Probability and Stochastic Analysis Seminar  RSS

Louis Fan 09/04/2025, 17:00 — 18:00 — Online
, University of North Carolina, USA

Conditional coalescent given the random pedigree

In theoretical population genetics, it is customary to describe gene genealogies by averaging over the pedigree (the global graph of reproductive relationships). This assumption is built into state-of-the-art statistical tools, classical work on the Kingman coalescent, and related work on multiple mergers. However, this tradition of averaging over the pedigree is questionable because there is only one population pedigree, and all genetic information is passed through this same pedigree. Here we study how the pedigree influences the genealogical relationships of a sample of gene copies at a single genetic locus. We perform this study through the lens of two different diploid exchangeable models: a Wright-Fisher model with occasional big families and a Moran model with partial selfing. For each model, we obtain a novel scaling limit for the conditional genealogy of an arbitrary sample of size n, as the population size N tends to infinity. These scaling limits retain essential information of the population pedigree. Our results offer new insight for ancestral inference and understanding of multi-locus data from populations whose single-locus genealogies are multiple merger coalescents. Joint work with F. Alberti, M. Birkner, D. Diamantidis, M. Newman, and J. Wakeley.


Except for a few of the oldest sessions these are from the Seminário de Probabilidade e Mecânica Estatística at IMPA which is co-sponsored by several institutions, in particular Instituto Superior Técnico.