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Convergence of the Genealogy of the Spatial Cannings Model

dc.contributor.advisorSturm, Anja Prof. Dr.
dc.contributor.authorHeuer, Benjamin
dc.date.accessioned2016-11-16T09:20:17Z
dc.date.available2016-11-16T09:20:17Z
dc.date.issued2016-11-16
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-002B-7CA9-7
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-5983
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-5983
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510de
dc.titleConvergence of the Genealogy of the Spatial Cannings Modelde
dc.typedoctoralThesisde
dc.contributor.refereeSturm, Anja Prof. Dr.
dc.date.examination2016-09-23
dc.description.abstractengIn this thesis we consider the genealogy of a spatial Cannings model. This is a population model in which individuals are distributed over a countable set of sites G. The reproduction of individuals at each site is panmictic (exchangeable) and preserves the local population size. The offspring then migrate to other sites in G, also in an exchangeable manner. We consider the spatial coalescent introduced by sampling n individuals at present time and tracking their ancestral lines back in time. The resulting process is the spatial Cannings coalescent. Our main result shows, that an appropriately time-rescaled spatial Cannings coalescent converges to a spatial Xi-coalescent in the large population limit. The key feature of our result is that the spatial structure is preserved into the limit as opposed to a fast migration limit. The influence of the migration on the local population size can yield a time-inhomogeneous limit and, in case of sites with a small population size, our limiting process may not have a strongly continuous semigroup.de
dc.contributor.coRefereeSchuhmacher, Dominic Prof. Dr.
dc.subject.engpopulation geneticsde
dc.subject.englarge population limitde
dc.subject.engCannings modelde
dc.subject.engspatialde
dc.subject.enggenealogyde
dc.subject.engcoalescensede
dc.subject.engtime-inhomogeneousde
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-002B-7CA9-7-8
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn872684164


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