For a beneficial allele which enters a large unstructured population and
eventually goes to fixation, it is known that the time to fixation is
approximately $2łog(\alpha)/\alpha$ for a large selection coefficent $\alpha$.
In the presence of spatial structure with migration between colonies we detect
various regimes of the migration rate $\mu$ for which the fixation times have
different asymptotics as $ınfty$. If $\mu$ is of order $\alpha$,
the allele fixes (as in the spatially unstructured case) in time $\sim
2łog(\alpha)/\alpha$. If $\mu$ is of order $\alpha^p, 0p 1$, the
fixation time is $(2 + (1-p)d) łog(\alpha)/\alpha$, where $d$ is the
maximum of the migration steps that are required from the colony where the
beneficial allele entered to any other colony. If $= 1/łog(\alpha)$, the
fixation time is $(2+S)łog(\alpha)/\alpha$, 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.
%0 Generic
%1 greven2014fixation
%A Greven, Andreas
%A Pfaffelhuber, Peter
%A Pokalyuk, Cornelia
%A Wakolbinger, Anton
%D 2014
%K ancestral_selection_graph beneficial_mutations branching_processes duality fixation_time selection spatial_structure
%T The fixation time of a strongly beneficial allele in a structured
population
%U http://arxiv.org/abs/1402.1769
%X For a beneficial allele which enters a large unstructured population and
eventually goes to fixation, it is known that the time to fixation is
approximately $2łog(\alpha)/\alpha$ for a large selection coefficent $\alpha$.
In the presence of spatial structure with migration between colonies we detect
various regimes of the migration rate $\mu$ for which the fixation times have
different asymptotics as $ınfty$. If $\mu$ is of order $\alpha$,
the allele fixes (as in the spatially unstructured case) in time $\sim
2łog(\alpha)/\alpha$. If $\mu$ is of order $\alpha^p, 0p 1$, the
fixation time is $(2 + (1-p)d) łog(\alpha)/\alpha$, where $d$ is the
maximum of the migration steps that are required from the colony where the
beneficial allele entered to any other colony. If $= 1/łog(\alpha)$, the
fixation time is $(2+S)łog(\alpha)/\alpha$, 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.
@misc{greven2014fixation,
abstract = {For a beneficial allele which enters a large unstructured population and
eventually goes to fixation, it is known that the time to fixation is
approximately $2\log(\alpha)/\alpha$ for a large selection coefficent $\alpha$.
In the presence of spatial structure with migration between colonies we detect
various regimes of the migration rate $\mu$ for which the fixation times have
different asymptotics as $\alpha \to \infty$. If $\mu$ is of order $\alpha$,
the allele fixes (as in the spatially unstructured case) in time $\sim
2\log(\alpha)/\alpha$. If $\mu$ is of order $\alpha^p, 0\leq p \leq 1$, the
fixation time is $\sim (2 + (1-p)d) \log(\alpha)/\alpha$, where $d$ is the
maximum of the migration steps that are required from the colony where the
beneficial allele entered to any other colony. If $\mu = 1/\log(\alpha)$, the
fixation time is $\sim (2+S)\log(\alpha)/\alpha$, 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.},
added-at = {2014-02-26T20:47:04.000+0100},
author = {Greven, Andreas and Pfaffelhuber, Peter and Pokalyuk, Cornelia and Wakolbinger, Anton},
biburl = {https://www.bibsonomy.org/bibtex/2a2b5ad073006bbfa30f0b24df8707459/peter.ralph},
interhash = {1bed06b94019971af32bfeb020e4acae},
intrahash = {a2b5ad073006bbfa30f0b24df8707459},
keywords = {ancestral_selection_graph beneficial_mutations branching_processes duality fixation_time selection spatial_structure},
note = {cite arxiv:1402.1769},
timestamp = {2014-02-26T22:39:03.000+0100},
title = {The fixation time of a strongly beneficial allele in a structured
population},
url = {http://arxiv.org/abs/1402.1769},
year = 2014
}