• List of notations
• Introduction
• Preliminaries
  • Background in Genetics
    • Genes, DNA, Chromosomes
    • Mutation
    • Recombination
  • Mathematical models of alleles
    • The infinitely-many-alleles model
    • The infinitely-many-sites model
  • Wright-Fisher Model
    • The simplest model
    • Wright-Fisher with mutation
    • Wright-Fisher model with selection
  • Coalescent
  • Ewens Sampling formula (without recombination)
  • Ancestral recombination graph
• On the height and the length of the Ancestral recombination Graph
  • Introduction and Preliminaries
  • Expectation of the height of ARG
  • Variance of the height of the ARG
  • Expectation of the length of the ARG
  • Variance of the length of the ARG
  • Expectation of the number of recombinations
  • Variance of the number of recombinations
  • The speed at which the ARG comes down from infinity
    • Proof of Proposition 2.8.3
    • Proof of Proposition 2.8.2
    • Proof of Theorem 2.8.1
  • Appendix
    • Proof of (2.2.3)
    • Proof of Theorem 2.3.2
    • Proof of Theorem 2.4.1
    • Proof of Theorem 2.5.1
    • Proof of Theorem 2.6.1
    • Proof of Theorem 2.7.1
• Generalized Ewens Sampling Formula (GESF)
  • Introduction and Preliminaries
  • The Model
  • A sample of size n=2
    • First method
    • The second method
  • A sample of size n=3
    • The probability that all the individuals in the sample are of the same type at both loci
    • GESF for a sample of size 3.
    • The joint law of T1L and T1R
    • The conditional law of (T2L, T2R), given (T1L, T1R)
    • Computation of the expectations given in 3.4.2 to complete the GESF
  • General case
• Recombinations and the infinitely-many-sites-model
  • The conditional law of L(1), given L(0)
    • Calculation of h0.
    • Calculation of h+.
    • Calculation of h-.
  • On the number of segregating sites
  • Appendix
    • Proof of (4.1.2)
    • E((L(0))2(L(1)-L(0))
• Bibliographie

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