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**Harvard**

Jagers, P. och Sagitov, S. (2004) *Convergence to the coalescent in populations of substantially varying size.*.

** BibTeX **

@article{

Jagers2004,

author={Jagers, Peter and Sagitov, Serik},

title={Convergence to the coalescent in populations of substantially varying size.},

journal={J. Appl. Probab. },

issn={0021-9002},

volume={41},

issue={2},

pages={368-378},

abstract={Kingman's classical coalescent uncovers the basic pattern of
genealogical trees of random samples of individuals in large
but time-constant populations. Time is viewed as discrete and identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance).
Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity,
towards the (time-scaled) coalescent is simply proved under minimal conditions. As a result, a formula for
effective population size obtains, generalising the well-knownharmonic mean expression for effective size. },

year={2004},

keywords={coalescent, exchangeability, population genetics},

}

** RefWorks **

RT Journal Article

SR Print

ID 107963

A1 Jagers, Peter

A1 Sagitov, Serik

T1 Convergence to the coalescent in populations of substantially varying size.

YR 2004

JF J. Appl. Probab.

SN 0021-9002

VO 41

IS 2

SP 368

OP 378

AB Kingman's classical coalescent uncovers the basic pattern of
genealogical trees of random samples of individuals in large
but time-constant populations. Time is viewed as discrete and identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance).
Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity,
towards the (time-scaled) coalescent is simply proved under minimal conditions. As a result, a formula for
effective population size obtains, generalising the well-knownharmonic mean expression for effective size.

LA eng

OL 30