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Full Description
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.
Contents
1. Using mathematical modeling to ask meaningful biological questions through combination of bifurcation analysis and population heterogeneity2. Inhomogeneous models of Malthusian type and the HKV method3. Some applications of inhomogeneous population models of Malthusian type4. Selection systems and the reduction theorem5. Some applications of the reduction theorem and the HKV methods6. Nonlinear replicator dynamics7. Inhomogeneous logistic equations and models for Darwinian and non-Darwinian evolution8. Replicator dynamics and the principle of minimal information gain9. Subexponential replicator dynamics and the principle of minimal Tsallis information gain10. Modeling extinction of inhomogeneous populations11. From experiment to theory: What can we learn from growth curves? 12. Traveling through phase-parameter portrait13. Evolutionary games: Natural selection of strategies14. Natural selection between two games with applications to game theoretical models of cancer15. Discrete-time selection systems16. Conclusions17. Moment-generating functions for various initial distributions
