Editing Evolutionary game theory (section)

==Coevolution==
{{main|Coevolution}}

Two types of dynamics:
* Evolutionary games which lead to a stable situation or point of stasis for contending strategies which result in an evolutionarily stable strategy
* Evolutionary games which exhibit a cyclic behaviour (as with RPS game) where the proportions of contending strategies continuously cycle over time within the overall population

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 | image1 =NHM_Taricha_granulosa_cropped.jpg
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 | caption1= Competitive Coevolution 
– The [[rough-skinned newt]] (''Tarricha granulosa'') is highly toxic, due to an [[evolutionary arms race]] with a predator, the [[common garter snake]] (''Thamnophis sirtalis''), which in turn is highly tolerant of the poison. The two are locked in a [[Red Queen's Hypothesis|Red Queen]] arms race.<ref>Pallen, M., ''Rough Guide to Evolution'', Penguin Books, 2009, p.123, {{ISBN|978-1-85828-946-5}}</ref> 
 | image2=NHM Xanthopan morgani.jpg
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 | caption2=Mutualistic Coevolution
– [[Darwin's orchid]] (''Angraecum sesquipedale'') and the moth [[Morgan's sphinx]] (''Xanthopan morgani'') have a mutual relationship where the moth gains pollen and the flower is [[pollination|pollinated]].
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A third, [[coevolution]]ary, dynamic, combines intra-specific and inter-specific competition. Examples include predator-prey competition and host-parasite co-evolution, as well as mutualism.  Evolutionary game models have been created for pairwise and multi-species coevolutionary systems.<ref>Matja, Szolnoki, "Coevolutionary games – a mini review", Biosystems, 2009</ref> The general dynamic differs between competitive systems and mutualistic systems.

In competitive (non-mutualistic) inter-species coevolutionary system the species are involved in an arms race – where adaptations that are better at competing against the other species tend to be preserved. Both game payoffs and replicator dynamics reflect this. This leads to a [[Red Queen's Hypothesis|Red Queen]] dynamic where the protagonists must "run as fast as they can to just stay in one place".<ref>Cliff and Miller, "Tracking the red queen: Measurements of adaptive progress in co-evolutionary simulations", European Conference on Artificial Life, p. 200–218, 1995</ref>

A number of evolutionary game theory models have been produced to encompass coevolutionary situations. A key factor applicable in these coevolutionary systems is the continuous adaptation of strategy in such arms races. Coevolutionary modelling therefore often includes [[genetic algorithm]]s to reflect mutational effects, while computers simulate the dynamics of the overall coevolutionary game.   The resulting dynamics are studied as various parameters are modified.  Because several variables are simultaneously at play, solutions become the province of multi-variable optimisation. The mathematical criteria of determining stable points are [[Pareto efficiency]] and Pareto dominance, a measure of solution optimality peaks in multivariable systems.<ref>Sevan, Ficici and Pollack, "Pareto optimality in coevolutionary learning", European Conference on Artificial Life, pp. 316–325, 2001</ref>

[[Carl Bergstrom]] and Michael Lachmann apply evolutionary game theory to the division of benefits in [[Mutualism (biology)|mutualistic]] interactions between organisms. Darwinian assumptions about fitness are modeled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship gains a disproportionately high share of the benefits or payoffs.<ref>{{cite journal | last1=Bergstrom | first1=C. | last2=Lachmann | first2=M. | year=2003 | title=The red king effect: when the slowest runner wins the coevolutionary race | journal= Proceedings of the National Academy of Sciences| volume=100 | issue=2| pages=593–598 | doi=10.1073/pnas.0134966100 | pmid=12525707 |bibcode=2003PNAS..100..593B | pmc=141041 | doi-access=free }}</ref>