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Probabilistic population genetics models for expanding populations

Abstract : This thesis focuses on the construction and study of stochastic population genetics models for expanding populations. We build different models using a concept from the theory of interacting particles systems, where empty sites are represented as occupied by particles with a specific type. These "ghost individuals" allow us to artificially keep population sizes constant, and build dual processes encoding genealogies. In our models, ghost individuals can reproduce as well in order to account for stochastic fluctuations in population sizes, but with a very strong selective disadvantage against "real" individuals.We first apply the concept of ghost individuals to a measure-valued process describing the reproduction dynamics of a population living in a continuous space. We construct the limit of the process when "selection" against ghost individuals becomes infinitely strong. The limiting process seems to be a space continuous equivalent of the Eden growth model. We study the expansion dynamics of real individuals in the limiting process, and show that the growth of the region they occupy is linear in time.We then focus on a variant of the spatially-structured Wright-Fisher model with a seed bank component and featuring frequent local extinction events. This was motivated by a question of ecological interest: understanding plant dynamics in urban tree bases. In a preliminary study on a real dataset, we show that it is necessary to account for the potential presence of a seed bank in order to answer this question. We use our variant of the Wright-Fisher model to show the existence of a critical patch extinction probability depending on seed bank parameters, above which a population expansion is not possible. We study the limit of the process under a strong selection regime, and show that it corresponds to an occupancy-based model. This limiting process belongs to a family of models widely used in metapopulation ecology.
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Submitted on : Thursday, June 16, 2022 - 10:58:47 AM
Last modification on : Friday, June 17, 2022 - 3:36:48 AM


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  • HAL Id : tel-03696751, version 1



Apolline Louvet. Probabilistic population genetics models for expanding populations. Probability [math.PR]. Institut Polytechnique de Paris, 2022. English. ⟨NNT : 2022IPPAX026⟩. ⟨tel-03696751⟩



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