Math. Model. Nat. Phenom.
Volume 9, Number 3, 2014Biological evolution
|Page(s)||68 - 95|
|Published online||28 May 2014|
Replicator Equations and Models of Biological Populations and Communities
1 National Center for Biotechnology
Information, National Institute of Health, Bldg. 38A, Rm. 5N511N, 8600 Rockville Pike,
2 Newman-Lakka Institute for Personalized Cancer Care, Floating Hospital for Children, Tufts Medical Center, 75 Kneeland St., Boston, MA, 02111
Corresponding author. E-mail: firstname.lastname@example.org
An overview of a general approach for mathematical modeling of evolving heterogeneous populations using a wide class of selection systems and replicator equations (RE) is presented. The method allows visualizing evolutionary trajectories of evolving heterogeneous populations over time, while still enabling use of analytical tools of bifurcation theory. The developed theory involves introducing escort systems of auxiliary “keystone" variables, which reduce complex multi-dimensional inhomogeneous models to low dimensional systems of ODEs that in many cases can be investigated analytically. In addition to a comprehensive theoretical framework, a set of examples of the method’s applicability to questions ranging from preventing the tragedy of the commons to cancer therapy is presented.
Mathematics Subject Classification: 37N25 / 92A30
Key words: population heterogeneity / replicator equation / selection system / tragedy of the commons / cancer
© EDP Sciences, 2014
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