Modeling Evolution of Heterogenous Populations - 1st Edition - ISBN: 9780128143681

Modeling Evolution of Heterogenous Populations

1st Edition

Theory and Applications

Authors: Irina Kareva Georgy Karev
Paperback ISBN: 9780128143681
Imprint: Academic Press
Published Date: 1st September 2019
Page Count: 300
Sales tax will be calculated at check-out Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


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 is 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. This book seeks to address this gap, helping biological scientists model the evolution of heterogenous populations and visualize evolutionary trajectories. 

Key Features

  • Includes an introductory primer on mathematical modeling with ordinary differential equations for biological systems
  • Provides worked examples of applications to various systems of differential equations
  • Helps interpret results and model modifications that can be translated to readers’ areas of interest


Biological scientists looking to expand their mathematical modelling toolbox. Advanced graduate and 1st year PhD students. The areas of applicability of the method involve microbiology, ecology, population biology, cancer, social sciences, and infectious diseases, among others

Table of 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


No. of pages:
© Academic Press 2019
Academic Press
Paperback ISBN:

About the Author

Irina Kareva

Irina Karev, 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.

Affiliations and Expertise

EMD Serono Research Center in Billerica, MA, USA

Georgy 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.

Affiliations and Expertise

NCBI, NIH, Bethesda, MD, USA

Ratings and Reviews