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Cannings models, population size changes and multiple-merger coalescents.

ABSTRACT: Multiple-merger coalescents, e.g. [Formula: see text]-n-coalescents, have been proposed as models of the genealogy of n sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's n-coalescent. [Formula: see text]-n-coalescents can be seen as the limit process of the discrete genealogies of Cannings models with fixed population size, when time is rescaled and population size [Formula: see text]. As established for Kingman's n-coalescent, moderate population size fluctuations in the discrete population model should be reflected by a time-change of the limit coalescent. For [Formula: see text]-n-coalescents, this has been explicitly shown for only a limited subclass of [Formula: see text]-n-coalescents and exponentially growing populations. This article gives a more general construction of time-changed [Formula: see text]-n-coalescents as limits of specific Cannings models with rather arbitrary time changes.

SUBMITTER: Freund F

PROVIDER: S-EPMC7052052 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature

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Cannings models, population size changes and multiple-merger coalescents.

Freund Fabian F

Journal of mathematical biology 20200201 5

Multiple-merger coalescents, e.g. [Formula: see text]-n-coalescents, have been proposed as models of the genealogy of n sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's n-coalescent. [Formula: see text]-n-coalescents can be seen as the limit process of the discrete genealogies of Cannings models with fixed population size, when time is rescaled and population size [Formula: see text]. As established for Kingman's n-coalescent, modera ...[more]

PMID: 32008102

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