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 study a one-dimensional spatial population model where the populationsizes at each site are chosen according to a translation invariant and ergodicdistribution and are uniformly bounded away from 0 and infinity. We supposethat the frequencies of a particular genetic type in the colonies evolveaccording to a system of interacting diffusions, following the stepping stonemodel of Kimura. We show that, over large spatial and temporal scales, thismodel behaves like the solution to a stochastic heat equation withWright-Fisher noise with constant coefficients. These coefficients are theeffective diffusion rate of genes within the population and the effective localpopulation density. We find that, in our model, the local heterogeneity leadsto a slower effective diffusion rate and a larger effective population densitythan in a uniform population. Our proof relies on duality techniques, aninvariance principle for reversible random walks in a random environment and aconvergence result for a system of coalescing random walks in a randomenvironment.

The stepping stone model in a random environment and the effect of local heterogneities on isolation by distance patterns