Fractals and multifractals in ecology and aquatic science:
"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 understan...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "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."--Publisher's description. |
| Beschreibung: | XV, 344 S. Ill., graph. Darst. |
| ISBN: | 9780849327827 9781138116399 |
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| 520 | 3 | |a "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."--Publisher's description. | |
| 650 | 4 | |a Biomathématiques | |
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Datensatz im Suchindex
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| adam_text | Titel: Fractals and multifractals in ecology and aquatic science
Autor: Seuront, Laurent
Jahr: 2010
Contents
Preface...........................................................................................................................................xiii
About the Author............................................................................................................................xv
1 Introduction...............................................................................................................................1
2 About Geometries and Dimensions.......................................................................................11
2.1 From Euclidean to Fractal Geometry...................................................................................11
2.2 Dimensions............................................................................................................................16
2.2.1 Euclidean, Topological, and Embedding Dimensions.............................................16
2.2.1.1 Euclidean Dimension.............................................................................16
2.2.1.2 Topological Dimension..........................................................................16
2.2.1.3 Embedding Dimension..........................................................................17
2.2.2 Fractal Dimension...................................................................................................18
2.2.2.1 Fractal Codimension..............................................................................22
2.2.2.2 Sampling Dimension..............................................................................23
3 Self-Similar Fractals..............................................................................................................25
3.1 Self-Similarity, Power Laws, and the Fractal Dimension.....................................................25
3.2 Methods for Self-Similar Fractals.........................................................................................28
3.2.1 Divider Dimension, Dd............................................................................................29
3.2.1.1 Theory....................................................................................................29
3.2.1.2 Case Study: Movement Patterns of the Ocean Sunfish, Mola Mola......32
3.2.1.3 Methodological Considerations.............................................................35
3.2.2 Box Dimension, Db..................................................................................................46
3.2.2.1 Theory....................................................................................................46
3.2.2.2 Case Study: Burrow Morphology of the Grapsid Crab,
Helograpsus Haswellianus....................................................................47
3.2.2.3 Methodological Considerations.............................................................51
3.2.2.4 Theoretical Considerations....................................................................52
3.2.3 Cluster Dimension, Dc.............................................................................................56
3.2.3.1 Theory....................................................................................................56
3.2.3.2 Case Study: The Microscale Distribution of the Amphipod
Corophium Arenarium...........................................................................57
3.2.3.3 Methodological Considerations: Constant Numbers or Constant
Radius?...................................................................................................59
3.2.4 Mass Dimension, Dm...............................................................................................60
3.2.4.1 Theory....................................................................................................60
3.2.4.2 Case Study: Microscale Distribution of Microphytobenthos Biomass.....61
3.2.4.3 Comparing the Mass Dimension Dm to Other Fractal Dimensions.......65
3.2.5 Information Dimension, D,.......................................................................................66
3.2.5.1 Theory....................................................................................................66
3.2.5.2 Comparing the Information Dimension D,
to Other Fractal Dimensions..................................................................67
VII
viii Contents
3.2.6 Correlation Dimension, Dcor..................................................................................68
3.2.6.1 Theory....................................................................................................68
3.2.6.2 Comparing the Correlation Dimension Dcor to Other Fractal
Dimensions............................................................................................69
3.2.7 Area-Perimeter Dimensions....................................................................................69
3.2.7.1 Perimeter Dimension, Dp.......................................................................70
3.2.7.2 Area Dimension, Da...............................................................................72
3.2.7.3 Landscape/Seascape Dimension, Ds......................................................72
3.2.7.4 Fractal Dimensions, Areas, and Perimeters...........................................73
3.2.8 Ramification Dimension, Dr....................................................................................87
3.2.8.1 Theory....................................................................................................87
3.2.8.2 Fractal Nature of Growth Patterns.........................................................87
3.2.9 Surface Dimensions.................................................................................................92
3.2.9.1 Transect Dimension, D,........................................................................93
3.2.9.2 Contour Dimension, Dco.......................................................................94
