The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection (London Mathematical Society Student Texts, Series Number 7)

This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy-Weinberg law, the Lotka-Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject. 1. Selection Dynamics And Population Genetics: A Discrete Introduction : The Biological Background ; The Hardy-weinberg Law ; Selection And The Fundamental Theorem ; Mutation And Recombination -- 2. Growth Rates And Ecological Models: An Abc On Ode : The Ecology Of Populations ; The Logistic Equation ; Lotka-volterra Equations For Predator Prey-systems ; Lotka-volterra Equations For Two Competing Species ; Lotka-volterra Equations For More Than Two Populations -- 3. Test Tube Evolution And Hypercycles: A Prebiotic Primer : Prebiotic Evolution ; Branching Processes And The Complexity Threshold ; Catalytic Growth Of Selfreproducing Molecules ; Permanence And The Evolution Of Hypercycles -- 4. Strategies And Stability: An Opening In Game Dynamics : Some Aspects Of Sociobiology ; Evolutionarily Stable Strategies ; Game Dynamics ; Asymmetric Conflicts -- 5. Compete, Predate Or Cooperate: The Struggle For Permanence : Ecological Equations For Two Species ; Criteria For Permanence ; Replicator Networks ; Stability In N-species Communities ; Some Low Dimensional Ecological Systems -- 6. Back To The Gene Pool: Gradients And Cycles : The Continuous Selection Model ; Gradient Systems ; Selection, Mutation And Recombination ; Fertility Selection -- 7. On Sex And Games: Strategic And Genetic Evolution : Evolutionary Dynamics For Bimatrix Games ; Game Dynamics For Mendelian Populations ; Cycles And The Battle Of The Sexes. Josef Hofbauer, Karl Sigmund. Translation Of: Evolutionstheorie Und Dynamische System. Includes Index. Bibliography: P. 322-336. This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology.The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy -- Weinberg law, the Lotka -- Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field.Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject. An introduction to dynamical systems theory and its applications to evolutionary game theory, mathematical ecology, prebiotic evolution and population genetics. The book's main aim is to develop the qualitative theory of differential equations by examples arising in evolutionary biology 1......Page 2 2......Page 6 3......Page 16 4......Page 24 5......Page 34 6......Page 44 7......Page 54 8......Page 78 9......Page 86 10......Page 92 11......Page 100 12......Page 110 13......Page 120 14......Page 130 15......Page 140 16......Page 172