Mathematical Methods of Population Biology (Cambridge Studies in Mathematical Biology, Series Number 4)

This Introduction To Mathematical Methods That Are Useful For Studying Population Phenomena Is Intended For Advanced Undergraduate And Graduate Students, And Will Be Accessible To Scientists Who Do Not Have A Strong Mathematics Background. The Material Is Graded In Mathematical Difficulty. The Earlier Parts Of The Book Involve Elementary Diference Equations While Later Chapters Present Topics That Require More Mathematical Preparation. Models Of Total Population And Population Age Structure Are First Derived And Studied, And Then Models Of Random Population Events Are Presented In Terms Of Markov Chains. The Last Two Chapters Deal With Mathematical Methods Used To Uncover Qualitative Behaviour Of More Complicated Difference Equations. Each Chapter Begins With A Simple Model, Usually Of Some Historical Interest, That Defines The Primary Goals Of The Chapter. Exercises, For Which Solutions Are Provided, Illustrate Material In The Text And Also Deal With Models More Advanced Than Those Derived And Studied In The Text.--publisher Website. Frank C. Hoppensteadt. Includes Indexes. Bibliography: P. 142-144. Cover......Page 1 Frontmatter......Page 2 Contents......Page 6 Preface......Page 8 1.1 Iteration and parameter estimation......Page 10 1.2 Synchronization of populations......Page 18 1.3 Exploitation of biological populations: fisheries......Page 25 Appendix: Least-squares approximation......Page 37 2.1 Fibonacci sequence......Page 40 2.2 Renewal equation......Page 46 2.3 Reproduction matrix: honest matrices......Page 49 2.4 Population waves: dishonest matrices......Page 52 3.1 Bacterial genetics......Page 56 3.2 Human genetics: Mendelian traits in diploid organisms......Page 69 3.3 Contagion......Page 78 3.4 Summary......Page 81 4.1 Approximations to dynamic processes: multiple-time-scale methods......Page 84 4.2 Static states: bifurcation methods......Page 91 5.1 Integer dispersal......Page 101 5.2 Diffusion approximations......Page 104 5.3 Transform methods: linear stability theory for diffusion equations......Page 106 5.4 Pattern formation......Page 110 5.5 Wave propagation: dynamic patterns......Page 123 Appendix: Derivation of the diffusion approximation......Page 137 Solutions to selected exercises......Page 144 References......Page 151 Author index......Page 154 Subject index......Page 156