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Preface to the Classics Edition | p. xv |
Preface | p. xxiii |
Acknowledgments | p. xxvii |
Errata | p. xxxi |
Discrete Process in Biology | p. 1 |
The Theory of Linear Difference Equations Applied to Population Growth | p. 3 |
Biological Models Using Difference Equations | p. 6 |
Cell Division | p. 6 |
An Insect Population | p. 7 |
Propagation of Annual Plants | p. 8 |
Statement of the Problem | p. 8 |
Definitions and Assumptions | p. 9 |
The Equations | p. 10 |
Condensing the Equations | p. 10 |
Check | p. 11 |
Systems of Linear Difference Equations | p. 12 |
A Linear Algebra Review | p. 13 |
Will Plants Be Successful? | p. 16 |
Qualitative Behavior of Solutions to Linear Difference Equations | p. 19 |
The Golden Mean Revisited | p. 22 |
Complex Eigenvalues in Solutions to Difference Equations | p. 22 |
Related Applications to Similar Problems | p. 25 |
Growth of Segmental Organisms | p. 26 |
A Schematic Model of Red Blood Cell Production | p. 27 |
Ventilation Volume and Blood CO[subscript 2] Levels | p. 27 |
For Further Study: Linear Difference Equations in Demography | p. 28 |
Problems | p. 29 |
References | p. 36 |
Nonlinear Difference Equations | p. 39 |
Recognizing a Nonlinear Difference Equation | p. 40 |
Steady States, Stability, and Critical Parameters | p. 40 |
The Logistic Difference Equation | p. 44 |
Beyond r = 3 | p. 46 |
Graphical Methods for First-Order Equations | p. 49 |
A Word about the Computer | p. 55 |
Systems of Nonlinear Difference Equations | p. 55 |
Stability Criteria for Second-Order Equations | p. 57 |
Stability Criteria for Higher-Order Systems | p. 58 |
For Further Study: Physiological Applications | p. 60 |
Problems | p. 61 |
References | p. 67 |
Appendix to Chapter 2: Taylor Series | p. 68 |
Functions of One Variable | p. 68 |
Functions of Two Variables | p. 70 |
Applications of Nonlinear Difference Equations to Population Biology | p. 72 |
Density Dependence in Single-Species Populations | p. 74 |
Two-Species Interactions: Host-Parasitoid Systems | p. 78 |
The Nicholson-Bailey Model | p. 79 |
Modifications of the Nicholson-Bailey Model | p. 83 |
Density Dependence in the Host Population | p. 83 |
Other Stabilizing Factors | p. 86 |
A Model for Plant-Herbivore Interactions | p. 89 |
Outlining the Problem | p. 89 |
Rescaling the Equations | p. 91 |
Further Assumptions and Stability Calculations | p. 92 |
Deciphering the Conditions for Stability | p. 96 |
Comments and Extensions | p. 98 |
For Further Study: Population Genetics | p. 99 |
Problems | p. 102 |
Projects | p. 109 |
References | p. 110 |
Continuous Processes and Ordinary Differential Equations | p. 113 |
An Introduction to Continuous Models | p. 115 |
Warmup Examples: Growth of Microorganisms | p. 116 |
Bacterial Growth in a Chemostat | p. 121 |
Formulating a Model | |
First Attempt | p. 122 |
Corrected Version | p. 123 |
A Saturating Nutrient Consumption Rate | p. 125 |
Dimensional Analysis of the Equations | p. 126 |
Steady-State Solutions | p. 128 |
Stability and Linearization | p. 129 |
Linear Ordinary Differential Equations: A Brief Review | p. 130 |
First-Order ODEs | p. 132 |
Second-Order ODEs | p. 132 |
A System of Two First-Order Equations (Elimination Method) | p. 133 |
A System of Two First-Order Equations (Eigenvalue-Eigenvector Method) | p. 134 |
When Is a Steady State Stable? | p. 141 |
Stability of Steady States in the Chemostat | p. 143 |
Applications to Related Problems | p. 145 |
Delivery of Drugs by Continuous Infusion | p. 145 |
Modeling of Glucose-Insulin Kinetics | p. 147 |
Compartmental Analysis | p. 149 |
Problems | p. 152 |
References | p. 162 |
Phase-Plane Methods and Qualitative Solutions | p. 164 |
First-Order ODEs: A Geometric Meaning | p. 165 |
Systems of Two First-Order ODEs | p. 171 |
Curves in the Plane | p. 172 |
The Direction Field | p. 175 |
Nullclines: A More Systematic Approach | p. 178 |
Close to the Steady States | p. 181 |
Phase-Plane Diagrams of Linear Systems | p. 184 |
Real Eigenvalues | p. 185 |
Complex Eigenvalues | p. 186 |
Classifying Stability Characteristics | p. 186 |
Global Behavior from Local Information | p. 191 |
Constructing a Phase-Plane Diagram for the Chemostat | p. 193 |
The Nullclines | p. 194 |
Steady States | p. 196 |
Close to Steady States | p. 196 |
Interpreting the Solutions | p. 197 |
Higher-Order Equations | p. 199 |
Problems | p. 200 |
References | p. 209 |
Applications of Continuous Models to Population Dynamics | p. 210 |
Models for Single-Species Populations | p. 212 |
Malthus Model | p. 214 |
Logistic Growth | p. 214 |
Allee Effect | p. 215 |
Other Assumptions; Gompertz Growth in Tumors | p. 217 |
Predator-Prey Systems and the Lotka-Volterra Equations | p. 218 |
