Evolutionarily stable state
Evolutionarily stable state
A population can be described as being in an evolutionarily stable state when that population's "genetic composition is restored by selection after a disturbance, provided the disturbance is not too large" (Maynard Smith, 1982). This population as a whole can be either monomorphic or polymorphic.
History and connection to evolutionary stable strategy While related to the concept of an evolutionarily-stable-strategy (ESS), evolutionarily stable states are not identical and the two terms cannot be used interchangeably.
An ESS is a strategy that, if adopted by all individuals within a population, cannot be invaded by alternative or mutant strategies.
The term ESS was first used by john-maynard-smith in an essay from the 1972 book On Evolution. Maynard Smith developed the ESS drawing in part from game theory and Hamilton's work on the evolution of sex ratio. The ESS was later expanded upon in his book [[evolution-and-the-theory-of-games]] in 1982, which also discussed the evolutionarily stable state. While the equilibrium may be disturbed by external factors, the population is considered to be in an evolutionarily stable state if it returns to the equilibrium state after the disturbance. Cressman further demonstrated that in habitat selection games modeling only a single species, the ideal free distribution (IFD) is itself an evolutionarily stable state containing mixed strategies.
In evolutionary game theory evolutionary-game-theory as a whole provides a theoretical framework examining interactions of organisms in a system where individuals have repeated interactions within a population that persists on an evolutionarily relevant timescale. This framework can be used to better understand the evolution of interaction strategies and stable states, though many different specific models have been used under this framework. The nash-equilibrium (NE) and folk theorem are closely related to the evolutionarily stable state. There are various potential refinements proposed to account for different theory games and behavioral models.
For the purpose of predicting evolutionary outcomes, the replicator equation is also a frequently utilized tool. Evolutionarily stable states are often taken as solutions to the replicator-equation, here in linear payoff form: :<math>\dot{x_i}=x_i\left(\left(Ax\right)_i-x^TAx\right),</math> The state <math>\hat{x}</math> is said to be evolutionarily stable if for all <math>x \neq \hat{x}</math> in some neighborhood of <math>\hat{x}</math>. :<math>x^TAx < \hat{x}^TAx</math>