Replicator trajectories generally fail to reach the global maximum of the mean fitness surface unless the fitness matrix satisfies specific structural conditions such as being circulant, in which case the unique stable equilibrium is both a local fitness maximum and evolutionarily stable.
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The chapter overviews replicator equations, hypercyclic replication, and quasispecies frameworks as a unified mathematical basis for evolutionary dynamics beyond biology.
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Chapter 2: Geometry of the Fitness Surface and Trajectory Dynamics of Replicator Systems
Replicator trajectories generally fail to reach the global maximum of the mean fitness surface unless the fitness matrix satisfies specific structural conditions such as being circulant, in which case the unique stable equilibrium is both a local fitness maximum and evolutionarily stable.
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Mathematical Models of Evolution and Replicator Systems Dynamics. Chapter 1: Introduction to Replicator Systems
The chapter overviews replicator equations, hypercyclic replication, and quasispecies frameworks as a unified mathematical basis for evolutionary dynamics beyond biology.