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dc.contributor.advisor Sturm, Anja Prof. Dr.
dc.contributor.author Heuer, Benjamin
dc.date.accessioned 2016-11-16T09:20:17Z
dc.date.available 2016-11-16T09:20:17Z
dc.date.issued 2016-11-16
dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-002B-7CA9-7
dc.language.iso eng de
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc 510 de
dc.title Convergence of the Genealogy of the Spatial Cannings Model de
dc.type doctoralThesis de
dc.contributor.referee Sturm, Anja Prof. Dr.
dc.date.examination 2016-09-23
dc.description.abstracteng In 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.coReferee Schuhmacher, Dominic Prof. Dr.
dc.subject.eng population genetics de
dc.subject.eng large population limit de
dc.subject.eng Cannings model de
dc.subject.eng spatial de
dc.subject.eng genealogy de
dc.subject.eng coalescense de
dc.subject.eng time-inhomogeneous de
dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-002B-7CA9-7-8
dc.affiliation.institute Fakultät für Mathematik und Informatik de
dc.subject.gokfull Mathematics (PPN61756535X) de
dc.identifier.ppn 872684164

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