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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider a continuous population whose dynamics is described by thestandard stationary Fleming-Viot process, so that the genealogy of $n$uniformly sampled individuals is distributed as the Kingman $n$-coalescent. Inthis note, we study some genealogical properties of this population when thesample is conditioned to fall entirely into a subpopulation with most recentcommon ancestor (MRCA) shorter than $\varepsilon$. First, using the combrepresentation of the total genealogy (Lambert & Uribe Bravo 2016), we showthat the genealogy of the descendance of the MRCA of the sample on thetimescale $\varepsilon$ converges as $\varepsilon\to 0$. The limit is theso-called Brownian coalescent point process (CPP) stopped at an independentGamma random variable with parameter $n$, which can be seen as the genealogy ata large time of the total population of a rescaled critical birth-deathprocess, biased by the $n$-th power of its size. Secondly, we show that in thislimit the coalescence times of the $n$ sampled individuals are i.i.d. uniformrandom variables in $(0,1)$. These results provide a coupling between twostandard models for the genealogy of a random exchangeable population: theKingman coalescent and the Brownian CPP.

Recovering the Brownian Coalescent Point Process from the Kingman Coalescent by Conditional Sampling