生物数学引论 英文PDF|Epub|txt|kindle电子书版本网盘下载

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1．Single Species Population Dynamics1

1.1 Introduction1

1.2 Linear and Nonlinear First Order Discrete Time Models2

1.2.1 The Biology of Insect Population Dynamics3

1.2.2 A Model for Insect Population Dynamics with Competition4

1.3 Differential Equation Models11

1.4 Evolutionary Aspects16

1.5 Harvesting and Fisheries17

1.6 Metapopulations21

1.7 Delay Effects24

1.8 Fibonacci's Rabbits27

1.9 Leslie Matrices:Age-structured Populations in Discrete Time30

1.10 Euler-Lotka Equations34

1.10.1 Discrete Time34

1.10.2 Continuous Time38

1.11 The McKendrick Approach to Age Structure41

1.12 Conclusions44

2．Population Dynamics of Interacting Species47

2.1 Introduction48

2.2 Host-parasitoid Interactions48

2.3 The Lotka-Volterra Prey-predator Equations54

2.4 Modelling the Predator Functional Response60

2.5 Competition66

2.6 Ecosystems Modelling70

2.7 Interacting Metapopulations74

2.7.1 Competition75

2.7.2 Predation77

2.7.3 Predator-mediated Coexistence of Competitors78

2.7.4 Effects of Habitat Destruction79

2.8 Conclusions81

3．Infectious Diseases83

3.1 Introduction83

3.2 The Simple Epidemic and SIS Diseases86

3.3 SIR Epidemics90

3.4 SIR Endemics96

3.4.1 No Disease-related Death97

3.4.2 Including Disease-related Death99

3.5 Eradication and Control100

3.6 Age-structured Populations103

3.6.1 The Equations103

3.6.2 Steady State105

3.7 Vector-borne Diseases107

3.8 Basic Model for Macroparasitic Diseases109

3.9 Evolutionary Aspects113

3.10 Conclusions115

4．Population Genetics and Evolution117

4.1 Introduction117

4.2 Mendelian Genetics in Populations with Non-overlapping Gen-erations119

4.3 Selection Pressure123

4.4 Selection in Some Special Cases127

4.4.1 Selection for a Dominant Allele127

4.4.2 Selection for a Recessive Allele127

4.4.3 Selection against Dominant and Recessive Alleles129

4.4.4 The Additive Case129

4.5 Analytical Approach for Weak Selection130

4.6 The Balance Between Selection and Mutation131

4.7 Wright's Adaptive Topography133

4.8 Evolution of the Genetic System134

4.9 Game Theory136

4.10 Replicator Dynamics142

4.11 Conclusions145

5．Biological Motion147

5.1 Introduction147

5.2 Macroscopic Theory of Motion;A Continuum Approach148

5.2.1 General Derivation148

5.2.2 Some Particular Cases151

5.3 Directed Motion,or Taxis154

5.4 Steady State Equations and Transit Times156

5.4.1 Steady State Equations in One Spatial Variable156

5.4.2 Transit Times157

5.4.3 Macrophages vs Bacteria160

5.5 Biological Invasions:A Model for Muskrat Dispersal160

5.6 Travelling Wave Solutions of General Reaction-diffusion Equa-tions164

5.6.1 Node-saddle Orbits(the Monostable Equation)166

5.6.2 Saddle-saddle Orbits(the Bistable Equation)167

5.7 Travelling Wave Solutions of Systems of Reaction-diffusion Equations:Spatial Spread of Epidemics168

5.8 Conclusions172

6．Molecular and Cellular Biology175

6.1 Introduction175

6.2 Biochemical Kinetics176

6.3 Metabolic Pathways183

6.3.1 Activation and Inhibition184

6.3.2 Cooperative Phenomena186

6.4 Neural Modelling191

6.5 Immunology and AIDS197

6.6 Conclusions202

7．Pattern Formation205

7.1 Introduction205

7.2 Turing Instability206

7.3 Turing Bifurcations211

7.4 Activator-inhibitor Systems214

7.4.1 Conditions for Turing Instability214

7.4.2 Short-range Activation,Long-range Inhibition219

7.4.3 Do Activator-inhibitor Systems Explain Biological Pat-tern Formation?223

