Geometry of Fitness Surfaces and Dynamics of Replicator Systems

A. S. Bratus (), A. S. Novozhilov and T. Yakushkina
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A. S. Bratus: Russian University of Transport, Department of Mathematical Modeling and System Analysis
A. S. Novozhilov: North Dakota State University, Department of Mathematics
T. Yakushkina: National Research University Higher School of Economics, School of Business Informatics

A chapter in Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, 2021, pp 69-77 from Springer

Abstract: Abstract This chapter focuses on the extremal properties of replicator systems’ fitness landscapes. We discuss a mathematical interpretation of Fisher’s theorem of natural selection and analyze cases that lie beyond its predictions. For general replicator equation, we examine how the location of the maximum depends on the fitness matrix composition. Using a concept of evolutionary stable strategy (ESS), we consider the connection between equilibrium and extremum types. The same framework is applied to Lotka–Volterra equations.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73241-7_5

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DOI: 10.1007/978-3-030-73241-7_5

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