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Part I: Ancestral Inference in Population Genetics

  • Simon TavaréEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1837)

Contents.

  • 1 Introduction
    • 1.1 Genealogical processes

    • 1.2 Organization of the notes

    • 1.3 Acknowledgements

  • 2 The Wright-Fisher model
    • 2.1 Random drift

    • 2.2 The genealogy of the Wright-Fisher model

    • 2.3 Properties of the ancestral process

    • 2.4 Variable population size

  • 3 The Ewens Sampling Formula
    • 3.1 The effects of mutation

    • 3.2 Estimating the mutation rate

    • 3.3 Allozyme frequency data

    • 3.4 Simulating an infinitely-many alleles sample

    • 3.5 A recursion for the ESF

    • 3.6 The number of alleles in a sample

    • 3.7 Estimating \(\theta \)

    • 3.8 Testing for selective neutrality

  • 4 The Coalescent
    • 4.1 Who is related to whom?

    • 4.2 Genealogical trees

    • 4.3 Robustness in the coalescent

    • 4.4 Generalizations

    • 4.5 Coalescent reviews

  • 5 The Infinitely-many-sites Model
    • 5.1 Measures of diversity in a sample

    • 5.2 Pairwise difference curves

    • 5.3 The number of segregating sites

    • 5.4 The infinitely-many-sites model and the coalescent

    • 5.5 The tree structure of the infinitely-many-sites model

    • 5.6 Rooted genealogical trees

    • 5.7 Rooted genealogical tree probabilities

    • 5.8 Unrooted genealogical trees

    • 5.9 Unrooted genealogical tree probabilities

    • 5.10 A numerical example

    • 5.11 Maximum likelihood estimation

  • 6 Estimation in the Infinitely-many-sites Model
    • 6.1 Computing likelihoods

    • 6.2 Simulating likelihood surfaces

    • 6.3 Combining likelihoods

    • 6.4 Unrooted tree probabilities

    • 6.5 Methods for variable population size models

    • 6.6 More on simulating mutation models

    • 6.7 Importance sampling

    • 6.8 Choosing the weights

  • 7 Ancestral Inference in the Infinitely-many-sites Model
    • 7.1 Samples of size two

    • 7.2 No variability observed in the sample

    • 7.3 The rejection method

    • 7.4 Conditioning on the number of segregating sites

    • 7.5 An importance sampling method

    • 7.6 Modeling uncertainty in N and \(\mu \)

    • 7.7 Varying mutation rates

    • 7.8 The time to the MRCA of a population given data from a sample

    • 7.9 Using the full data

  • 8 The Age of a Unique Event Polymorphism
    • 8.1 UEP trees

    • 8.2 The distribution of \(T_\Delta \)

    • 8.3 The case \(\mu = 0\)

    • 8.4 Simulating the age of an allele

    • 8.5 Using intra-allelic variability

  • 9 Markov Chain Monte Carlo Methods
    • 9.1 K-Allele models

    • 9.2 A biomolecular sequence model

    • 9.3 A recursion for sampling probabilities

    • 9.4 Computing probabilities on trees

    • 9.5 The MCMC approach

    • 9.6 Some alternative updating methods

    • 9.7 Variable population size

    • 9.8 A Nuu Chah Nulth data set

    • 9.9 The age of a UEP

    • 9.10 A Yakima data set

  • 10 Recombination
    • 10.1 The two locus model

    • 10.2 The correlation between tree lengths

    • 10.3 The continuous recombination model

    • 10.4 Mutation in the ARG

    • 10.5 Simulating samples

    • 10.6 Linkage disequilibrium and haplotype sharing

  • 11 ABC: Approximate Bayesian Computation
    • 11.1 Rejection methods

    • 11.2 Inference in the fossil record

    • 11.3 Using summary statistics

    • 11.4 MCMC methods

    • 11.5 The genealogy of a branching process

  • 12 Afterwords
    • 12.1 The effects of selection

    • 12.2 The combinatorics connection

    • 12.3 Bugs and features

  • References

Keywords

Approximate Bayesian Computation Much Recent Common Ancestor Unrooted Tree Constant Population Size Coalescence Time 
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.

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Program in Molecular and Computational Biology, Department of Biological SciencesUniversity of Southern CaliforniaLos AngelesUSA

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