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.
Laurent Seuront (Flinders University Adelaide South Australia)
Country of Publication:
12 September 2017
Professional and scholarly
Introduction About Geometries and Dimensions From Euclidean to Fractal Geometry Dimensions 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.