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Exact numerical calculation of fixation probability and time on graphs

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons118330

Hindersin,  Laura
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons104390

Bauer,  Benedikt
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Hindersin, L., Möller, M., Traulsen, A., & Bauer, B. (2016). Exact numerical calculation of fixation probability and time on graphs. Biosystems [Elektronische Ressource]: Journal of Biological and Information Processing Sciences, 150, 87-91. doi:10.1016/j.biosystems.2016.08.010.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-3AD8-4
Abstract
The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth–death or death–Birth), as well as arbitrary directed or undirected graphs. © 2016 Elsevier Ireland Ltd