# The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation

Baake E, Lenz U, Wakolbinger A (2016)
Electronic Communications in Probability 21: 59.

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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 Λ. 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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Baake E, Lenz U, Wakolbinger A. The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation. Electronic Communications in Probability. 2016;21: 59.
Baake, E., Lenz, U., & Wakolbinger, A. (2016). The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation. Electronic Communications in Probability, 21, 59. doi:10.1214/16-ecp16
Baake, E., Lenz, U., and Wakolbinger, A. (2016). The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation. Electronic Communications in Probability 21:59.
Baake, E., Lenz, U., & Wakolbinger, A., 2016. The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation. Electronic Communications in Probability, 21: 59.
E. Baake, U. Lenz, and A. Wakolbinger, “The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation”, Electronic Communications in Probability, vol. 21, 2016, : 59.
Baake, E., Lenz, U., Wakolbinger, A.: The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation. Electronic Communications in Probability. 21, : 59 (2016).
Baake, Ellen, Lenz, Ute, and Wakolbinger, Anton. “The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation”. Electronic Communications in Probability 21 (2016): 59.
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