Evolutionarily Stable Strategies and Behavior

Evolutionary biologists imagine a time before a particular trait emerges. Then, they postulate that a rare gene arises in an individual, and they ask what circumstances would favor the spread of that gene throughout the population. If natural selection favors the gene, then the individuals with the genotypes incorporating that particular gene will have increased fitness. A gene must compete with other genes in the gene pool, and resist any invasion from mutants, to become established in a population’s gene pool.

In considering evolutionary strategies that influence behavior, we visualize a situation in which changes in genotype lead to changes in behavior. By ‘the gene for sibling care’ we mean that genetic differences exist in the population such that some individuals aid their siblings while others do not. Similarly, by ‘dove strategy’ we mean that animals exist in the population that do not engage in fights and that they pass this trait from one generation to the next.

At first sight, it might seem that the most successful evolutionary strategy will invariably spread throughout the population and, eventually, will supplant all others. While this does occur, it is far from always being so. Sometimes, there is no single dominant strategy. Competing strategies may be interdependent in that the success of one depends upon the existence of the other and the frequency with which the population adopts the other. For example, the strategy of mimicry has no value if the warning strategy of the model is not efficient.

Game theory belongs to mathematics and economics, and it studies situations where players choose different actions in an attempt to maximize their returns. It is a good model for evolutionary biologists to approach situations in which various decision makers interact. The payoffs in biological simulations correspond to fitness—comparable to money in economics. Simulations focus on achieving a balance that evolutionary strategies would maintain. The Evolutionarily Stable Strategy (ESS), introduced by John Maynard Smith in 1973 (and published in 1982), is the most well known of these strategies. Maynard Smith used the hawk-dove simulation to analyze fighting and territorial behavior. Together with Harper in 2003, he employed an ESS to explain the emergence of animal communication.

An evolutionarily stable strategy (ESS) is a strategy that no other feasible alternative can better, given that sufficient members of the population adopt it. The best strategy for an individual depends upon the strategy or strategies that other members of the same population adopt. Since the same applies to all individuals in that particular population, a mutant gene cannot invade an  ESS successfully.

The traditional way to illustrate this problem is by simulating the encounter between two strategies, hawk and dove. When a hawk meets a hawk, it wins on half of the occasions, and it loses and suffers an injury on the other half. Hawks always beat doves. Doves always retreat against hawks. Whenever a dove meets another dove, there is always a display, and it wins on half of the occasions. Under these rules, populations of only hawks or doves are no ESS because a hawk can invade a population made up entirely of doves, and a dove can invade a population of hawks only. Both would have an advantage and would spread in the population. A hawk in a population of doves would win all contests, and a dove in a population of hawks would never get injured because it wouldn’t fight.

However, it is possible for a mixture of hawks and doves to provide a stable situation when their numbers reach a certain proportion of the total population. For example, with payoffs as winner +50, injury -100, loser 0, display -10, a population comprising hawks and doves (or individuals adopting a mixed strategy of alternating between playing hawk and dove strategies) is an ESS whenever 58,3% of the population are hawks and 41,7% doves; or when all individuals behave at random as hawks in 58,3% of the encounters and doves in 41,7%. The percentages (the point of equilibrium) depend on costs and benefits (or the pay-off, which is equal to benefits minus costs).

Evolutionarily stable strategies are not artificial constructs. They exist in nature. The Oryx, Oryx gazella, have sharp pointed horns, which they never use in contests with rivals, except in a ritualised manner, and only in defense against predators. They play the dove strategy. They hawk strategy is rarely seen in nature except when competing for mating partners. However, up to 10% per year of Musk Ox, Ovibos moschatus, adult males die because of injuries sustained while fighting over females.

An ESS is a modified form of a Nash equilibrium. In most simple games, the ESSes and Nash equilibria coincide perfectly, but some games may have Nash equilibria that are not ESSes. Furthermore, even if a game has pure strategy Nash equilibria, it might be that none of those pure strategies are ESSes. We can prove both Nash equilibria and ESS mathematically (see references).

Peer-to-peer file sharing is a good example of an ESS in our modern society. Bit Torrent peers use Tit-for-Tat strategy to optimize their download speed. They achieve cooperation exchanging upload bandwidth with download bandwidth.

Evolutionary biology and sociobiology attempt to explain animal behavior and social structures (humans included), primarily in terms of evolutionarily stable strategies.

References

• Brockmann, H. J. and Dawkins, R. (1979). Joint nesting in a digger wasp as an evolutionarily stable preadaptation to social life. Behaviour 71, 203-245.
• Hines, W.G.S. (1982b), Mutations, perturbations and evolutionarily stable strategies, J. Appl. Probab. 19, 204–209. https://doi.org/10.2307/3213929.
• McFarland, D. (1999). Animal Behavior. Pearson Prentice Hall, England. 3rd ed.ISBN-10: 0582327326.
• Maynard Smith, J. (1972). Game Theory and The Evolution of Fighting. On Evolution. Edinburgh University Press. ISBN 0-85224-223-9.
• Maynard Smith, J. and Price, G.R. (1973). The logic of animal conflict. Nature. 246 (5427): 15–18.  doi:10.1038/246015a0. S2CID 4224989.
• Maynard Smith, J. (1982). Evolution and the Theory of Games. ISBN 0-521-28884-3.
• Maynard Smith, J. and Harper, D. (2003) Animal Signals. Oxford Series in Ecology and Evolution. ISBN: 9780198526858
• Møller A.P. (1993). Developmental stability, sexual selection, and the evolution of secondary sexual characters. Etologia 3:199—208. ISBN : 978-3-0348-9813-3
• Nash, J. F. (May 1950). Non-Cooperative Games (PDF). PhD thesis. Princeton University. Retrieved May 24, 2015.
• Parker, G.A. (1984) Evolutionarily Stable Strategies. In Krebs, J.R. and Davis, N.B. (eds), Behavioral Ecology, 2nd ed. Blackwell Scientific Pub., Oxford.
• Reynolds, P. (1998). Dynamics and Range Expansion of a Reestablished Muskox Population. The Journal of Wildlife Management, 62(2), 734-744. doi:10.2307/3802350.
• Walther F.R. (1980). Aggressive behavior of oryx antelope at water-holes in the Etosha National Park. Madoqua 11:271-302.

Featured image: The traditional way to illustrate Evolutionarily Stable Strategies is the simulation of the encounter between two strategies, the hawk and the dove.

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