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Universality of weak selection

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons57014

Wu,  Bin
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons56574

Altrock,  Philipp M.
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons56973

Traulsen,  Arne
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Wu, B., Altrock, P. M., Wang, L., & Traulsen, A. (2010). Universality of weak selection. Physical Review E, 82(4): 046106. doi:10.1103/PhysRevE.82.046106.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-D44E-1
Abstract
Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently, it has been introduced into evolutionary game theory. In evolutionary game dynamics, the probability to be imitated or to reproduce depends on the performance in a game. The influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection. In many models of both unstructured and structured populations, a key assumption allowing analytical calculations is weak selection, which means that all individuals perform approximately equally well. In the weak selection limit many different microscopic evolutionary models have the same or similar properties. How universal is weak selection for those microscopic evolutionary processes? We answer this question by investigating the fixation probability and the average fixation time not only up to linear but also up to higher orders in selection intensity. We find universal higher order expansions, which allow a rescaling of the selection intensity. With this, we can identify specific models which violate linear weak selection results, such as the one-third rule of coordination games in finite but large populations