Looking Backward in Time: The Coalescent

  • Warren J. Ewens
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 27)


It is remarkable that the elegant Watterson formulation for the probability distribution for S n , given implicitly by (9.52), together with the perceptive remark following it, as well as the elegance and simplicity of many of the “age” formulas in Section 9.9, were not immediately seized upon and investigated at greater length immediately after they appeared to determine why formulas of these elegant forms arise. Since these formulas relate to the past history of the population, historical factors must explain them. Similarly, the unequal frequencies that tend to arise even among selectively equivalent alleles, as shown, for example, by (3.83), must be explained by historical factors: The oldest allele in a sample will tend to have a higher frequency than a newly arisen mutant allele. It fell to Kingman (1982a,b,c) to recognize the importance of these historical factors, to see that they are most simply approached by a retrospective analysis of the ancestry of the genes in a sample, to introduce the concept of the coalescent, which provides the framework for this retrospective analysis, and then to lay down the basic mathematical machinery of the coalescent process.


Ancestor Gene Recent Common Ancestor Death Event Moran Model Complete Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Warren J. Ewens
    • 1
  1. 1.Department of BiologyUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations