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Documents  Blath, Jochen | enregistrements trouvés : 3

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- xiii; 248 p.
ISBN 978-3-03719-072-2

Series of congress reports

Localisation : Colloque 1er étage (BERL)

processus stochastique # processus spécial # finances # probabilités

60-06 ; 60Gxx ; 60Jxx ; 60Kxx ; 00B25

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Research talks;Mathematics in Science and Technology;Probability and Statistics

We analyse patterns of genetic variability of populations in the presence of a large seed bank with the help of a new coalescent structure called seed bank coalescent. This ancestral process appears naturally as scaling limit of the genealogy of large populations that sustain seed banks, if the seed bank size and individual dormancy times are of the same order as the active population. Mutations appear as Poisson process on the active lineages, and potentially at reduced rate also on the dormant lineages. The presence of ‘dormant’ lineages leads to qualitatively altered times to the most recent common ancestor and non-classical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with seed bank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seed bank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Commonly employed distance statistics, in the presence and absence of a seed bank, are compared. The effect of a seed bank on the expected site-frequency spectrum is also investigated. Our results indicate that the presence of a large seed bank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect the presence of a large seed bank in genetic data. Joint work with Bjarki Eldon, Adrián González Casanova, Noemi Kurt, Maite Wilke-Berenguer We analyse patterns of genetic variability of populations in the presence of a large seed bank with the help of a new coalescent structure called seed bank coalescent. This ancestral process appears naturally as scaling limit of the genealogy of large populations that sustain seed banks, if the seed bank size and individual dormancy times are of the same order as the active population. Mutations appear as Poisson process on the active lineages, ...

92D10 ; 60K35 ; 62P10

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- V-390 p.
ISBN 978-0-521-71821-9

London mathematical society lecture note series , 0353

Localisation : Collection 1er étage

analyse stochastique # Heinrich von Weizsäcker

60-06 ; 60Hxx ; 00B15

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