Network models in population biology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer-Verlag
1977
|
| Schriftenreihe: | Biomathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 402 Seiten Diagramme |
| ISBN: | 354008214X 038708214X |
Internformat
MARC
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| 245 | 1 | 0 | |a Network models in population biology |c Edwin R. Lewis |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer-Verlag |c 1977 | |
| 300 | |a XII, 402 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Biomathematics |v 7 | |
| 650 | 4 | |a Biologie des populations - Modèles mathématiques | |
| 650 | 7 | |a Biologie des populations - Modèles mathématiques |2 ram | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Genetics, Population | |
| 650 | 4 | |a Models, Biological | |
| 650 | 4 | |a Population biology |x Mathematical models | |
| 650 | 0 | 7 | |a Modell |0 (DE-588)4039798-1 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Populationsbiologie |0 (DE-588)4046800-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001288487 | ||
Datensatz im Suchindex
| _version_ | 1804116419961421824 |
|---|---|
| adam_text | Table of Contents
Introduction 1
Why Model? 2
1. Foundations of Modeling Dynamic Systems
1.1. Time 4
1.2. Dynamics 5
1.3. State 5
1.4. Discrete and Continuous Representations of Time 6
1.5. The Discrete Nature of Observed Time and Observed States ... 7
1.6. State Spaces 8
1.7. Progress Through State Space 11
1.8. The Conditional Probability of Transition from State to State ... 14
1.9. Network Representations of Primitive Markovian State Spaces . . 18
1.10. Conservation 21
1.11. State Variables Associated with Individual Organisms 22
1.12. Basic Analysis of Markov Chains 24
1.13. Vector Notation, State Projection Matrices 27
1.14. Elementary Dynamics of Homogeneous Markov Chains 30
1.15. Observation of Transition Probabilities 43
1.16. The Primitive State Space for an Entire Population of Identical Ob¬
jects 46
1.17. Dynamics of Populations Comprising Indistinguishable Members . 49
1.18. Deduction of Population Dynamics Directly from the Member State
Space 55
1.19. A Situation in Which Member State Space Cannot be Used to Deduce
Population Dynamics 58
1.20. The Law of Large Numbers 61
1.21. Summary 62
1.22. Some References for Chapter 1 64
2. General Concepts of Population Modeling
2.1. Lumped Markovian States from Irreducible Primitive Markovian
State Spaces 65
2.2. Shannon s Measure: Uncertainty in State Spaces and Lumped States 71
2.3. Lumped Markovian States from Reducible Primitive Markovian State
Spaces 76
X Table of Contents
2.4. Frequency Aliasing: The Artifact of Lumped Time 87
2.5. Idealizations: Thought Experiments and Hypothesis Testing ... 90
2.6. Conservation: Defining Membership in a Given Population .... 91
2.7. Conservation and Constitutive Relationships for a Single State . . 93
2.8. Reproduction, Death and Life as Flow Processes 96
2.9. Further Lumping: Combining Age Classes for Simplified Situations
and Hypotheses 100
2.10. The Use of Network Diagrams to Construct Models 102
2.11. Basic Principles of Network Construction Ill
2.12. Some Alternative Representations of Common Network Configura¬
tions 122
2.13. Some References for Chapter 2 126
3. A Network Approach to Population Modeling
3.1. Introduction to Network Modeling of Populations 128
3.2. Network Models for Some Basic, Idealized Life Cycles 129
3.2.1. Simple Life Cycles 130
3.2.2. Models with Overlapping Time Classes 144
3.3. Scalor Parameters and Multiplier Functions 150
3.3.1. Single Species Models 151
3.3.2. Two Species Models 163
3.4. Time Delay Durations 176
3.5. Conversion to a Stochastic Model 183
3.5.1. Models without Interactions of Correlated Variables .... 185
3.5.2. Models with Interactions of Correlated Variables 187
3.5.3. Examples of Stochastic Network Models 190
3.6. Some References for Chapter 3 197
4. Analysis of Network Models
4.1. Introduction to Network Analysis 198
4.2. Interval by Interval Accounting on a Digital Computer 200
4.2.1. Digital Representation of Time Delays in Large Numbers Mo¬
dels 200
4.2.2. Digital Representations for Stochastic Network Models . . . 205
4.2.3. Examples of Digital Modeling 208
4.3. Graphical Analysis of One Loop Networks with Lumpable Param¬
eters 209
4.4. Large Numbers Models with Constant Parameters 225
4.5. Inputs and Outputs of Network Models 226
4.6. Linearity, Cohorts, and Superposition Convolution 227
4.7. The z Transform: A Shorthand Notation for Discrete Functions . 235
4.8. The Application of z Transforms to Linear Network Functions . . 238
4.8.1. Straight Chain Networks 240
4.8.2. Networks with Feed Forward Loops 241
4.8.3. Networks with Feedback Loops 241
Table of Contents XI
4.9. Linear Flow Graph Analysis 247
4.9.1. Graphical Reduction of Flow Graphs 248
4.9.2. Mason s Rule 258
4.10. Interpretation of Unit Cohort Response Functions: The Inverse z
Transform 263
4.10.1. Partial Fraction Expansion 265
4.10.2. Finding the Coefficients of an Expansion 268
4.10.3. Dealing with Multiple Roots at the Origin 272
4.10.4. Exercises 275
4.11. Types of Common Ratios and Their Significances 275
4.11.1. The General Nature of Common Ratios 276
4.11.2. Real Common Ratios 278
4.11.3. Complex Common Ratios 280
4.11.4. Exercises 286
4.12. The Patterns of Linear Dynamics 286
4.12.1. Growth Patterns in Low Level Populations and Populations
