Temperature-Dependent Sex Determination (TSD) Versus Genetic Sex Determination (GSD)

Transcription

1 Preface to the Third Edition Preface to the First Edition Continuous Population Models for Single Species p. 1 Continuous Growth Models p. 1 Insect Outbreak Model: Spruce Budworm p. 7 Delay Models p. 13 Linear Analysis of Delay Population Models: Periodic Solutions p. 17 Delay Models in Physiology: Periodic Dynamic Diseases p. 21 Harvesting a Single Natural Population p. 30 Population Model with Age Distribution p. 36 Exercises p. 40 Discrete Population Models for a Single Species p. 44 Introduction: Simple Models p. 44 Cobwebbing: A Graphical Procedure of Solution p. 49 Discrete Logistic-Type Model: Chaos p. 53 Stability, Periodic Solutions and Bifurcations p. 59 Discrete Delay Models p. 62 Fishery Management Model p. 67 Ecological Implications and Caveats p. 69 Tumour Cell Growth p. 72 Exercises p. 75 Models for Interacting Populations p. 79 Predator-Prey Models: Lotka-Volterra Systems p. 79 Complexity and Stability p. 83 Realistic Predator-Prey Models p. 86 Analysis of a Predator-Prey Model with Limit Cycle Periodic Behaviour: Parameter Domains of Stability p. vii p. xi p. 88 Competition Models: Competitive Exclusion Principle p. 94 Mutualism or Symbiosis p. 99 General Models and Cautionary Remarks p. 101 Threshold Phenomena p. 105 Discrete Growth Models for Interacting Populations p. 109 Predator-Prey Models: Detailed Analysis p. 110 Exercises p. 115 Temperature-Dependent Sex Determination (TSD) p. 119 Biological Introduction and Historical Asides on the Crocodilia p. 119 Nesting Assumptions and Simple Population Model p. 124 Age-Structured Population Model for Crocodilia p. 130 Density-Dependent Age-Structured Model Equations p. 133 Stability of the Female Population in Wet Marsh Region I p. 135 Sex Ratio and Survivorship p. 137

2 Temperature-Dependent Sex Determination (TSD) Versus Genetic Sex Determination (GSD) p. 139 Related Aspects on Sex Determination p. 142 Exercise p. 144 Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair p. 146 Psychological Background and Data: Gottman and Levenson Methodology p. 147 Marital Typology and Modelling Motivation p. 150 Modelling Strategy and the Model Equations p. 153 Steady States and Stability p. 156 Practical Results from the Model p. 164 Benefits, Implications and Marriage Repair Scenarios p. 170 Reaction Kinetics p. 175 Enzyme Kinetics: Basic Enzyme Reaction p. 175 Transient Time Estimates and Nondimensionalisation p. 178 Michaelis-Menten Quasi-Steady State Analysis p. 181 Suicide Substrate Kinetics p. 188 Cooperative Phenomena p. 197 Autocatalysis, Activation and Inhibition p. 201 Multiple Steady States, Mushrooms and Isolas p. 208 Exercises p. 215 Biological Oscillators and Switches p. 218 Motivation, Brief History and Background p. 218 Feedback Control Mechanisms p. 221 Oscillators and Switches with Two or More Species: General Qualitative Results p. 226 Simple Two-Species Oscillators: Parameter Domain Determination for Oscillations p. 234 Hodgkin-Huxley Theory of Nerve Membranes: FitzHugh-Nagumo Model p. 239 Modelling the Control of Testosterone Secretion and Chemical Castration p. 244 Exercises p. 253 BZ Oscillating Reactions p. 257 Belousov Reaction and the Field-Koros-Noyes (FKN) Model p. 257 Linear Stability Analysis of the FKN Model and Existence of Limit Cycle Solutions p. 261 Nonlocal Stability of the FKN Model p. 265 Relaxation Oscillators: Approximation for the Belousov-Zhabotinskii Reaction p. 268 Analysis of a Relaxation Model for Limit Cycle Oscillations in the Belousov-Zhabotinskii Reaction p. 271 Exercises p. 277 Perturbed and Coupled Oscillators and Black Holes p. 278 Phase Resetting in Oscillators p. 278 Phase Resetting Curves p. 282 Black Holes p. 286 Black Holes in Real Biological Oscillators p. 288

