Looking Backward in Time: The Coalescent
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.
KeywordsAncestor Gene Recent Common Ancestor Death Event Moran Model Complete Distribution
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