3.2.9.3 Geostatistical Dimension, Dg.................................................................95
3.2.9.4 Elevation Dimension, De........................................................................96
4 Self-Affine Fractals.................................................................................................................99
4.1 Several Steps toward Self-Affinity........................................................................................99
4.1.1 Definitions...............................................................................................................99
4.1.2 Fractional Brownian Motion...................................................................................99
4.1.3 Dimension of Self-Affine Fractals.........................................................................100
4.1.4 lf Noise, Self-Affinity, and Fractal Dimensions..................................................102
4.1.5 Fractional Brownian Motion, Fractional Gaussian Noise, and
Fractal Analysis.....................................................................................................103
4.2 Methods for Self-Affine Fractals........................................................................................106
4.2.1 Power Spectrum Analysis......................................................................................106
4.2.1.1 Theory..................................................................................................106
4.2.1.2 Spectral Analysis in Aquatic Sciences................................................108
4.2.1.3 Case Study: Eulerian and Lagrangian Scalar Fluctuations in
Turbulent Flows...................................................................................109
4.2.2 Detrended Fluctuation Analysis............................................................................117
4.2.2.1 Theory..................................................................................................117
4.2.2.2 Case Study: Assessing Stress in Interacting Bird Species...................119
4.2.3 Scaled Windowed Variance Analysis....................................................................124
4.2.3.1 Theory..................................................................................................124
4.2.3.2 Case Study: Temporal Distribution of the Calanoid Copepod,
Temora Longicornis.............................................................................125
4.2.4 Signal Summation Conversion Method.................................................................128
4.2.5 Dispersion Analysis...............................................................................................128
4.2.6 Rescaled Range Analysis and the Hurst Dimension, DH......................................128
4.2.6.1 Theory..................................................................................................128
4.2.6.2 Example: R/S Analysis and River Flushing Rates...............................131
4.2.7 Autocorrelation Analysis.......................................................................................131
4.2.8 Semivariogram Analysis.......................................................................................133
4.2.8.1 Theory..................................................................................................133
4.2.8.2 Case Study: Vertical Distribution of Phytoplankton in Tidally
Mixed Coastal Waters..........................................................................134
4.2.9 Wavelet Analysis...................................................................................................139
Contents ix
4.2.10 Assessment of Self-Affine Methods......................................................................140
4.2.10.1 Comparing Self-Affine Methods.........................................................140
4.2.10.2 From Self-Affinity to Intermittent Self-Affinity..................................143
5 Frequency Distribution Dimensions...................................................................................147
5.1 Cumulative Distribution Functions and Probability Density Functions.............................147
5.1.1 Theory...................................................................................................................147
5.1.2 Case Study: Motion Behavior of the Intertidal Gastropod,
Littorina Littorea...................................................................................................147
5.1.2.1 The Study Organism............................................................................147
5.1.2.2 Experimental Procedures and Data Analysis......................................148
5.1.2.3 Results..................................................................................................149
5.1.2.4 Ecological Interpretation.....................................................................150
5.2 The Patch-Intensity Dimension, Dpi...................................................................................151
5.3 The Korcak Dimension, DK................................................................................................153
5.4 Fragmentation and Mass-Size Dimensions, Dfr and Dms....................................................154
5.5 Rank-Frequency Dimension, D^........................................................................................155
5.5.1 Zipf s Law, Human Communication, and the Principle
of Least Effort.......................................................................................................155
5.5.2 Zipf s Law, Information, and Entropy...................................................................156
5.5.3 From the Zipf Law to the Generalized Zipf Law..................................................158
5.5.4 Generalized Rank-Frequency Diagram for Ecologists.........................................160
5.5.5 Practical Applications of Rank-Frequency Diagrams for Ecologists....................161
5.5.5.1 Zipf s Law as a Diagnostic Tool to
Assess Ecosystem Complexity.............................................................161
5.5.5.2 Case Study: Zipf Laws of Two-Dimensional Patterns.........................177
5.5.5.3 Distance between Zipf s Laws.............................................................188
5.5.6 Beyond Zipf s Law and Entropy............................................................................189
5.5.6.1 n-Tuple Zipf s Law...............................................................................189
5.5.6.2 n-Gram Entropy and «-Gram Redundancy.........................................193
6 Fractal-Related Concepts: Some Clarifications.................................................................201
