Open Access
2016 The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation
Ellen Baake, Ute Lenz, Anton Wakolbinger
Electron. Commun. Probab. 21: 1-16 (2016). DOI: 10.1214/16-ECP16


Using graphical methods based on a ‘lookdown’ and pruned version of the ancestral selection graph, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection, conditional on the overall type frequency in the old population. This extends results from [17] to the case of heavy-tailed offspring, directed by a reproduction measure $\Lambda$. The representation is in terms of the equilibrium tail probabilities of the line-counting process $L$ of the graph. We identify a strong pathwise Siegmund dual of $L$, and characterise the equilibrium tail probabilities of $L$ in terms of hitting probabilities of the dual process.


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Ellen Baake. Ute Lenz. Anton Wakolbinger. "The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation." Electron. Commun. Probab. 21 1 - 16, 2016.


Received: 11 March 2016; Accepted: 8 August 2016; Published: 2016
First available in Project Euclid: 9 September 2016

zbMATH: 1346.60131
MathSciNet: MR3548771
Digital Object Identifier: 10.1214/16-ECP16

Primary: 05C80 , 60C05 , 60J75 , 92D15

Keywords: $\Lambda$-Wright-Fisher diffusion , ancestral selection graph , common ancestor type distribution , flights , lookdown graph , mutation , Pruning , selection , strong pathwise Siegmund duality

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