ESS
An evolutionarily stable strategy (ESS) is a behavioral or phenotypic strategy in evolutionary game theory such that, if adopted by nearly all members of a biologically reproducing population, no rare alternative mutant strategy can successfully invade and increase in frequency under natural selection.[1][2][3] The concept was formalized in the 1970s by British evolutionary biologist John Maynard Smith, who extended classical game-theoretic equilibria—originally developed for rational human decision-making—to heritable traits shaped by Darwinian selection pressures, often in collaboration with George Price's mathematical frameworks for evolutionary change.[3][4] ESS analysis has proven instrumental in resolving longstanding biological conundrums, including the near-universal 1:1 sex ratio in sexually reproducing species (predicted as an ESS against biased parental investment) and the conditional persistence of aggressive versus submissive tactics in animal contests, where strategies like "hawk-dove" polymorphisms emerge as stable outcomes resistant to exploitation.[5][6] While ESS provides a rigorous refinement of Nash equilibria for finite, frequency-dependent selection in biology—emphasizing resistance to invasion via pairwise fitness comparisons over strict optimality—critics have noted potential instabilities in finite populations or fluctuating environments, where small perturbations or demographic stochasticity can disrupt apparent stability, and limitations in assuming continuous strategy spaces without explicit genetic underpinnings.[7][8] These extensions have nonetheless cemented ESS as a cornerstone for modeling cooperation, signaling, and parental investment, influencing fields from ecology to epidemiology.[3][9]Biology and Game Theory
Evolutionarily Stable Strategy
An evolutionarily stable strategy (ESS) is a behavioral strategy or set of strategies in a population that, once prevalent, resists invasion by rare alternative (mutant) strategies through natural selection, assuming fitness is determined by pairwise contests.[9] This concept refines game-theoretic equilibria by incorporating evolutionary dynamics, where strategies evolve based on relative reproductive success rather than rational choice.[9] ESS assumes infinite population sizes and asexual reproduction in basic models, though extensions handle finite populations and sexual reproduction.[3] The term was formalized by biologist John Maynard Smith and mathematician George R. Price in their 1973 paper "The Logic of Animal Conflict," published on November 3 in Nature, which modeled animal aggression as symmetric games to explain why fights often end in displays rather than lethal combat.[10] Maynard Smith drew from earlier ideas like Ronald Fisher's 1930 principle on sex ratios and John Nash's 1950 equilibrium concept, adapting game theory to biological contexts where strategies are genetically inherited and selected via frequency-dependent fitness.[11] The framework gained prominence in the 1980s through Maynard Smith's book Evolution and the Theory of Games (1982), which applied ESS to phenomena like parental care and altruism.[11] Formally, for strategies I and J in a symmetric two-player game, with E(S, T) denoting the expected fitness of S when paired against T, strategy I is an ESS if, for every J \neq I,- E(I, I) > E(J, I), or
- E(I, I) = E(J, I) and E(I, J) > E(J, J).