6.1 Fractals and Deterministic Chaos.......................................................................................201
6.1.1 Chaos Theory........................................................................................................201
6.1.2 Feigenbaum Universal Numbers...........................................................................205
6.1.3 Attractors...............................................................................................................205
6.1.3.1 Visualizing Attractors: Packard-Takens Method.................................206
6.1.3.2 Quantifying Attractors: Diagnostic Methods for Deterministic
Chaos....................................................................................................209
6.1.3.3 Case Study: Plankton Distribution in
Turbulent Coastal Waters.....................................................................213
6.1.3.4 Chaos, Attractors, and Fractals............................................................224
6.1.4 Chaos in Ecological Sciences................................................................................224
6.1.5 A Few Misconceptions about Chaos.....................................................................225
6.1.6 Then, What Is Chaos?............................................................................................225
6.2 Fractals and Self-Organization...........................................................................................226
6.3 Fractals and Self-Organized Criticality..............................................................................226
6.3.1 Defining Self-Organized Criticality......................................................................226
6.3.2 Self-Organized Criticality in Ecology and Aquatic Sciences...............................229
x Contents
7 Estimating Dimensions with Confidence............................................................................231
7.1 Scaling or Not Scaling? That Is the Question.....................................................................231
7.1.1 Identifying Scaling Properties...............................................................................232
7.1.1.1 Procedure l:R2-SSR Procedure........................................................233
7.1.1.2 Procedure 2: Zero-Slope Procedure....................................................234
7.1.1.3 Procedure 3: Compensated-Slope Procedure......................................238
7.1.2 Scaling, Multiple Scaling, and Multiscaling: Demixing Apples
and Oranges...........................................................................................................239
7.2 Errors Affecting Fractal Dimension Estimates..................................................................241
7.2.1 Geometrical Constraint, Shape Topology, and Digitization Biases......................241
7.2.2 Isotropy..................................................................................................................243
7.2.3 Stationarity............................................................................................................243
7.2.3.1 Statistical Stationarity..........................................................................243
7.2.3.2 Fractal Stationarity..............................................................................244
7.3 Defining the Confidence Limits of Fractal Dimension Estimates......................................246
7.4 Performing a Correct Analysis...........................................................................................246
7.4.1 Self-Similar Case...................................................................................................247
7.4.2 Self-Affine Case....................................................................................................247
8 From Fractals to Multifractals............................................................................................249
8.1 A Random Walk toward Multifractality.............................................................................249
8.1.1 A Qualitative Approach to Multifractality............................................................249
8.1.2 Multifractality So Far............................................................................................250
8.1.3 From Fractality to Multifractality: Intermittency.................................................253
8.1.3.1 A Bit of History....................................................................................253
8.1.3.2 Intermittency in Ecology and Aquatic Sciences..................................253
8.1.3.3 Defining Intermittency.........................................................................253
8.1.4 Variability, Inhomogeneity, and Heterogeneity: Terminological
Considerations.......................................................................................................255
8.1.5 Intuitive Multifractals for Ecologists....................................................................257
8.2 Methods for Multifractals...................................................................................................260
8.2.1 Generalized Correlation Dimension Function D(q) and
the Mass Exponents t(q)........................................................................................260
8.2.1.1 Theory..................................................................................................260
8.2.1.2 Application: Salinity Stress in the Cladoceran Daphniopsis
Australis...............................................................................................262
8.2.2 Multifractal Spectrum/(a)....................................................................................262
8.2.2.1 Theory..................................................................................................262
8.2.2.2 Application: Temperature Stress in the Calanoid Copepod Temora
Longicornis..........................................................................................265
8.2.3 Codimension Function c(y) and Scaling Moment Function K(q)..........................265
8.2.4 Structure Function Exponents £(q)........................................................................268
8.2.4.1 Theory..................................................................................................268
8.2.4.2 Eulerian and Lagrangian Multiscaling Relations for Turbulent
Velocity and Passive Scalars................................................................271
8.3 Cascade Models for Intermittency......................................................................................276
