title: When the mean is not enough: Calculating fixation time distributions in birth-death processes.
abstract: Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Peter
authors.initials: P
authors.lastname: Ashcroft
authors.affiliation: Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany.
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Tobias
authors.initials: T
authors.lastname: Galla
mesh_terms: D005075:Biological Evolution; D003643:Death; D005716:Game Theory; D009154:Mutation; D013997:Time Factors