7.5 Bifurcations with Domain Size224

7.6 Incorporating Biological Movement229

7.7 Mechanochemical Models233

7.8 Conclusions233

8．Tumour Modelling235

8.1 Introduction235

8.2 Phenomenological Models237

8.3 Nutrients:the Diffusion-limited Stage240

8.4 Moving Boundary Problems242

8.5 Growth Promoters and Inhibitors245

8.6 Vascularisation247

8.7 Metastasis248

8.8 Immune System Response249

8.9 Conclusions251

Further Reading253

A．Some Techniques for Difference Equations257

A.1 First-order Equations257

A.1.1 Graphical Analysis257

A.1.2 Linearisation258

A.2 Bifurcations and Chaos for First-order Equations260

A.2.1 Saddle-node Bifurcations260

A.2.2 Transcritical Bifurcations261

A.2.3 Pitchfork Bifurcations262

A.2.4 Period-doubling or Flip Bifurcations263

A.3 Systems of Linear Equations:Jury Conditions266

A.4 Systems of Nonlinear Difference Equations267

A.4.1 Linearisation of Systems268

A.4.2 Bifurcation for Systems268

B．Some Techniques for Ordinary Differential Equations271

B.1 First-order Ordinary Differential Equations271

B.1.1 Geometric Analysis271

B.1.2 Integration272

B.1.3 Linearisation272

B.2 Second-order Ordinary Differential Equations273

B.2.1 Geometric Analysis(Phase Plane)273

B.2.2 Linearisation274

B.2.3 Poincaré-Bendixson Theory276

B.3 Some Results and Techniques for mth Order Systems277

B.3.1 Linearisation278

B.3.2 Lyapunov Functions278

B.3.3 Some Miscellaneous Facts279

B.4 Bifurcation Theory for Ordinary Differential Equations279

B.4.1 Bifurcations with Eigenvalue Zero279

B.4.2 Hopf Bifurcations280

C．Some Techniques for Partial Differential Equations283

C.1 First-order Partial Differential Equations and Characteristics283

C.2 Some Results and Techniques for the Diffusion Equation284

C.2.1 The Fundamental Solution284

C.2.2 Connection with Probabilities287

C.2.3 Other Coordinate Systems288

C.3 Some Spectral Theory for Laplace's Equation289

C.4 Separation of Variables in Partial Differential Equations291

C.5 Systems of Diffusion Equations with Linear Kinetics295

C.6 Separating the Spatial Variables from Each Other297

D．Non-negative Matrices299

D.1 Perron-Frobenius Theory299

E．Hints for Exercises301

Index329

1.1 World human population growth over the last 2000 years2

1.2 Cobweb maps for idealised contest and scramble competition6

1.3 Cobweb maps for the Hassell equation7

1.4 Parameter space for the Hassell equation8

1.5 Cobwebbing variant10

1.6 Logistic population growth14

1.7 Yield-effort curves19

1.8 The archetypal metapopulation model22

1.9 The archetypal metapopulation growth rate23

1.10 Instability in a delay equation26

1.11 Fibonacci's rabbits32

1.12 A Lexis diagram41

1.13 Archetypal survivorship curves43

2.1 The functions log R0 and 1-1/R051

2.2 Some numerical solutions of the Nicholson-Bailey host-parasitoid model51

2.3 Negative binomial and Poisson distributions53

2.4 Results of host-parasitoid model with negative binomial search func-tion53

2.5 Winter moth host-parasitoid simulations and data54

2.6 Results of Lotka-Volterra prey-predator model57

2.7 Hare-lynx population data58

2.8 Predator functional response curves61

2.9 Rosenzweig-MacArthur phase planes63

2.10 Lotka-Volterra competition phase planes68

2.11 Parameter space for Lotka-Volterra competition equations68

2.12 Numerical solution of a planktonic ecosystem model73

2.13 Huffaker's prey-predator experiments75

