Evolutionarily Stable Strategies

by

Michael D. Breed

• LAST REVIEWED: 19 November 2021
• LAST MODIFIED: 25 September 2019
• DOI: 10.1093/obo/9780199830060-0228

Introduction

Evolutionarily stable strategies (ESS) are phenotypes that persist in populations over evolutionary time and cannot be replaced by invading strategies. Cases in which alternative strategies coexist stand as being of particular interest. Evolutionary biologists were introduced to the concept of ESS through the efforts of John Maynard Smith and George R. Price, whose work remains the keystone expression of this concept. Maynard Smith and Price dealt with animal conflicts, in which combatants may have differing strategies and physical abilities. The stability of evolutionary strategies is often analyzed using the tools of game theory, which allows determination of the persistence of strategies when played against one another. Game theory also opens the door to assessing the potential success of novel strategies upon introduction into a population. ESS often coincide with the Nash equilibrium, a game theory concept that describes conditions under which cognitively aware players in a game cannot gain by changing their individual strategy. In addition to animal conflict, analyses of ESS have been applied in a wide variety of evolutionary contexts and indeed are applicable whenever alternative heritable phenotypes are present. One possibility is that ESS occur as alternative genotypes within populations and thus should be analyzed using population-genetic approaches. ESS can also be conditionally expressed by individuals, depending on environmental and social context. This second option also requires a genotypic basis for strategies but allows for more strategical complexity through responses that may shift over developmental time or with experience. Interspecific interactions are an additional context for ESS, in which ESS drive evolutionary arms races between predators and prey or hosts and diseases or parasites. Maynard Smith and Price built on a conceptual framework in evolutionary ecology developed by William D. Hamilton in studies of kin selection, sex ratios, and herding behavior, and by Geoff Parker, working on sperm competition. ESS offer convenient latticework for thinking about many ecological and evolutionary trade-offs in which organisms balance costs and benefits of potential strategic choices in development and behavior, either in within-generation decision-making or between-generation evolution.

General Overviews and Foundational Work

John Maynard Smith deserves full credit for bringing game theory and ESS to the attention of the community of biological scientists working on animal behavior and evolution (Maynard Smith 1972, Maynard Smith 1974, Maynard Smith 1982, Maynard Smith and Price 1973), but others, such as Peter Taylor and Leo Jonker (Taylor and Jonker 1978), made substantive contributions to bringing ESS into the sphere of evolutionary biology. In a broader perspective, game theory has its roots in mid-20th-century mathematics, with John von Neumann having made substantial contributions in the 1940s. Hamilton 1967 and Hamilton 1971, on sex ratios and selfish herds, respectively, prefigured Maynard Smith in expressing evolutionary solutions as alternative strategies that might coexist genetically in a population. Geoffrey Parker’s earliest work, Parker 1970, on sperm competition and strategies in mating games, was contemporaneous with William Hamilton and Maynard Smith’s publications, and Parker and Stuart 1976 added a route to broad application of ESS analyses in biology. Dugatkin and Reeve 2000 provides a very useful overview and summary of the extensive early literature on game theory.

• Dugatkin, L. A., and H. K. Reeve, eds. 2000. Game theory and animal behavior. Oxford: Oxford Univ. Press.

  Excellent book-length overview of this topic.

• Hamilton, W. D. 1967. Extraordinary sex ratios. Science 156.3774: 477–488.

  DOI: 10.1126/science.156.3774.477

  Hamilton’s work set the stage for the development of ESS theory in two ways. First, he helped evolutionary biologists focus both on the population mean for a strategy and the underlying variation for that mean. This led to the insight that alternative individual strategies might be obscured within a single, population-level measure.

• Hamilton, W. D. 1971. Geometry for selfish herd. Journal of Theoretical Biology 31.2: 295–311.

  DOI: 10.1016/0022-51937190189-5

  As with his paper on sex ratios, Hamilton pushed the idea that different animals within a social group could have alternative outcomes in social competition, and that each animal might have ways of improving its outcome, even if competition prevents obtaining the optimal spatial position in the group.

• Maynard Smith, J. 1972. Game theory and the evolution of fighting: On evolution. Edinburgh: Edinburgh Univ. Press.

  Lore has it that Maynard Smith and George Price’s Nature paper (Maynard Smith and Price 1973) was written to appear before this book chapter, but the journal’s extended review of the paper led to the chapter appearing first, and thus Maynard Smith gains the chronological credit for introducing game theory and ESS to evolutionary biology.

• Maynard Smith, J. 1974. Theory of games and evolution of animal conflicts. Journal of Theoretical Biology 47.1: 209–221.

  DOI: 10.1016/0022-51937490110-6

  This is a more thorough, and more mathematically based, exposition of the principles expressed in Maynard Smith and Price 1973.

• Maynard Smith, J. 1982. Evolution and the theory of games. Cambridge, UK: Cambridge Univ. Press.

  Following on his earlier book by a decade, Maynard Smith gives a fully amplified account of the utility of game theory in evolutionary biology.

• Maynard Smith, J., and G. R. Price. 1973. The logic of animal conflict. Nature 246.5427: 15–18.

  DOI: 10.1038/246015a0

  Brilliant but troubled, Price had developed the idea of using game theory to study strategies in conflicts among animals. Maynard Smith developed the ideas to their full extent and took the lead in publishing about game theory.

• Parker, G. A. 1970. Sperm competition and its evolutionary consequences in the insects. Biological Reviews of the Cambridge Philosophical Society 45.4: 525–567.

  DOI: 10.1111/j.1469-185X.1970.tb01176.x

  Parker’s work on sperm competition, like Hamilton’s on sex ratios and herd, preceded the first expositions of game theory but fit extraordinarily well with the formulation in Maynard Smith and Price 1973 of alternative coexisting strategies in populations.

• Parker, G. A., and R. A. Stuart. 1976. Animal behavior as a strategy optimizer: Evolution of resource assessment strategies and optimal emigration thresholds. American Naturalist 110.976: 1055–1076.

  DOI: 10.1086/283126

  Building on the momentum developed in Maynard Smith and Price 1973, Parker integrated his ideas on sperm competition with game theory. This paper takes a broader look at the general applicabiity of game theory to animal behavior.

• Taylor, P. D., and L. B. Jonker. 1978. Evolutionarily stable strategies and game dynamics. Mathematical Biosciences 40.1–2: 145–156.

  DOI: 10.1016/0025-55647890077-9

  This paper is emblematic of the deeper dive into mathematics and its application to evolution that the ESS concept stimulated.