995 .

[9]  J. Harper Population Biology of Plants , 1979 .

[10]  Ganapati P. Patil,et al.  Ecological Diversity in Theory and Practice. , 1980 .

[11]  S. Díaz,et al.  Morphological analysis of herbaceous communities under different grazing regimes , 1992 .

[12]  George Sugihara,et al.  Fractals: A User's Guide for the Natural Sciences , 1993 .

[13]  H. Mooney,et al.  CONVERGENT EVOLUTION OF MEDITERRANEAN‐CLIMATE EVERGREEN SCLEROPHYLL SHRUBS , 1970, Evolution; international journal of organic evolution.

[14]  Benoit B. Mandelbrot,et al.  Multifractal measures, especially for the geophysicist , 1989 .

[15]  Bruce T. Milne,et al.  Indices of landscape pattern , 1988, Landscape Ecology.

[16]  Carlo Ricotta,et al.  From theoretical ecology to statistical physics and back: self-similar landscape metrics as a synthesis of ecological diversity and geometrical complexity , 2000 .

[17]  E. H. Simpson Measurement of Diversity , 1949, Nature.

[18]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[19]  C. Ricotta,et al.  Quantitative comparison of the diversity of landscapes with actual vs. potential natural vegetation , 2000 .

[20]  Z. Naveh Meditteranean Ecosystems and Vegetation Types in California and Israel , 1967 .

[21]  H. Stanley,et al.  Multifractal phenomena in physics and chemistry , 1988, Nature.

[22]  Thomas M. Smith,et al.  Plant functional types : their relevance to ecosystem properties and global change , 1998 .

[23]  W. Berger,et al.  Diversity of Planktonic Foraminifera in Deep-Sea Sediments , 1970, Science.

[24]  A. Magurran Ecological Diversity and Its Measurement , 1988, Springer Netherlands.

[25]  M. Hill Diversity and Evenness: A Unifying Notation and Its Consequences , 1973 .

[26]  E. Box Macroclimate and Plant Forms , 1981, Tasks for Vegetation Science.

[27]  G. Patil,et al.  Diversity as a Concept and its Measurement , 1982 .

[28]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[29]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[30]  I. R. Noble,et al.  What are functional types and how should we seek them , 1997 .

[31]  Robert M. Gray,et al.  Entropy and Information , 1990 .

[32]  C. Beck,et al.  Thermodynamics of chaotic systems , 1993 .

[33]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.