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n Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie - Die evolusiespel : 'n eenvoudige algoritme vir die bepaling van 'n evolusionêr stabiele strategie : research and review article

Volume 21, Issue 4
  • ISSN : 0254-3486
  • E-ISSN: 2222-4173

Abstract

<b>The evolution game : a simple algorithm for the determination of an evolutionary stable strategy</b> <br>As a result of the complex nature of genetic models used to describe intricate survival strategies of living organisms during the process of evolution, principles of game theory are often used as an alternative. In such cases it is important to be able to determine which strategy - out of a set of possible strategies - would be optimal, in the sense that populations of which all members are using this strategy, can not be invaded by individuals following any other possible strategy from the feasible set. Such a strategy is known as an Evolutionary Stable Strategy (ESS), and much research has been done on the properties of an ESS, as far as it could be associated with mathematical population growth models. In this article we discuss a simple algorithm by which an ESS can be calculated in the case of non linear discrete models with a single strategy variable. We also give the theoretical basis of the algorithm, and show that it can be used even in the case of fairly complicated population situations.

As gevolg van die ingewikkelde aard van genetiese modelle om die rol van redelik komplekse oorlewingstrategieë van lewende organismes in die evolusieproses te beskryf, word daar dikwels van spelteoriebeginsels gebruik gemaak. In sulke gevalle is dit belangrik om te kan vasstel watter strategie uit 'n versameling van moontlike strategieë optimaal sal wees, in die sin dat bevolkings wat almal hierdie strategie volg, nie verdring sal kan word deur individue wat enige ander moontlike strategie uit die toelaatbare versameling volg nie. So 'n strategie staan bekend as 'n Evolusionêr Stabiele Strategie (ESS), en heelwat navorsing is al gedoen oor die eienskappe van 'n ESS, vir sover dit gekoppel kan word aan wiskundige bevolkingsgroeimodelle. In hierdie artikel bespreek ons 'n eenvoudige algoritme waarmee 'n ESS bereken kan word in die geval van nieliniêre diskrete modelle waarin 'n enkele strategieveranderlike voorkom. Ons gee onder meer ook die teoretiese grondslag van die algoritme, en wys dat dit selfs in betreklike komplekse bevolkingsituasies sal werk.

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/content/aknat/21/4/EJC20315
2002-12-01
2019-12-15

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