1st Edition

Fractals and Multifractals in Ecology and Aquatic Science

By Laurent Seuront Copyright 2010
    364 Pages 186 B/W Illustrations
    by CRC Press

    364 Pages 186 B/W Illustrations
    by CRC Press

    Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques for utilizing them when analyzing ecological phenomenon.

    With illustrations, tables, and graphs on virtually every page – several in color – this book is a comprehensive source of state-of-the-art ecological scaling and multiscaling methods at temporal and spatial scales, respectfully ranging from seconds to months and from millimeters to thousands of kilometers. It illustrates most of the data analysis techniques with real case studies often based on original findings. It also incorporates descriptions of current and new numerical techniques to analyze and deepen understanding of ecological situations and their solutions.

    Includes a Wealth of Applications and Examples

    This book also includes nonlinear analysis techniques and the application of concepts from chaos theory to problems of spatial and temporal patterns in ecological systems. Unlike other books on the subject, Fractals and Multifractals in Ecology and Aquatic Science is readily accessible to researchers in a variety of fields, such as microbiology, biology, ecology, hydrology, geology, oceanography, social sciences, and finance, regardless of their mathematical backgrounds. This volume demystifies the mathematical methods, many of which are often regarded as too complex, and allows the reader to access new and promising concepts, procedures, and related results.


    About Geometries and Dimensions

    From Euclidean to Fractal Geometry


    Self-Similar Fractals

    Self-Similarity, Power Laws, and the Fractal Dimension

    Methods for Self-Similar Fractals

    Self-Affine Fractals

    Several Steps toward Self-Affinity

    Methods for Self-Affine Fractals

    Frequency Distribution Dimensions

    Cumulative Distribution Functions and Probability Density Functions

    The Patch-Intensity Dimension, Dpi

    The Korcak Dimension, DK

    Fragmentation and Mass-Size Dimensions, Dfr and Dms

    Rank-Frequency Dimension, Drf

    Fractal-Related Concepts Some Clarifications

    Fractals and Deterministic Chaos

    Fractals and Self-Organization

    Fractals and Self-Organized Criticality

    Estimating Dimensions with Confidence

    Scaling or Not Scaling? That Is the Question

    Errors Affecting Fractal Dimension Estimates

    Defining the Confidence Limits of Fractal Dimension Estimates

    Performing a Correct Analysis

    From Fractals to Multifractals

    A Random Walk toward Multifractality

    Methods for Multifractals

    Cascade Models for Intermittency

    Multifractals: Misconceptions and Ambiguities

    Joint Multifractals

    Intermittency and Multifractals: Biological and Ecological Implications


    Laurent Seuront is a Professor in Biological Oceanography at the Flinders University (Adelaide, Australia) and a Senior Research Scientist at the South Australian Research and Development Institute (West Beach, Australia). Prior to his present position, he was a research fellow of the Japanese Society for the Promotion of Science at the Tokyo University of Fisheries (1999-2000) and a research scientist at the Centre National de la Recherche Scientifique (CNRS) in France (2001-2008). Among multiple awards, he recently received the CNRS Bronze Medal in France (2007) in recognition of his early career achievements, and a prestigious Australian Professorial Fellowship from the Australian Research Council.