2.14 State transitions for the metapopulation model with two competitors75

2.15 Numerical results for a metapopulation model with competition76

2.16 State transitions for patches in a metapopulation model for predation77

2.17 Numerical results for a metapopulation model of a predator-prey interaction78

2.18 State transitions for a metapopulation model with two competing prey and one predator79

2.19 Numerical results for a metapopulation model of predator-mediated coexistence80

3.1 Progress of a disease within an individual85

3.2 Phase planes for the SIR epidemic91

3.3 The final size of an SIR epidemic93

3.4 Bombay plague of 190694

3.5 Numerical solutions for an SIR endemic98

3.6 A typical time series for measles100

3.7 The basic reproductive ratio R0 as a function of the virulence c114

4.1 Hardy-Weinberg genotype frequencies121

4.2 Diagram of a typical life cycle123

4.3 Numerical solutions for weak and strong selection against a domi-nant and a recessive allele128

4.4 Central dogma of modern evolutionary biology132

4.5 Wright's adaptive topography135

4.6 Invasibility plots140

4.7 The evolutionary trajectories for the rock-scissors-paper game144

5.1 Flux in a general direction149

5.2 Conservation in one dimension152

5.3 Data for the invasion of muskrats in Europe161

5.4 Reaction-diffusion invasion wave162

5.5 Phase plane for the node-saddle orbit166

5.6 The Black Death in Europe,1347-1350169

5.7 Diagrammatic representation of a propagating epidemic169

5.8 Proof of a travelling wave in the rabies model171

6.1 Michaelis-Menten reaction dynamics178

6.2 Michaelis-Menten and cooperative reaction velocity curves186

6.3 FitzHugh-Nagumo phase plane194

6.4 A numerical solution of the excitatory FitzHugh-Nagumo equations195

6.5 A numerical solution of the oscillatory FitzHugh-Nagumo equations196

7.1 The early stages of development of a vertebrate egg206

7.2 Turing dispersion relations212

7.3 Spatial eigenvalues for Turing instability216

7.4 Marginal Turing instability in diffusion-coefficient space219

7.5 Pure activation-inhibition and cross-activation-inhibition220

7.6 Turing bifurcations with domain size225

7.7 Numerical solutions and real tail patterns227

7.8 Examples of biological patterns229

7.9 Turing bifurcation with chemotaxis231

8.1 Tumour growth models238

8.2 The profile of the tumour growth inhibitor246

A.1 Some examples of cobweb maps259

A.2 Behaviour of solutions of a first-order linear difference equation260

A.3 Saddle-node bifurcations261

A.4 A transcritical bifurcation262

A.5 A pitchfork bifurcation263

A.6 Period-doubling bifurcations and the cascade to chaos265

A.7 Naimark-Sacker bifurcation268

B.1 Geometrical method for first-order ordinary differential equations272

B.2 An example of a phase plane274

B.3 Properties of the roots of a quadratic276

B.4 A second example of a phase plane277

B.5 Sub-and supercritical Hopf bifurcations281

E.1 Cobweb maps for the sterile insect control equation302

E.2 Leslie phase plane and time series306

E.3 Phase planes for an ecosystem with photosynthesis307

E.4 Leslie phase plane and time series308

E.5 Population genetics of sickle cell anaemia314

E.6 Evolutionary dynamics for the rock-scissors-paper game with reward317

E.7 Turing instability in Gierer-Meinhardt parameter space323

E.8 Mimura-Murray phase plane for ecological patchiness324

E.9 Bifurcation diagram for tumour growth inhibitor327

E.10 Bifurcation diagram for tumour immune response328