Joint colloquium of the probability and statistics workgroups
TU Darmstadt / Goethe-Universität Frankfurt / Gutenberg-Universität Mainz
Winter term 2022/23
Freitag, 3. Februar 2023, 15 c.t., JGU Mainz
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).
und
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.
Freitag, 13. Januar 2023, 16 s.t., Goethe-Universität Frankfurt/M.
Achtung Programmänderung!!!!
16:00 Uhr Kaffee zum Beginn
16:45 Uhr Dr. Marcel Ortgiese, University of Bath
“The contact process on tree-like graphs”
The contact process is a simple model for the spread of an infection in a structured population. I will first survey some of the recent results for the contact process when the underlying graph is either a finite or infinite random graph that is locally tree-like. The main focus of the talk will be to understand what changes when the underlying graph also evolves over time. We will look both at the case when edges update independently of the infection, but also the dependent case. In the latter case, the random graph reacts to the infection by only resampling connections to neighbours that are infected. The main question we will answer is first of all whether the contact process exhibits a phase transition. If it does, we will look at how the phase transition depends on the underlying graph dynamics.
Ort: Robert-Mayer-Str. 10, Campus Bockenheim, Frankfurt/Main, Raum 711 gr.
Wegbeschreibungen
zur Anreise an die Uni Mainz finden Sie unter https://www.mathematik.uni-mainz.de/anfahrt/,
zur Anreise an die Uni Frankfurt unter https://www.uni-frankfurt.de/38074653/campus_bockenheim und https://www.uni-frankfurt.de/38093742/Campus_Bockenheim-pdf.pdf,
zur Anreise an die TU Darmstadt unter http://www3.mathematik.tu-darmstadt.de/fb/mathe/wir-ueber-uns/adresse-und-lageplan/anreise.html
Termine in früheren Semestern finden Sie hier.
stochastik@uni-mainz.de