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Convergence to the coalescent in populations of substantially varying size.

Peter Jagers (Institutionen för matematisk statistik) ; Serik Sagitov (Institutionen för matematisk statistik)
J. Appl. Probab. (0021-9002). Vol. 41 (2004), 2, p. 368-378.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: coalescent, exchangeability, population genetics



Denna post skapades 2010-01-15. Senast ändrad 2014-12-09.
CPL Pubid: 107963

 

Institutioner (Chalmers)

Institutionen för matematisk statistik (2002-2004)

Ämnesområden

Matematisk statistik
Genetik

Chalmers infrastruktur