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Calculating the Secrets of Life Contributions of the Mathematical Sciences to Molecular Biology (1995) / Chapter Skim
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Pages 119-121

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From page 119...
... In the next section we digress to present a mathematical vignette in the area of random combinatorial structures. The Ewens sampling formula was derived as a means to analyze allozyme frequency data that became prevalent in the late 1960s.
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From page 120...
... . From the description of the genealogy, it is clear that the time In back to the common ancestor has mean
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From page 121...
... , and assume that 2Nu - 0 as N - no, then the Poisson approximation to the binomial distribution shows that the number of mutations in time t has in the limit a Poisson distribution with mean Ot / 2 . This argument can be extended to show that the mutations that arise on different branches of the coalescent tree follow independent Poisson processes, each of rate ~ / 2 .
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Key Terms

  • population genetics
  • segregating sites
  • ewens sampling
  • sampling formula
  • common ancestor

  • independent poisson
  • coalescent tree
  • dna sequence
  • combinatorial structures
  • poisson approximation

  • random variables
  • likelihood methods
  • mathematical vignette
  • poisson process
  • random variable


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