Populations in Competition | p. 224 |
Multiple-Species Communities and the Routh-Hurwitz Criteria | p. 231 |
Qualitative Stability | p. 236 |
The Population Biology of Infectious Diseases | p. 242 |
For Further Study: Vaccination Policies | p. 254 |
Eradicating a Disease | p. 254 |
Average Age of Acquiring a Disease | p. 256 |
Models for Molecular Events | p. 271 |
Michaelis-Menten Kinetics | p. 272 |
The Quasi-Steady-State Assumption | p. 275 |
A Quick, Easy Derivation of Sigmoidal Kinetics | p. 279 |
Cooperative Reactions and the Sigmoidal Response | p. 280 |
A Molecular Model for Threshold-Governed Cellular Development | p. 283 |
Species Competition in a Chemical Setting | p. 287 |
A Bimolecular Switch | p. 294 |
Stability of Activator-Inhibitor and Positive Feedback Systems | p. 295 |
The Activator-Inhibitor System | p. 296 |
Positive Feedback | p. 298 |
Some Extensions and Suggestions for Further Study | p. 299 |
Limit Cycles, Oscillations, and Excitable Systems | p. 311 |
Nerve Conduction, the Action Potential, and the Hodgkin-Huxley Equations | p. 314 |
Fitzhugh's Analysis of the Hodgkin-Huxley Equations | p. 323 |
The Poincare-Bendixson Theory | p. 327 |
The Case of the Cubic Nullclines | p. 330 |
The Fitzhugh-Nagumo Model for Neural Impulses | p. 337 |
The Hopf Bifurcation | p. 341 |
Oscillations in Population-Based Models | p. 346 |
Oscillations in Chemical Systems | p. 352 |
Criteria for Oscillations in a Chemical System | p. 354 |
For Further Study: Physiological and Circadian Rhythms | p. 360 |
Appendix to Chapter 8. Some Basic Topological Notions | p. 375 |
Appendix to Chapter 8. More about the Poincare-Bendixson Theory | p. 379 |
Spatially Distributed Systems and Partial Differential Equation Models | p. 381 |
An Introduction to Partial Differential Equations and Diffusion in Biological Settings | p. 383 |
Functions of Several Variables: A Review | p. 385 |
A Quick Derivation of the Conservation Equation | p. 393 |
Other Versions of the Conservation Equation | p. 395 |
Tubular Flow | p. 395 |
Flows in Two and Three Dimensions | p. 397 |
Convection, Diffusion, and Attraction | p. 403 |
Convection | p. 403 |
Attraction or Repulsion | p. 403 |
Random Motion and the Diffusion Equation | p. 404 |
The Diffusion Equation and Some of Its Consequences | p. 406 |
Transit Times for Diffusion | p. 410 |
Can Macrophages Find Bacteria by Random Motion Alone? | p. 412 |
Other Observations about the Diffusion Equation | p. 413 |
An Application of Diffusion to Mutagen Bioassays | p. 416 |
Appendix to Chapter 9. Solutions to the One-Dimensional Diffusion Equation | p. 426 |
Partial Differential Equation Models in Biology | p. 436 |
Population Dispersal Models Based on Diffusion | p. 437 |
Random and Chemotactic Motion of Microorganisms | p. 441 |
Density-Dependent Dispersal | p. 443 |
Apical Growth in Branching Networks | p. 445 |
Simple Solutions: Steady States and Traveling Waves | p. 447 |
Nonuniform Steady States | p. 447 |
Homogeneous (Spatially Uniform) Steady States | p. 448 |
Traveling-Wave Solutions | p. 450 |
Traveling Waves in Microorganisms and in the Spread of Genes | p. 452 |
Fisher's Equation: The Spread of Genes in a Population | p. 452 |
Spreading Colonies of Microorganisms | p. 456 |
Some Perspectives and Comments | p. 460 |
Transport of Biological Substances Inside the Axon | p. 461 |
Conservation Laws in Other Settings: Age Distributions and the Cell Cycle | p. 463 |
The Cell Cycle | p. 463 |
Analogies with Particle Motion | p. 466 |
A Topic for Further Study: Applications to Chemotherapy | p. 469 |
Summary | p. 469 |
A Do-It-Yourself Model of Tissue Culture | p. 470 |
A Statement of the Biological Problem | p. 470 |
A Simple Case | p. 471 |
A Slightly More Realistic Case | p. 472 |
Writing the Equations | p. 473 |
The Final Step | p. 475 |
Discussion | p. 476 |
For Further Study: Other Examples of Conservation Laws in Biological Systems | p. 477 |
Models for Development and Pattern Formation in Biological Systems | p. 496 |
Cellular Slime Molds | p. 498 |
Homogeneous Steady States and Inhomogeneous Perturbations | p. 502 |
Interpreting the Aggregation Condition | p. 506 |
A Chemical Basis for Morphogenesis | p. 509 |
Conditions for Diffusive Instability | p. 512 |
A Physical Explanation | p. 516 |
Extension to Higher Dimensions and Finite Domains | p. 520 |
Applications to Morphogenesis | p. 528 |
For Further Study | p. 535 |
Patterns in Ecology | p. 535 |
Evidence for Chemical Morphogens in Developmental Systems | p. 537 |
A Broader View of Pattern Formation in Biology | p. 539 |
Selected Answers | p. 556 |
Author Index | p. 571 |
Subject Index | p. 575 |
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