RMKS Mainz 03.02.2023
Zeit: 15:15–18:00 Uhr
Emmanuel Schertzer (Universität Wien):
Pushed and pulled waves in population genetics
In this talk, I will present recent results motivated by recent results on the noisy F-FPP equation with
Allee effect. Numerical results and heuristics suggest the existence of an interesting
phase transition between a pulled, semi pushed and fully pushed regimes.
In order to explain those different phases, I will introduce a class of branching Brownian motions with
inhomogeneous branching rates. This class of model was recently introduced in Tourniaire (22) and can
be described as a perturbation of the celebrated model of Berestycki, Berestycki, Schweinsberg (13). I
will show the existence of a phase transition mirroring the one observed in the noisy F-KPP equation.
The proof is based on a general approach that consists in computing the “moments” of a branching
process from spinal decompositions (Foutel–Rodier, Schertzer 22).
Amaury Lambert (Collège de France und École Normale Supérieure, Paris):
Stochastic models coupling the evolution of genomes and species
Due to recombination and to hybridization between species, the genealogies of genes, even sampled from distantly related species, are usually different at different genes, and (so) distinct from the species tree. We review models coupling gene trees and species tree including the popular multispecies coalescent as well as three alternative models that our team has devised and studied: the nested coalescent, Kingman's coalescent with erosion and the gene-based diversification model, acknowledging the importance of gene flow and where gene histories shape the species tree rather than the opposite. These models are meant to pave the way for approaches of diversification using the richer signal contained in genomic evolutionary histories rather than in the mere species tree.
- Amaury Lambert, Collège de France und École Normale Supérieure, Paris
- Emmanuel Schertzer, Universität Wien
- Uni Mainz, Institut für Mathematik, Raum 05-136
- Johannes-Gutenberg-Universität Mainz, Institut für Mathematik, Staudingerweg 9, 55128 Mainz, Deutschland
- Johannes Gutenberg-Universität Mainz
Technische Universität Darmstadt, Goethe-Universität Frankfurt am Main