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Mathematical Model of Evolution of Non-Degenerate Replicator Systems
Alexander S. Bratus, Sergey Drozhzhin, Tatiana Yakushkina
We propose and analyse a mathematical model of evolutionary adaptation for non-degenerate (permanent) replicator systems, in which the fitness landscape matrix evolves on a slow ti…
Chapter 2: Geometry of the Fitness Surface and Trajectory Dynamics of Replicator Systems
A. S. Bratus, S. Drozhzhin, T. Yakushkina
We study the geometry of the mean fitness surface of replicator systems and its relationship to evolutionary trajectory dynamics. Using the symmetric--antisymmetric decomposition o…
Mathematical Models of Evolution and Replicator Systems Dynamics
A. S. Bratus, S. Drozhzhin, T. Yakushkina
This is an edited English version of the authors' monograph "Mathematical Models of Evolution and Replicator Systems Dynamics", posted on arXiv as a single document to which chapte…
Flow-Based Modelling of Population Dynamics with Consecutive Continuous Mutations
Alexander Bratus, Tatiana Yakushkina, Vladimir Posvyanski
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype de…
Fitness landscape adaptation in open replicator systems with competition: application to cancer therapy
Igor Samokhin, Tatiana Yakushkina, Dmitry Markin +1
This study focuses on open quasispecies systems with competition and death flow, described by modified Eigen and Crow-Kimura models. We examine the evolutionary adaptation process…
Open Quasispecies Systems: New Approach to Evolutionary Adaptation
Igor Samokhin, Tatiana Yakushkina, Alexander S. Bratus
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model…