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Theses

Random Structured Phylogenies

Abstract : This thesis consists of four self-contained chapters whose motivations stem from population genetics and evolutionary biology, and related to the theory of fragmentation or coalescent processes. Chapter 2 introduces an infinite random binary tree built from a so-called coalescent point process equipped with Poissonian mutations along its branches and with a finite measure on its boundary. The allelic partition -- partition of the boundary into groups carrying the same combination of mutations -- is defined for this tree and its intensity measure is described. Chapters 3 and 4 are devoted to the study ofnested -- i.e. taking values in the space of nested pairs of partitions --coalescent and fragmentation processes, respectively. These Markov processes are analogs of Λ-coalescents and homogeneous fragmentations in a nested setting-- modeling a gene tree nested within a species tree. Nested coalescents are characterized in terms of Kingman coefficients and (possibly bivariate) coagulation measures, while nested fragmentations are similarly characterized in terms of erosion coefficients and (possibly bivariate) dislocation measures. Finally Chapter 5 gives a construction of fragmentation processes with speedmarks, which are fragmentation processes where each fragment is given a mark that speeds up or slows down its rate of fragmentation, and where the marks evolve as positive self-similar Markov processes. A Lévy-Khinchin representation of these generalized fragmentation processes is given, as well as sufficient conditions for their absorption in finite time to a frozen state,and for the genealogical tree of the process to have finite total length.
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  • HAL Id : tel-02485010, version 2

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Jean-Jil Duchamps. Random Structured Phylogenies. Probability [math.PR]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS597⟩. ⟨tel-02485010v2⟩

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