English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the spatial Lambda-Fleming-Viot process model for frequencies ofgenetic types in a population living in R^d, with two types of individuals (0and 1) and natural selection favouring individuals of type 1. We first provethat the model is well-defined and provide a measure-valued dual processencoding the locations of the `potential ancestors' of a sample taken from sucha population. We then consider two cases, one in which the dynamics of theprocess are driven by events of bounded radii and one incorporating large-scaleevents whose radii have a polynomial tail distribution. In both cases, weconsider a sequence of spatial Lambda-Fleming-Viot processes indexed by n, andwe assume that the fraction of individuals replaced during a reproduction eventand the relative frequency of events during which natural selection acts tendto 0 as n tends to infinity. We choose the decay of these parameters in such away that when reproduction is only local, the measure-valued process describingthe local frequencies of the less favoured type converges in distribution to a(measure-valued) solution to the stochastic Fisher-KPP equation in onedimension, and to a (measure-valued) solution to the deterministic Fisher-KPPequation in more than one dimension. When large-scale extinction-recolonisationevents occur, the sequence of processes converges instead to the solution tothe analogous equation in which the Laplacian is replaced by a fractionalLaplacian. We also consider the process of `potential ancestors' of a sample ofindividuals taken from these populations, which we see as a system of branchingand coalescing symmetric jump processes. We show their convergence indistribution towards a system of Brownian or stable motions which branch atsome finite rate. In one dimension, in the limit, pairs of particles alsocoalesce at a rate proportional to their collision local time.

Rescaling limits of the spatial Lambda-Fleming-Viot process with selection