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# What is an ESS? - Evolutionarily Stable Strategies Explained

Updated on December 14, 2011

## What is an ESS?

An evolutionarily stable strategy is a lifestyle strategy that, once in place, cannot be supplanted by alternate strategies in a population. This means that once such a strategy is fixed, the fitness conferred by it is enough for Natural Selection to prevent rarer, alternative strategies (such as those resulting from mutation) from invading successfully. ESS came about as an adaptation of Game Theory to the field of evolution and can be used to explain phenomena such as altruism.

Individuals that are using an ESS have a higher overall fitness that individuals who are using any other non-ESS. However, this does not mean that there can be only one possible ESS in a population, it merely means that once an ESS is in place that it cannot be replaced.

## What is a Payoff Matrix?

A payoff matrix is a diagram used in game theory that represents the results of players moves in a game. In the context of evolution, a payoff matrix shows the outcomes of various evolutionary strategies. As an example, consider the matrix below:

In this population, two evolutionary strategies exist, A and B. Each column represents the common strategy that is used in the population (or what an individual is interacting with). The column on the left, for example, is a population of A-using individuals where the use of B is rare.

The rows, on the other hand, represent how effective a particular strategy is. The top row represents the A strategy and the bottom row represents the B strategy.

In this example, both the A strategy (in red) and the B strategy (in blue) are evolutionarily stable strategies since their fitness ratings are higher than any invading strategies (rare A in common B or rare B in common A).

## Why doesn’t an ESS necessarily maximize a population’s mean fitness?

Consider the payoff matrix example above. Let's say that the A strategy is fixed (red), it is an ESS after all. "But wait, how is this possible?!" you ask. "The mean fitness for strategy B (blue) is 10 and strategy A is only 6. Why isn't strategy B fixed?????"

Well consider the possibility that strategy A developed first, and that B developed later. Since the fitness of strategy B users in a population of A users is less than that of the A users (3 vs. 6) then it is impossible for the ESS (Strategy A) to be supplanted!!

Remember, that natural selection does not necessarily act towards the benefit of the species overall!!

Now consider the following matrix:

What is the evolutionarily stable strategy in this case?

Surprisingly, the answer is neither A nor B. Both strategies can be invaded (rare B in A is 6 vs 4 and rare A in B is 3 vs 2) therefore neither is stable!

Alright, now we'll have one final example:

In this case strategy B is the ESS. If we start out with a population A users, strategy B can invade due to its higher fitness and will result in a population of B users. Likewise, it is impossible for strategy A to invade in a population of B since its fitness is so much lower (3 vs 7).

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