Authors: Sandra Kluth Thiemo Hustedt Ellen Baake
Publish Date: 2013/09/18
Volume: 75, Issue: 11, Pages: 2003-2027
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 pictureIt 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 DFGSPP 1590 Grant no BA2469/51In Sect 41 we have presented an alternative derivation of the boundary value problem for the conditional probability h It remains to prove that lim N to infty hN k N = hx with x∈01 0k N N lim N to infty frack NN = x and h as given as in 7
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