The fixation time of a strongly beneficial allele in a structured population

Abstract: For a beneficial allele which enters a large unstructured population and eventually goes to fixation, it is known that the time to fixation is approximately 2log(α)/α for a large selection coefficient α. For a population that is distributed over finitely many colonies, with migration between these colonies, we detect various regimes of the migration rate μ for which the fixation times have different asymptotics as α→∞.

If μ is of order α, the allele fixes (as in the spatially unstructured case) in time ∼2log(α)/α. If μ is of order αγ,0≤γ≤1, the fixation time is ∼(2+(1−γ)Δ)log(α)/α, where Δ is the number of migration steps that are needed to reach all other colonies starting from the colony where the beneficial allele appeared. If μ=1/log(α), the fixation time is ∼(2+S)log(α)/α, where S is a random time in a simple epidemic model.

The main idea for our analysis is to combine a new moment dual for the process conditioned to fixation with the time reversal in equilibrium of a spatial version of Neuhauser and Krone’s ancestral selection graph

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch
• Anmerkungen: Electronic journal of probability. - 21 (2016) , 1-42, ISSN: 1083-6489

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wo): Freiburg
• (wer): Universität
• (wann): 2021
• Urheber: Greven, Andreas ; Pfaffelhuber, Peter ; Pokalyuk, Cornelia ; Wakolbinger, Anton
• Beteiligte Personen und Organisationen: Abteilung für Mathematische Stochastik, Prof. Dr. Peter Pfaffelhuber

Weitere Informationen

• DOI: 10.1214/16-EJP3355
• URN: urn:nbn:de:bsz:25-freidok-2217648
• Rechteinformation: Kein Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 25.03.2025, 13:44 MEZ