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The spatial structure of genetic diversity under natural selection and in heterogeneous environments

Abstract : This thesis deals with the spatial structure of genetic diversity. We first study a measure-valued process describing the evolution of the genetic composition of a population subject to natural selection. We show that this process satisfies a central limit theorem and that its fluctuations are given by the solution to a stochastic partial differential equation. We then use this result to obtain an estimate of the drift load in spatially structured populations.Next we investigate the genetic composition of a populations whose individuals move more freely in one part of space than in the other (a situation called dispersal heterogeneity). We show in this case the convergence of allele frequencies via the convergence of ancestral lineages to a system of skew Brownian motions.We then detail the effect of a barrier to gene flow dividing the habitat of a population. We show that ancestral lineages follow partially reflected Brownian motions, of whom we give several constructions.To apply these results, we adapt a method for demographic inference to the setting of dispersal heterogeneity. This method makes use of long blocks of genome along which pairs of individuals share a common ancestry, and allows to estimate several demographic parameters when they vary accross space. To conclude, we demonstrate the accuracy of our method on simulated datasets.
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Submitted on : Monday, January 15, 2018 - 9:25:06 PM
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  • HAL Id : tel-01684947, version 1


Raphael Forien. The spatial structure of genetic diversity under natural selection and in heterogeneous environments. Probability [math.PR]. Université Paris Saclay (COmUE), 2017. English. ⟨NNT : 2017SACLX082⟩. ⟨tel-01684947⟩



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