Modeling Evolution of Heterogeneous Populations: Theory and Applications describes, develops and provides applications of a method that allows incorporating population heterogeneity into systems of ordinary and discrete differential equations without significantly increasing system dimensionality. The method additionally allows making use of results of bifurcation analysis performed on simplified homogeneous systems, thereby building on the existing body of tools and knowledge and expanding applicability and predictive power of many mathematical models.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Dedication - p. v 6. Chapter 1: Using mathematical modeling to ask meaningful biological questions - p. v 7. Chapter 2: Inhomogeneous models of Malthusian type and the HKV method - p. 5 8. Chapter 3: Some applications of inhomogeneous population models of Malthusian type - p. 23 9. Chapter 4: Selection systems and the Reduction theorem - p. 40 10. Chapter 5: Some applications of the Reduction theorem and the HKV method - p. 55 11. Chapter 6: Nonlinear replicator dynamics - p. 77 12. Chapter 7: Inhomogeneous logistic equations and models for Darwinian and non-Darwinian evolution - p. 98 13. Chapter 8: Replicator dynamics and the principle of minimal information gain - p. 128 14. Chapter 9: Subexponential replicator dynamics and the principle of minimal Tsallis information gain - p. 154 15. Chapter 10: Modeling extinction of inhomogeneous populations - p. 167 16. Chapter 11: From experiment to theory: What can we learn from growth curves? - p. 191 17. Chapter 12: Traveling through phase-parameter portrait - p. 223 18. Chapter 13: Evolutionary games: Natural selection of strategies - p. 249 19. Chapter 14: Natural selection between two games with applications to game theoretical models of cancer - p. 277 20. Chapter 15: Discrete-time selection systems - p. 290 21. Chapter 16: Conclusions - p. 321 22. Chapter 17. Math Appendix: Moment-generating functions for various initial distributions - p. 321 23. Bibliogrpahy - p. 327 24. Index - p. 337
Modeling Evolution of Heterogeneous Populations: Theory and Applications describes, develops and provides applications of a method that allows incorporating population heterogeneity into systems of ordinary and discrete differential equations without significantly increasing system dimensionality. The method additionally allows making use of results of bifurcation analysis performed on simplified homogeneous systems, thereby building on the existing body of tools and knowledge and expanding applicability and predictive power of many mathematical models.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Dedication - p. v 6. Chapter 1: Using mathematical modeling to ask meaningful biological questions - p. v 7. Chapter 2: Inhomogeneous models of Malthusian type and the HKV method - p. 5 8. Chapter 3: Some applications of inhomogeneous population models of Malthusian type - p. 23 9. Chapter 4: Selection systems and the Reduction theorem - p. 40 10. Chapter 5: Some applications of the Reduction theorem and the HKV method - p. 55 11. Chapter 6: Nonlinear replicator dynamics - p. 77 12. Chapter 7: Inhomogeneous logistic equations and models for Darwinian and non-Darwinian evolution - p. 98 13. Chapter 8: Replicator dynamics and the principle of minimal information gain - p. 128 14. Chapter 9: Subexponential replicator dynamics and the principle of minimal Tsallis information gain - p. 154 15. Chapter 10: Modeling extinction of inhomogeneous populations - p. 167 16. Chapter 11: From experiment to theory: What can we learn from growth curves? - p. 191 17. Chapter 12: Traveling through phase-parameter portrait - p. 223 18. Chapter 13: Evolutionary games: Natural selection of strategies - p. 249 19. Chapter 14: Natural selection between two games with applications to game theoretical models of cancer - p. 277 20. Chapter 15: Discrete-time selection systems - p. 290 21. Chapter 16: Conclusions - p. 321 22. Chapter 17. Math Appendix: Moment-generating functions for various initial distributions - p. 321 23. Bibliogrpahy - p. 327 24. Index - p. 337
