Greven A, Pokalyuk C, Pfaffelhuber P, Wakolbinger A (2016)
Publication Type: Journal article, Online publication
Publication year: 2016
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
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.
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://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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