The fixation time of a strongly benefical allele in a structured population

Greven A, Pokalyuk C, Pfaffelhuber P, Wakolbinger A (2016)

Publication Type: Journal article, Online publication

Publication year: 2016

Journal

Electronic Journal of Probability Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics

Publisher: Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics

Book Volume: 21

Pages Range: 1-42

Article Number: 1083-6489

Journal Issue: 61

URI: https://projecteuclid.org/euclid.ejp/1475586182

DOI: 10.1214/16-EJP3355

Abstract

For a beneficial allele which enters a large unstructured popu-
lation and eventually goes to fixation, it is known that the time to fixation
is approximately 2 log(α)/α for a large selection coefficient α. For a popula-
tion that is distributed over finitely many colonies, with migration between
these colonies, we detect various regimes of the migration rate μ for which
the fixation times have different asymptotics as α → ∞.
If μ is of order α, the allele fixes (as in the spatially unstructured case)
in time ∼ 2 log(α)/α. If μ is of order α γ , 0 ≤ γ ≤ 1, the fixation time
is ∼ (2 + (1 − γ)∆) log(α)/α, where ∆ is the number of migration steps
that are needed to reach all other colonies starting from the colony where
the beneficial allele appeared. If μ = 1/ log(α), the fixation time is ∼ (2 +
S) log(α)/α, where S is a random time in a simple epidemic model.
The main idea for our analysis is to combine a new moment dual for
the process conditioned to fixation with the time reversal in equilibrium of
a spatial version of Neuhauser and Krone’s ancestral selection graph.

Authors with CRIS profile

Andreas Greven Lehrstuhl für Mathematische Stochastik

Involved external institutions

Otto-von-Guericke-Universität Magdeburg DE Germany (DE) Goethe-Universität Frankfurt am Main DE Germany (DE)

How to cite

APA:

Greven, A., Pokalyuk, C., Pfaffelhuber, P., & Wakolbinger, A. (2016). The fixation time of a strongly benefical allele in a structured population. Electronic Journal of Probability, 21(61), 1-42. https://dx.doi.org/10.1214/16-EJP3355

MLA:

Greven, Andreas, et al. "The fixation time of a strongly benefical allele in a structured population." Electronic Journal of Probability 21.61 (2016): 1-42.

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