Modeling Biological Systems:: Principles and Applications

James W. Haefner

Springer Science & Business Media, May 6, 2005 - Science - 475 pages

I Principles 1 1 Models of Systems 3 1. 1 Systems. Models. and Modeling . . . . . . . . . . . . . . . . . . . . 3 1. 2 Uses of Scientific Models . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 3 Example: Island Biogeography . . . . . . . . . . . . . . . . . . . . . 6 1. 4 Classifications of Models . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5 Constraints on Model Structure . . . . . . . . . . . . . . . . . . . . . 12 1. 6 Some Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 7 Misuses of Models: The Dark Side . . . . . . . . . . . . . . . . . . . 13 1. 8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 The Modeling Process 17 2. 1 Models Are Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. 2 Two Alternative Approaches . . . . . . . . . . . . . . . . . . . . . . 18 2. 3 An Example: Population Doubling Time . . . . . . . . . . . . . . . . 24 2. 4 Model Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2. 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Qualitative Model Formulation 32 3. 1 How to Eat an Elephant . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 2 Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3. 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 4 Errors in Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . 44 3. 5 Advantages and Disadvantages of Forrester Diagrams . . . . . . . . . 44 3. 6 Principles of Qualitative Formulation . . . . . . . . . . . . . . . . . . 45 3. 7 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 8 Other Modeling Problems . . . . . . . . . . . . . . . . . . . . . . . . 49 viii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. 9 Exercises 53 4 Quantitative Model Formulation: I 4. 1 From Qualitative to Quantitative . . . . . . . . . . . . . . . . . Finite Difference Equations and Differential Equations 4. 2 . . . . . . . . . . . . . . . . 4. 3 Biological Feedback in Quantitative Models . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 4 Example Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 5 Exercises 5 Quantitative Model Formulation: I1 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 1 Physical Processes 81 . . . . . . . . . . . . . . . 5. 2 Using the Toolbox of Biological Processes 89 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 3 Useful Functions 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 4 Examples 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 5 Exercises 104 6 Numerical Techniques 107 . . . . . . . . . . . . . . . . . . . . . . . 6. 1 Mistakes Computers Make 107 . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 2 Numerical Integration 110 . . . . . . . . . . . . . . . . 6. 3 Numerical Instability and Stiff Equations 115 . . . . . . . . . . . . . .

Contents

• III: 3
• VI: 4
• VII: 6
• VIII: 10
• IX: 12
• XI: 13
• XII: 15
• XIII: 17
• XV: 18
• XVI: 24
• XVII: 28
• XVIII: 30
• XIX: 32
• XX: 33
• XXI: 36
• XXII: 44
• XXIV: 45
• XXV: 47
• XXVI: 49
• XXVII: 53
• XXVIII: 58
• XXX: 59
• XXXI: 63
• XXXII: 79
• XXXIV: 81
• XXXVI: 89
• XXXVII: 96
• XXXVIII: 102
• XXXIX: 104
• XL: 107
• XLIII: 110
• XLIV: 115
• XLV: 117
• XLVI: 118
• XLVII: 121
• XLVIII: 123
• L: 125
• LI: 128
• LII: 130
• LIII: 138
• LIV: 139
• LV: 140
• LVI: 141
• LVII: 144
• LXI: 151
• LXII: 164
• LXIII: 174
• LXIV: 175
• LXV: 176
• LXVI: 178
• LXVII: 192
• LXVIII: 210
• LXIX: 213
• LXX: 215
• LXXI: 217
• LXXII: 223
• LXXIII: 225
• LXXIV: 228
• LXXV: 231
• LXXVI: 235
• LXXVII: 237
• LXXX: 242
• LXXXI: 250
• LXXXII: 259
• LXXXIII: 260
• LXXXV: 262
• LXXXVI: 268
• LXXXVIII: 272
• LXXXIX: 276
• XC: 281
• XCI: 292
• XCII: 295
• XCIII: 299
• XCIV: 302
• XCV: 304
• XCVI: 307
• XCVII: 309
• XCVIII: 314
• XCIX: 318
• C: 321
• CI: 322
• CII: 324
• CIII: 325
• CIV: 333
• CV: 339
• CVI: 342
• CVII: 350
• CVIII: 354
• CIX: 356
• CX: 367
• CXI: 369
• CXII: 370
• CXIII: 371
• CXIV: 373
• CXV: 374
• CXVI: 386
• CXVII: 388
• CXVIII: 390
• CXIX: 391
• CXX: 392
• CXXI: 394
• CXXII: 406
• CXXIII: 412
• CXXIV: 413
• CXXV: 415
• CXXVI: 416
• CXXVIII: 421
• CXXIX: 426
• CXXX: 433
• CXXXII: 435
• CXXXIII: 463

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Bibliographic information

• Title: Modeling Biological Systems:: Principles and Applications
• Author: James W. Haefner
• Edition: 2, illustrated
• Publisher: Springer Science & Business Media, 2005
• ISBN: 0387250115, 9780387250113
• Length: 475 pages
• Subjects: Science / Life Sciences / Anatomy & Physiology; Science / Life Sciences / Biology; Science / Life Sciences / Ecology; Science / Life Sciences / General; Science / Life Sciences / Molecular Biology; Science / Life Sciences / Zoology / General