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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. This is now referred to as convergent stability.
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. This strategy becomes fixed in the population because alternatives provide no fitness benefit that would be selected for. In comparison, an evolutionarily stable state describes a population that returns as a whole to its previous composition even after being disturbed. In short: the ESS refers to the strategy itself, uninterrupted and supported through natural selection, while the evolutionarily stable state refers more broadly to a population-wide balance of one or more strategies that may be subjected to temporary change.
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.
There has been variation in how the term is used and exploration of under what conditions an evolutionarily stable state might exist. In 1984, Benhard Thomas compared "discrete" models in which all individuals use only one strategy to "continuous" models in which individuals employ mixed strategies. While Maynard Smith had originally defined an ESS as being a single "uninvadable strategy," Thomas generalized this to include a set of multiple strategies employed by individuals. In other words, a collection of simultaneously present strategies could be considered uninvadable as a group. Thomas noted that evolutionary stability can exist in either model, allowing for an evolutionarily stable state to exist even when multiple strategies are used within the population.
The strategy employed by individuals (or ESS) is thought to depend on fitness: the better the strategy is at supporting fitness, the more likely the strategy is to be used. When it comes to an evolutionarily stable state, all of the strategies used within the population must have equal fitness. 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.
One of the base mathematical models for identifying an evolutionarily stable state was outlined by Taylor & Jonker in 1978. Their base equilibrium model for ES states stipulates that
A state p is called an ESS (evolutionary stable state) if for every state q ≠ p, if we let p̅ =(1-ε)p + εq (the perturbed state), then F(q|p̅) < F(p|p̅) for sufficiently small ε>0.
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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. This is now referred to as convergent stability.
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. This strategy becomes fixed in the population because alternatives provide no fitness benefit that would be selected for. In comparison, an evolutionarily stable state describes a population that returns as a whole to its previous composition even after being disturbed. In short: the ESS refers to the strategy itself, uninterrupted and supported through natural selection, while the evolutionarily stable state refers more broadly to a population-wide balance of one or more strategies that may be subjected to temporary change.
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.
There has been variation in how the term is used and exploration of under what conditions an evolutionarily stable state might exist. In 1984, Benhard Thomas compared "discrete" models in which all individuals use only one strategy to "continuous" models in which individuals employ mixed strategies. While Maynard Smith had originally defined an ESS as being a single "uninvadable strategy," Thomas generalized this to include a set of multiple strategies employed by individuals. In other words, a collection of simultaneously present strategies could be considered uninvadable as a group. Thomas noted that evolutionary stability can exist in either model, allowing for an evolutionarily stable state to exist even when multiple strategies are used within the population.
The strategy employed by individuals (or ESS) is thought to depend on fitness: the better the strategy is at supporting fitness, the more likely the strategy is to be used. When it comes to an evolutionarily stable state, all of the strategies used within the population must have equal fitness. 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.
One of the base mathematical models for identifying an evolutionarily stable state was outlined by Taylor & Jonker in 1978. Their base equilibrium model for ES states stipulates that
A state p is called an ESS (evolutionary stable state) if for every state q ≠ p, if we let p̅ =(1-ε)p + εq (the perturbed state), then F(q|p̅) < F(p|p̅) for sufficiently small ε>0.