Evolutionarily stable state

"A population is said to be in an evolutionarily stable state if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large. Such a population can be genetically monomorphic or polymorphic." —Maynard Smith (1982).

Contrast this with the definition of an evolutionarily stable strategy, which is a game theory concept.

"An ESS or evolutionarily stable strategy is a strategy such that, if all the members of a population adopt it, no mutant strategy can invade." —Maynard Smith (1982).

Evolutionarily stable states are frequently used to identify solutions to the replicator equation, given in its linear payoff form by

The state ${\displaystyle {\hat {x}}}$ is said to be evolutionarily stable if for all ${\displaystyle x\neq {\hat {x}}}$ in some neighborhood of ${\displaystyle {\hat {x}}}$

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