Journal of Statistical Physics

, Volume 172, Issue 1, pp 156–174 | Cite as

Lines of Descent Under Selection

  • Ellen Baake
  • Anton Wakolbinger


We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed ancestral selection graph and the pruned lookdown ancestral selection graph. The killed ancestral selection graph gives a representation of the type of a random individual from a stationary population, based upon the individual’s potential ancestry back until the mutations that define the individual’s type. The pruned lookdown ancestral selection graph allows one to trace the ancestry of individuals from a stationary distribution back into the distant past, thus leading to the stationary distribution of ancestral types. We illustrate the results by applying them to a prototype model for the error threshold phenomenon.


Mutation-selection model Killed ancestral selection graph Pruned lookdown ancestral selection graph Error threshold 

Mathematics Subject Classification

60J27 60J75 92D15 05C80 



It is our pleasure to thank Fernando Cordero, Sebastian Hummel, and Ute Lenz for fruitful discussions. This project received financial support from Deutsche Forschungsgemeinschaft (Priority Programme SPP 1590 Probabilistic Structures in Evolution, Grant Nos. BA 2469/5-1 and WA 967/4-1).


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Authors and Affiliations

  1. 1.Faculty of TechnologyBielefeld UniversityBielefeldGermany
  2. 2.Institute of MathematicsGoethe-Universität FrankfurtFrankfurt am MainGermany

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