Project Details
Projekt
Ancestral lineages and long-time behaviour of population models with interactions
Subject Area
Mathematics
Term
from 2012 to 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 221577488
The goal is to understand the longtime behaviour of stochastic spatial population models with interaction and the spatial embeddings of their genealogies. The paper (Birkner und Depperschmidt, 2007) treated logistic branching random walks and showed that non-trivial equilibria exist if the interaction is weak enough. We plan to generalize these results to different interactions as well as to spatial models, and to several species. Then, we want to establish `true phase transitions': there should be a critical competition parameter such that the system survives when competition is below and dies out when it is above that value.Ancestral lineages can be described as random walks in dynamic random environment, see (Birkner et al, 2013, 2015). For such processes, we investigate the following topics: the almost sure central limit theorem, the rescaling of several ancestry lines in the same environment, the invariant measure for the environment seen from the particle. Finally, we also aim at a more explicit description of the coalescence probability for coalescent walkers in the same medium which isrelated to the `effective population size': a simplified model yields a pinning model which is of independent interest.
DFG Programme
Priority Programmes
Subproject of
SPP 1590:
Probabilistic Structures in Evolution
Co-Investigator
Dr. Andrej Depperschmidt
