%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 }