Modeling Evolution of Heterogenous Populations Theory and Applications

About this book

Natural selection and evolution cannot act on any population that is not genetically heterogeneous. However, in a vast majority of conceptual, and often even descriptive mathematical models of population dynamics, whether it be predator-prey type models, spread of infectious diseases, or tumour growth, population homogeneity is the first assumption that is made. It is not regarded as homogeneity per se – rather, one assumes that an average approximation of rate of growth or infectiousness is sufficient as a reasonable enough assumption if the system has already reached some kind of a stable state. However, by ignoring population heterogeneity, or assuming that it has already "done its work", one loses the dynamics that may be driving most systems that are of interest and importance. Partially, the assumption of homogeneity is necessary to make systems manageable and available for analysis, since including assumptions about heterogeneity can increase system dimensionality to unmanageable levels. This in summary impacts the results that can be achieved. Modeling Evolution of Heterogenous Populations seeks to address this gap, helping biological scientists model the evolution of heterogenous populations and visualize evolutionary trajectories.

Contents

1. Introduction. Mathematical modeling of evolution of heterogeneous populations
2. Hidden keystone variables method and models of Malthusian type
3. Selection systems and the Reduction theorem
4. Inhomogeneous population models
5. Inhomogeneous logistic equations and non-Darwinian evolution
6. Discrete time selection system
7. Replicator dynamics and the Principle of minimum of information gain
8. Inhomogeneous models of population extinction
9. What can we learn from growth curves
10. Inhomogeneous models of communities
11. Applications to ecological problems
12. Natural selection of strategies. Allocation of resources in biological systems
13. Evolutionary game theory

Customer Reviews

Biography

Irina Kareva, PhD, is currently a scientist in Simulation and Modeling and EMD Serono Research Center in Billerica, MA. She has been working in mathematical modelling of ecological systems, with a particular emphasis on cancer, for ten years. She has applied the Reduction Theorem in several publications, some of which were co-authored with Dr. Karev.

Georgy Karev, PhD, is a staff scientist at NCBI, NIH. He has published numerous papers on the subject of this book for over 15 years, and expanded its application to various areas of mathematics, including continuous and discrete time selection systems and game theory.