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          Institute: MPI für Evolutionsbiologie     Collection: Research Group Evolutionary Theory     Display Documents

ID: 609166.0, MPI für Evolutionsbiologie / Research Group Evolutionary Theory
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
Authors:Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph
Date of Publication (YYYY-MM-DD):2012-04-03
Title of Journal:Physical Rewiew E
Issue / Number:4
Sequence Number of Article:041901
Review Status:not specified
Audience:Not Specified
Abstract / Description:We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in
finite populations based on stochastic differential equations (SDEs). For large, but finite populations this allows
us to include demographic noise without requiring explicit simulations. Instead, the population size only rescales
the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types,
provided that mutation rates μ are not too small compared to the inverse population size 1/N. This ensures that
all types are almost always represented in the population and that the occasional extinction of one type does
not result in an extended absence of that type. For μN  1 this limits the use of SDEs, but in this case there
are well established alternative approximations based on time scale separation. We illustrate our approach by
a rock-scissors-paper game with mutations, where we demonstrate excellent agreement with simulation based
results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small
population sizes.
External Publication Status:published
Document Type:Article
Communicated by:Brigitte Lechner
Affiliations:MPI für Evolutionsbiologie/AG Evolutionstheorie
External Affiliations:Institute for Neuro- and Bioinformatics, University of Lübeck, 23562 Lübeck, Germany; Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
Identifiers:ISSN:1063-651X (print) [ID-No:1]
ISSN:1539-3755 (print) [ID-No:2]
ISSN:1095-3787 (online) [ID-No:3]
ISSN:1550-2376 (online) [ID-No:4]
DOI:10.1103/PhysRevE.85.041901 [ID-No:5]
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