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The general coalescent with asynchronous mergers of ancestral lines
Abstract
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.
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Cited by
Combinatorial Stochastic Processes
(2006) · Lecture Notes in Mathematics · doi:10.1007/b11601500 · Cited by 935
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Keinan, A., & Clark, A. G. (2012) · Science · doi:10.1126/science.1217283 · Cited by 548
Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)
Greven, A., Pfaffelhuber, P., & Winter, A. (2009) · Probability Theory and Related Fields · doi:10.1007/s00440-008-0169-3 · Cited by 157
Metadata
- Authors
- Sagitov, S.
- Venue
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Published
- 1999-12
- Volume
- 36
- Issue
- 4
- Pages
- 1116-1125
- ISSN
- 0021-9002 (ISSN-L)
- 1475-6072
- OpenAlex
- W1986342834
- Cited by
- 350
- References
- 0
- FWCI
- 4.97
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The general coalescent with asynchronous mergers of ancestral lines. https://app.cochat.ai/papers/10.1239/jap/1032374759
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- Sagitov, S. (1999). The general coalescent with asynchronous mergers of ancestral lines. Journal of Applied Probability. https://doi.org/10.1239/jap/1032374759
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
