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The general coalescent with asynchronous mergers of ancestral lines

The general coalescent with asynchronous mergers of ancestral lines <jats:p>Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral process. We describe a class of asymptotic structures for the ancestral process via a convergence criterion. One of the basic conditions of the criterion prevents simultaneous mergers of ancestral lines. Another key condition implies that the marginal distribution of the family size is attracted by an infinitely divisible distribution. If the latter is normal the coalescent allows only for pairwise mergers (Kingman's coalescent). Otherwise multiple mergers happen with positive probability.</jats:p> http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Probability CrossRef

The general coalescent with asynchronous mergers of ancestral lines

Journal of Applied Probability , Volume 36 (4): 1116-1125 – Dec 1, 1999

The general coalescent with asynchronous mergers of ancestral lines


Abstract

<jats:p>Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral process. We describe a class of asymptotic structures for the ancestral process via a convergence criterion. One of the basic conditions of the criterion prevents simultaneous mergers of ancestral lines. Another key condition implies that the marginal distribution of the family size is attracted by an infinitely divisible distribution. If the latter is normal the coalescent allows only for pairwise mergers (Kingman's coalescent). Otherwise multiple mergers happen with positive probability.</jats:p>

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Publisher
CrossRef
ISSN
0021-9002
DOI
10.1239/jap/1032374759
Publisher site
See Article on Publisher Site

Abstract

<jats:p>Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral process. We describe a class of asymptotic structures for the ancestral process via a convergence criterion. One of the basic conditions of the criterion prevents simultaneous mergers of ancestral lines. Another key condition implies that the marginal distribution of the family size is attracted by an infinitely divisible distribution. If the latter is normal the coalescent allows only for pairwise mergers (Kingman's coalescent). Otherwise multiple mergers happen with positive probability.</jats:p>

Journal

Journal of Applied ProbabilityCrossRef

Published: Dec 1, 1999

References