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Bulletin of Mathematical Biology

, Volume 75, Issue 11, pp 2003–2027 | Cite as

The Common Ancestor Process Revisited

  • Sandra Kluth
  • Thiemo Hustedt
  • Ellen Baake
Original Article

Abstract

We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Probab. 39 (2002), 38–54) and Taylor (Electron. J. Probab. 12 (2007), 808–847), we characterise this distribution via the fixation probability of the offspring of all individuals of favourable type (regardless of the offspring’s types). We concentrate on a finite population and stay with the resulting discrete setting all the way through. This way, we extend previous results and gain new insight into the underlying particle picture.

Keywords

Moran model Ancestral process with selection Ancestral line Common ancestor process Fixation probabilities 

Notes

Acknowledgements

It is our pleasure to thank Anton Wakolbinger for enlightening discussions, and for Fig. 2. We are grateful to Jay Taylor for valuable comments on the manuscript, and to Barbara Gentz for pointing out a gap in an argument at an earlier stage of the work. This project received financial support by Deutsche Forschungsgemeinschaft (DFG-SPP 1590), Grant no. BA2469/5-1.

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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.Technische FakultätUniversität BielefeldBielefeldGermany

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