Dispersal heterogeneity in the spatial Λ-Fleming-Viot process

Abstract : We study the evolution of gene frequencies in a spatially distributed population when the dispersal of individuals is not uniform in space. We adapt the spatial Λ-Fleming-Viot process to this setting and consider that individuals spread their offspring farther from themselves at each generation in one halfspace than in the other. We study the large scale behaviour of this process and show that the motion of ancestral lineages is asymptotically close to a family of skew Brownian motions which coalesce upon meeting in one dimension, but never meet in higher dimension. This leads to a generalization of a result due to Nagylaki on the scaling limits of the gene frequencies: the non-uniform dispersal causes a discontinuity in the slope of the gene frequencies but the gene frequencies themselves are continuous across the interface.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01612032
Contributeur : Raphaël Forien <>
Soumis le : jeudi 2 novembre 2017 - 10:59:14
Dernière modification le : jeudi 10 mai 2018 - 02:05:36
Document(s) archivé(s) le : samedi 3 février 2018 - 12:19:41

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dispersal_heterogeneity.pdf
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  • HAL Id : hal-01612032, version 1

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Raphaël Forien. Dispersal heterogeneity in the spatial Λ-Fleming-Viot process. 2017. 〈hal-01612032〉

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