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Replicator Equations and Models of Biological Populations andCommunities

Published online by Cambridge University Press:  28 May 2014

G. P. Karev  and
I. G. Kareva
G. P. Karev*
Affiliation:
National Center for Biotechnology Information, National Institute of Health, Bldg. 38A, Rm. 5N511N, 8600 Rockville Pike, Bethesda, MD 20894, USA
I. G. Kareva
Affiliation:
Newman-Lakka Institute for Personalized Cancer Care, Floating Hospital for Children, Tufts Medical Center, 75 Kneeland St., Boston, MA, 02111
*
⋆Corresponding author. E-mail: karev@ncbi.nlm.nih.gov
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Abstract

An overview of a general approach for mathematical modeling of evolving heterogeneouspopulations using a wide class of selection systems and replicator equations (RE) ispresented. The method allows visualizing evolutionary trajectories of evolvingheterogeneous populations over time, while still enabling use of analytical tools ofbifurcation theory. The developed theory involves introducing escort systems of auxiliary“keystone" variables, which reduce complex multi-dimensional inhomogeneous models tolow dimensional systems of ODEs that in many cases can be investigated analytically. Inaddition to a comprehensive theoretical framework, a set of examples of the method’sapplicability to questions ranging from preventing the tragedy of the commons to cancertherapy is presented.

Keywords

population heterogeneityreplicator equationselection systemtragedy of the commonscancer
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 3: Biological evolution , 2014 , pp. 68 - 95
Copyright
© EDP Sciences, 2014

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