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Darwinian dynamics based on mutation and selection form thecore of mathematical models for adaptation and coevolution ofbiological populations. The evolutionary outcome is often nota fitness-maximizing equilibrium but can include oscillationsand chaos. For studying frequency-dependent selection, game-theoreticarguments are more appropriate than optimization algorithms.Replicator and adaptive dynamics describe short- and long-termevolution in phenotype space and have found applications rangingfrom animal behavior and ecology to speciation, macroevolution,and human language. Evolutionary game theory is an essentialcomponent of a mathematical and computational approach to biology.
1 Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, 1 Brattle Square, Cambridge, MA 02138, USA. 2 Faculty for Mathematics, University of Vienna, Nordberggasse 15, A-1090 Vienna, Austria. 3 International Institute for Applied Systems Analysis (IIASA), A-2361 Laxenburg, Austria.
* To whom correspondence should be addressed. E-mail: martin_nowak{at}harvard.edu
