Modeling Evolution of Heterogeneous Populations

Dr. Irina Kareva is a theoretical biologist, and the primary focus of her research involves using mathematical modeling to study cancer as an evolving ecosystem within the human body, where heterogeneous populations of cancer cells compete for limited resources (i.e., oxygen and glucose), cooperate with each other to fight off predators (the immune system), and disperse and migrate (metastases). In 2017 Dr. Kareva gave a TED talk on using mathematical modeling for biological research. Dr. Kareva's book Understanding cancer from a systems biology point of view: from observation to theory and back was published by Elsevier in 2018. Dr. Kareva is a Senior Scientist in Simulation and Modeling at EMD Serono, Merck KGaA, where she develops quantitative systems pharmacology (QSP) models to help understand and predict dynamics of new therapeutics. Dr. Georgy Karev has significant research experience in various fields of applied mathematics, mathematical modeling, and mathematical biology. His research spans computational biology and bioinformatics, modeling of genome evolution, Markov models, mathematical genetics, ecological modeling and modeling of dynamics of biological populations and communities. Dr. Karev has developed three new directions in mathematical biology: 1) theory of inhomogeneous population dynamics with applications to models of early biological evolution, population extinction, global demography, and ecology; 2) stochastic modeling of population size dynamics; and 3) theory of multi-dimensional structural models with applications to hierarchical models of complex biological systems. His current research is devoted to problems of computational biology including genome evolution, free-scaling networks, evolution of horizontally transferred genes, conceptual cancer models, replicator dynamics, and general theory of selection. Dr. Karev is a member of the Evolutionary Genomics Research Group at NCBI.

• 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