The general coalescent with asynchronous mergers of ancestral lines

@article{Sagitov1999TheGC,
  title={The general coalescent with asynchronous mergers of ancestral lines},
  author={Serik Sagitov},
  journal={Journal of Applied Probability},
  year={1999},
  volume={36},
  pages={1116 - 1125}
}
  • S. Sagitov
  • Published 1 December 1999
  • Mathematics
  • Journal of Applied Probability
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… 

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References

SHOWING 1-10 OF 11 REFERENCES

Robustness results for the coalescent

  • M. Möhle
  • Mathematics
    Journal of Applied Probability
  • 1998
A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is

THE COALESCENT

On the genealogy of large populations

  • J. Kingman
  • Mathematics
    Journal of Applied Probability
  • 1982
A new Markov chain is introduced which can be used to describe the family relationships among n individuals drawn from a particular generation of a large haploid population. The properties of this

More Exact Statements of Several Theorems in the Theory of Branching Processes

Theorems proved by A. N. Kolmogorov [2], A. M. Yaglom [3] and B. A. Sevastyanov [1] on regular branching processes with particles of one type homogeneous in time (parameter t being continuous) are

An Introduction to Probability Theory and Its Applications

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to

An Introduction to Probability Theory and its Applications

A branching process with mean one and possibly infinite variance

Reduced Branching Processes

Exchangeability and the evolution of large populations

  • Exchangeability in Probability and Statistics