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.
On the change of population fitness by natural select ion
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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.