Preface ....................................................... vii
1 DISCRETE POPULATION MODELS .................................... 1
1.1 Nonoverlapping Generations and Discrete Time Models ....... 1
1.2 Population with Age Structure ............................ 12
2 POPULATION DYNAMICS IN CONTINUOUS TIME ....................... 17
2.1 The Logistic Equation and Human Demography ............... 17
2.2 Two Interacting Species-Predator and Prey ................ 20
2.3 Two Interacting Species-Competition and Cooperation ...... 30
2.4 More Species ............................................. 38
2.5 More Realism ............................................. 48
3 EPIDEMICS .................................................... 63
3.1 The Spread of Diseases and Susceptibles/Infectives/
Removed Models ........................................... 63
3.2 Sexually Transmitted Diseases ............................ 67
3.3 A Model of Pair Formation ................................ 69
3.4 The Spread of Epidemics in Space ......................... 73
4 EVOLUTION AND POPULATION GENETICS ............................ 79
4.1 The Phase Space of Genotypes and the Hardy-Weinberg
Law ...................................................... 79
4.2 Equations of Selection, Recombination, and Mutation ...... 83
4.3 The Origins of Life and Bigen's Hypercycle ............... 91
4.4 The Immune System ........................................ 98
5 MORPHOGENESIS AND PATTERN FORMATION ......................... 105
5.1 Modeling the Embryo-Thorn's Catastrophe Theory .......... 105
5.2 Animal Hide and Shell Patterns .......................... 114
Appendix 1 DISCRETE MATHEMATICS .............................. 125
A1.1 Linear Algebra ......................................... 125
A1.2 One-Dimensional Discrete Semiflows ..................... 129
A1.3 Discrete Dynamical Systems ............................. 136
A1.4 Brandling Processes .................................... 139
Appendix 2 ORDINARY DIFFERENTIAL EQUATIONS ................... 143
A2.1 Basic Facts ............................................ 143
A2.2 Stability .............................................. 146
A2.3 Bifurcations ........................................... 151
Appendix 3 PARTIAL DIFFERENTIAL EQUATIONS .................... 157
A3.1 First-Order Linear Equations ........................... 157
A3.2 Reaction-Diffusion Equations ........................... 161
A3.3 Turing Bifurcation ..................................... 164
Appendix 4 RIEMANNIAN GEOMETRY ............................... 171
A4.1 Local Riemannian Geometry .............................. 171
A4.2 Shahshahani's Metric ................................... 176
References .................................................... 179
Index ......................................................... 184
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