with Constant Parameters 287
4.12.2. Time Required for Establishment of Dominance 288
4.12.3. Geometric Patterns of Growth and the Biotic Potential . . 293
4.12.4. Patterns of Dynamics Near Nonzero Critical Levels .... 295
4.12.5. Exercises 296
4.13. Constant Parameter Models for Nonzero Critical Levels 296
4.13.1. Replacement for the Scalor 296
4.13.2. Modification of the Time Delay 300
4.13.3. Dynamics Close to a Nonzero Critical Level 300
4.14. Finding the Roots of Q(z) 302
4.14.1. Euclid s Algorithm 305
4.14.2. Descartes Rule and Sturm Sequences 309
4.14.3. Locating the Real Roots 313
4.14.4. Locating Imaginary and Complex Roots 317
4.14.5. Estimating the Magnitude of the Dominant Common Ratio 321
4.15. Network Responses to More Complicated Input Patterns 328
4.15.1. The Natural Frequencies of a Constant Parameter Network
Model 329
4.15.2. Exciting and Observing the Natural Frequencies of a Network 330
4.15.3. Responses to Category 1 Inputs 333
4.15.4. The Initial and Final Value Theorems, Steady State Analysis 338
4.16. Elements of Dynamic Control of Networks 341
4.16.1. Linear Control with Category 2 Inputs 342
4.16.2. Comments on Nonlinear Control and Regulation 347
4.17. Dynamics of Constant Parameter Models with Stochastic Time
Delays 348
4.17.1. z Transforms of Stochastic Time Delays 349
4.17.2. Moments of Stochastic Time Delay Distributions 350
4.17.3. Examples of Stochastic Time Delays and Their Transforms 351
4.17.4. Effects of Time Delay Distributions on Dynamics in a One
Loop Model 351
XII Table of Contents
4.17.5. An Elementary Sensitivity Analysis 354
4.17.6. When the Minimum Latency is Not Finite 357
4.18. The Inverse Problem: Model Synthesis 358
4.19. Application of Constant Parameter Network Analysis to More Gen¬
eral Homogeneous Markov Chains 360
4.20. Some References for Chapter 4 365
Appendix A. Probability Arrays, Array Manipulation 367
A.I. Definitions 367
A.2. Manipulation of Arrays 370
A. 3. Operations on Probability Arrays 375
Appendix B. Bernoulli Trials and the Binomial Distribution 378
Bibliography 384
Subject Index 394
|
| any_adam_object | 1 |
| author | Lewis, Edwin R. 1934- |
| author_GND | (DE-588)172238293 |
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| dewey-full | 574.5/24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 574 - [Unassigned] |
| dewey-raw | 574.5/24 |
| dewey-search | 574.5/24 |
| dewey-sort | 3574.5 224 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| format | Book |
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| id | DE-604.BV001975486 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:13Z |
| institution | BVB |
| isbn | 354008214X 038708214X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001288487 |
| oclc_num | 2912287 |
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| physical | XII, 402 Seiten Diagramme |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
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| series | Biomathematics |
| series2 | Biomathematics |
| spelling | Lewis, Edwin R. 1934- (DE-588)172238293 aut Network models in population biology Edwin R. Lewis Berlin ; Heidelberg ; New York Springer-Verlag 1977 XII, 402 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Biomathematics 7 Biologie des populations - Modèles mathématiques Biologie des populations - Modèles mathématiques ram Mathematisches Modell Genetics, Population Models, Biological Population biology Mathematical models Modell (DE-588)4039798-1 gnd rswk-swf Netzwerkmodell (DE-588)4131643-5 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 s Modell (DE-588)4039798-1 s DE-604 Netzwerkmodell (DE-588)4131643-5 s Erscheint auch als Online-Ausgabe 978-3-642-81134-0 Biomathematics 7 (DE-604)BV000894631 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lewis, Edwin R. 1934- Network models in population biology Biomathematics Biologie des populations - Modèles mathématiques Biologie des populations - Modèles mathématiques ram Mathematisches Modell Genetics, Population Models, Biological Population biology Mathematical models Modell (DE-588)4039798-1 gnd Netzwerkmodell (DE-588)4131643-5 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| subject_GND | (DE-588)4039798-1 (DE-588)4131643-5 (DE-588)4046800-8 |
| title | Network models in population biology |
| title_auth | Network models in population biology |
| title_exact_search | Network models in population biology |
| title_full | Network models in population biology Edwin R. Lewis |
| title_fullStr | Network models in population biology Edwin R. Lewis |
| title_full_unstemmed | Network models in population biology Edwin R. Lewis |
| title_short | Network models in population biology |
| title_sort | network models in population biology |
| topic | Biologie des populations - Modèles mathématiques Biologie des populations - Modèles mathématiques ram Mathematisches Modell Genetics, Population Models, Biological Population biology Mathematical models Modell (DE-588)4039798-1 gnd Netzwerkmodell (DE-588)4131643-5 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| topic_facet | Biologie des populations - Modèles mathématiques Mathematisches Modell Genetics, Population Models, Biological Population biology Mathematical models Modell Netzwerkmodell Populationsbiologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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