3 Coupled Oscillators: Motivation and Model System p. 293 Phase Locking of Oscillations: Synchronisation in Fireflies p. 295 Singular Perturbation Analysis: Preliminary Transformation p. 299 Singular Perturbation Analysis: Transformed System p. 302 Singular Perturbation Analysis: Two-Time Expansion p. 305 Analysis of the Phase Shift Equation and Application to Coupled Belousov-Zhabotinskii Reactions p. 310 Exercises p. 313 Dynamics of Infectious Diseases p. 315 Historical Aside on Epidemics p. 315 Simple Epidemic Models and Practical Applications p. 319 Modelling Venereal Diseases p. 327 Multi-Group Model for Gonorrhea and Its Control p. 331 AIDS: Modelling the Transmission Dynamics of the Human Immunodeficiency Virus (HIV) p. 333 HIV: Modelling Combination Drug Therapy p. 341 Delay Model for HIV Infection with Drug Therapy p. 350 Modelling the Population Dynamics of Acquired Immunity to Parasite Infection p. 351 Age-Dependent Epidemic Model and Threshold Criterion p. 361 Simple Drug Use Epidemic Model and Threshold Analysis p. 365 Bovine Tuberculosis Infection in Badgers and Cattle p. 369 Modelling Control Strategies for Bovine Tuberculosis in Badgers and Cattle p. 379 Exercises p. 393 Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms p. 395 Simple Random Walk and Derivation of the Diffusion Equation p. 395 Reaction Diffusion Equations p. 399 Models for Animal Dispersal p. 402 Chemotaxis p. 405 Nonlocal Effects and Long Range Diffusion p. 408 Cell Potential and Energy Approach to Diffusion and Long Range Effects p. 413 Exercises p. 416 Oscillator-Generated Wave Phenomena p. 418 Belousov-Zhabotinskii Reaction Kinematic Waves p. 418 Central Pattern Generator: Experimental Facts in the Swimming of Fish p. 422 Mathematical Model for the Central Pattern Generator p. 424 Analysis of the Phase Coupled Model System p. 431 Exercises p. 436 Biological Waves: Single-Species Models p. 437 Background and the Travelling Waveform p. 437 Fisher-Kolmogoroff Equation and Propagating Wave Solutions p. 439 Asymptotic Solution and Stability of Wavefront Solutions of the Fisher-Kolmogoroff Equation p. 444

4 Density-Dependent Diffusion-Reaction Diffusion Models and Some Exact Solutions p. 449 Waves in Models with Multi-Steady State Kinetics: Spread and Control of an Insect Population p. 460 Calcium Waves on Amphibian Eggs: Activation Waves on Medaka Eggs p. 467 Invasion Wavespeeds with Dispersive Variability p. 471 Species Invasion and Range Expansion p. 478 Exercises p. 482 Use and Abuse of Fractals p. 484 Fractals: Basic Concepts and Biological Relevance p. 484 Examples of Fractals and Their Generation p. 487 Fractal Dimension: Concepts and Methods of Calculation p. 490 Fractals or Space-Filling? p. 496 Appendices p. 501 Phase Plane Analysis p. 501 Routh-Hurwitz Conditions, Jury Conditions, Descartes' Rule of Signs, and Exact Solutions of a Cubic p. 507 Polynomials and Conditions p. 507 Descartes' Rule of Signs p. 509 Roots of a General Cubic Polynomial p. 510 Bibliography p. 513 Index p. 537 J.D. Murray: Mathematical Biology, II: Spatial Models and Biomedical Applications Preface to the Third Edition Preface to the First Edition Multi-Species Waves and Practical Applications Intuitive Expectations Waves of Pursuit and Evasion in Predator-Prey Systems Competition Model for the Spatial Spread of the Grey Squirrel in Britain Spread of Genetically Engineered Organisms Travelling Fronts in the Belousov-Zhabotinskii Reaction Waves in Excitable Media Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics Spiral Waves Spiral Wave Solutions of [lambda]-[omega] Reaction Diffusion Systems Spatial Pattern Formation with Reaction Diffusion Systems Role of Pattern in Biology Reaction Diffusion (Turing) Mechanisms General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models

