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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process in a long time scale when the population size grows to \(+\infty \) and the mutation probability decreases to 0. We prove the convergence towards a jump process that jumps in the infinite dimensional space containing the monomorphic stable spatial distributions. The proof requires specific studies of the microscopic model. First, we study the extinction time of the branching diffusion processes that approximate small size populations. Then, we examine the upper bound of large deviation principle around the deterministic large population limit of the microscopic process. Finally, we find a lower bound on the exit time of a neighborhood of a stationary spatial distribution.

Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence