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.
Table of Contents
About Geometries and Dimensions
From Euclidean to Fractal Geometry
Self-Similarity, Power Laws, and the Fractal Dimension
Methods for Self-Similar 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
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.