5 Mode Selection and the Dispersion Relation Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms Mammalian Coat Patterns--'How the Leopard Got Its Spots' Teratologies: Examples of Animal Coat Pattern Abnormalities A Pattern Formation Mechanism for Butterfly Wing Patterns Modelling Hair Patterns in a Whorl in Acetabularia Pattern Formation on Growing Domains: Alligators and Snakes Stripe Pattern Formation in the Alligator: Experiments Modelling Concepts: Determining the Time of Stripe Formation Stripes and Shadow Stripes on the Alligator Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance Biology of Tooth Initiation Modelling Tooth Primordium Initiation: Background Model Mechanism for Alligator Teeth Patterning Results and Comparison with Experimental Data Prediction Experiments Concluding Remarks on Alligator Tooth Spatial Patterning Pigmentation Pattern Formation on Snakes Cell-Chemotaxis Model Mechanism Simple and Complex Snake Pattern Elements Propagating Pattern Generation with the Cell-Chemotaxis System Bacterial Patterns and Chemotaxis Background and Experimental Results Model Mechanism for E. coli in the Semi-Solid Experiments Liquid Phase Model: Intuitive Analysis of Pattern Formation Interpretation of the Analytical Results and Numerical Solutions Semi-Solid Phase Model Mechanism for S. typhimurium Linear Analysis of the Basic Semi-Solid Model Brief Outline and Results of the Nonlinear Analysis Simulation Results, Parameter Spaces, Basic Patterns Numerical Results with Initial Conditions from the Experiments Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism Branching Patterns in Bacillus subtilis Mechanical Theory for Generating Pattern and Form in Development Introduction, Motivation and Background Biology Mechanical Model for Mesenchymal Morphogenesis

6 Linear Analysis, Dispersion Relation and Pattern Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations Periodic Patterns of Feather Germs Cartilage Condensation in Limb Morphogenesis and Morphogenetic Rules Embryonic Fingerprint Formation Mechanochemical Model for the Epidermis Formation of Microvilli Complex Pattern Formation and Tissue Interaction Models Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies Evolution and Morphogenesis Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb Teratologies (Monsters) Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution A Mechanical Theory of Vascular Network Formation Biological Background and Motivation Cell-Extracellular Matrix Interactions for Vasculogenesis Parameter Values Analysis of the Model Equations Network Patterns: Numerical Simulations and Conclusions Epidermal Wound Healing Brief History of Wound Healing Biological Background: Epidermal Wounds Model for Epidermal Wound Healing Nondimensional Form, Linear Stability and Parameter Values Numerical Solution for the Epidermal Wound Repair Model Travelling Wave Solutions for the Epidermal Model Clinical Implications of the Epidermal Wound Model Mechanisms of Epidermal Repair in Embryos Actin Alignment in Embryonic Wounds: A Mechanical Model Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions Dermal Wound Healing Background and Motivation--General and Biological Logic of Wound Healing and Initial Models Brief Review of Subsequent Developments Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling Solutions of the Model Equation Solutions and Comparison with Experiment Wound Healing Model of Cook (1995) Matrix Secretion and Degradation Cell Movement in an Oriented Environment

7 Model System for Dermal Wound Healing with Tissue Structure One-Dimensional Model for the Structure of Pathological Scars Open Problems in Wound Healing Concluding Remarks on Wound Healing Growth and Control of Brain Tumours Medical Background Basic Mathematical Model of Glioma Growth and Invasion Tumour Spread In Vitro: Parameter Estimation Tumour Invasion in the Rat Brain Tumour Invasion in the Human Brain Modelling Treatment Scenarios: General Comments Modelling Tumour Resection (Removal) in Homogeneous Tissue Analytical Solution for Tumour Recurrence After Resection Modelling Surgical Resection with Brain Tissue Heterogeneity Modelling the Effect of Chemotherapy on Tumour Growth Modeling Tumour Polyclonality and Cell Mutation Neural Models of Pattern Formation Spatial Patterning in Neural Firing with a Simple Activation-Inhibition Model A Mechanism for Stripe Formation in the Visual Cortex A Model for the Brain Mechanism Underlying Visual Hallucination Patterns Neural Activity Model for Shell Patterns Shamanism and Rock Art Geographic Spread and Control of Epidemics Simple Model for the Spatial Spread of an Epidemic Spread of the Black Death in Europe Brief History of Rabies: Facts and Myths The Spatial Spread of Rabies Among Foxes I: Background and Simple Model Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model Control Strategy Based on Wave Propagation into a Non-epidemic Region: Estimate of Width of a Rabies Barrier Analytic Approximation for the Width of the Rabies Control Break Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densitics: Quantitative Predictions for a Rabies Outbreak in England Effect of Fox Immunity on Spatial Spread of Rabies Wolf Territoriality, Wolf-Deer Interaction and Survival Introduction and Wolf Ecology Models for Wolf Pack Territory Formation: Single Pack--Home Range Model Multi-Wolf Pack Territorial Model Wolf-Deer Predator-Prey Model Concluding Remarks on Wolf Territoriality and Deer Survival Coyote Home Range Patterns Chippewa and Sioux Intertribal Conflict c

8 Appendix General Results for the Laplacian Operator in Bounded Domains Bibliography Index Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.