8.3.1 Historical Background...........................................................................................276
Contents xi
8.3.2 Cascade Models for Turbulence............................................................................278
8.3.2.1 Lognormal Model................................................................................278
8.3.2.2 The Log-Le vy Model...........................................................................279
8.3.2.3 Log-Poisson Model..............................................................................280
8.3.3 Assessment of Cascade Models for Passive Scalars in a Turbulent Flow.............280
8.4 Multifractals: Misconceptions and Ambiguities.................................................................282
8.4.1 Spikes, Intermittency, and Power Spectral Analysis.............................................282
8.4.2 Frequency Distributions and Multifractality.........................................................284
8.5 Joint Multifractals...............................................................................................................285
8.5.1 Joint Multifractal Measures...................................................................................285
8.5.2 The Generalized Correlation Functions................................................................287
8.5.2.1 Definition.............................................................................................287
8.5.2.2 Applications.........................................................................................290
8.6 Intermittency and Multifractals: Biological and Ecological Implications..........................293
8.6.1 Intermittency, Local Dissipation Rates, and Zooplankton Swimming
Abilities.................................................................................................................294
8.6.2 Intermittency, Local Dissipation Rates, and Biological Fluxes in the Ocean.......296
8.6.2.1 Intermittency, Turbulence, and Nutrient Fluxes toward
Phytoplankton Cells.............................................................................297
8.6.2.2 Intermittency, Turbulence, and Physical Coagulation of
Phytoplankton Cells.............................................................................298
8.6.2.3 Intermittency, Turbulence, and Encounter Rates in the Plankton.......299
9 Conclusion.............................................................................................................................301
References.....................................................................................................................................303
Index..............................................................................................................................................337
|
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[u.a.]</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 344 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">"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. 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| id | DE-604.BV035679808 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:43:15Z |
| institution | BVB |
| isbn | 9780849327827 9781138116399 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017734091 |
| oclc_num | 424330908 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-634 DE-11 DE-83 |
| owner_facet | DE-M49 DE-BY-TUM DE-634 DE-11 DE-83 |
| physical | XV, 344 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Seuront, Laurent Verfasser aut Fractals and multifractals in ecology and aquatic science Laurent Seuront Boca Raton, Fla. [u.a.] CRC Press 2010 XV, 344 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier "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."--Publisher's description. Biomathématiques Fractales - Applications scientifiques Multifractales - Applications scientifiques Sciences aquatiques - Mathématiques Écologie - Mathématiques Mathematik Ökologie Aquatic sciences Mathematics Biomathematics Ecology Mathematics Fractals Mathematics in nature Multifractals Hydrobiologie (DE-588)4026300-9 gnd rswk-swf Ökologie (DE-588)4043207-5 gnd rswk-swf Multifraktal (DE-588)4808941-2 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Ökologie (DE-588)4043207-5 s Fraktal (DE-588)4123220-3 s DE-604 Multifraktal (DE-588)4808941-2 s Hydrobiologie (DE-588)4026300-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017734091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seuront, Laurent Fractals and multifractals in ecology and aquatic science Biomathématiques Fractales - Applications scientifiques Multifractales - Applications scientifiques Sciences aquatiques - Mathématiques Écologie - Mathématiques Mathematik Ökologie Aquatic sciences Mathematics Biomathematics Ecology Mathematics Fractals Mathematics in nature Multifractals Hydrobiologie (DE-588)4026300-9 gnd Ökologie (DE-588)4043207-5 gnd Multifraktal (DE-588)4808941-2 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4026300-9 (DE-588)4043207-5 (DE-588)4808941-2 (DE-588)4123220-3 |
| title | Fractals and multifractals in ecology and aquatic science |
| title_auth | Fractals and multifractals in ecology and aquatic science |
| title_exact_search | Fractals and multifractals in ecology and aquatic science |
| title_full | Fractals and multifractals in ecology and aquatic science Laurent Seuront |
| title_fullStr | Fractals and multifractals in ecology and aquatic science Laurent Seuront |
| title_full_unstemmed | Fractals and multifractals in ecology and aquatic science Laurent Seuront |
| title_short | Fractals and multifractals in ecology and aquatic science |
| title_sort | fractals and multifractals in ecology and aquatic science |
| topic | Biomathématiques Fractales - Applications scientifiques Multifractales - Applications scientifiques Sciences aquatiques - Mathématiques Écologie - Mathématiques Mathematik Ökologie Aquatic sciences Mathematics Biomathematics Ecology Mathematics Fractals Mathematics in nature Multifractals Hydrobiologie (DE-588)4026300-9 gnd Ökologie (DE-588)4043207-5 gnd Multifraktal (DE-588)4808941-2 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Biomathématiques Fractales - Applications scientifiques Multifractales - Applications scientifiques Sciences aquatiques - Mathématiques Écologie - Mathématiques Mathematik Ökologie Aquatic sciences Mathematics Biomathematics Ecology Mathematics Fractals Mathematics in nature Multifractals Hydrobiologie Multifraktal Fraktal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017734091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT seurontlaurent fractalsandmultifractalsinecologyandaquaticscience |