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  Fixation probabilities in populations under demographic fluctuations

Czuppon, P., & Traulsen, A. (2018). Fixation probabilities in populations under demographic fluctuations. Journal of Mathematical Biology, 77, 1233-1277. doi:10.1007/s00285-018-1251-9.

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Czuppon-Traulsen2018_Article_FixationProbabilitiesInPopulat.pdf (Publisher version), 2MB
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https://arxiv.org/abs/1708.09665 (Preprint)
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 Creators:
Czuppon, Peter1, Author           
Traulsen, Arne1, Author           
Affiliations:
1Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society, ou_1445641              

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Free keywords: Demographic Stochasticity; Diffusion Theory; Evolutionary Games; Fixation Probability; Weak Selection; Quantitative Biology; Populations and Evolution; MSC 60J60; MSCV91A22; MSC 92D25
 Abstract: We study the fixation probability of a mutant type when introduced into
a resident population. We implement a stochastic competitive Lotka–Volterra model
with two types and intra- and interspecific competition. The model further allows for
stochastically varying population sizes. The competition coefficients are interpreted in
terms of inverse payoffs emerging from an evolutionary game. Since our study focuses
on the impact of the competition values, we assume the same net growth rate for both
types. In this general framework, we derive a formula for the fixation probability
φ
of the mutant type under weak selection. We find that the most important parameter
deciding over the invasion success of the mutant is its death rate due to competition
with the resident. Furthermore, we compare our approximation to results obtained
by implementing population size changes deterministically in order to explore the
parameter regime of validity of our method. Finally, we put our formula in the context
of classical evolutionary game theory and observe similarities and differences to the
results obtained in that constant population size setting.

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Language(s): eng - English
 Dates: 2018-05-082017-08-312018-06-07
 Publication Status: Published online
 Pages: 31
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1708.09665v1
DOI: 10.1007/s00285-018-1251-9
 Degree: -

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Title: Journal of Mathematical Biology
Source Genre: Journal
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Publ. Info: Heidelberg : Springer
Pages: - Volume / Issue: 77 Sequence Number: - Start / End Page: 1233 - 1277 Identifier: ISSN: 0303-6812
CoNE: https://pure.mpg.de/cone/journals/resource/954925511424