Spatial population models with local self-interactions


Description Phase 2

We consider spatial population models with local (self-)interactions. The interaction can be induced by a common random (spatial) environment in which the individuals live (branching random walk in random environment). It can also be given by a local feed-back mechanism which regulates an individual's offspring law depending on the configuration in a certain neighbourhood around it. These models are more realistic than classical branching random walks, where particles move and branch completely independently. In the first case, they take into account inhomogeneities in the habitat. In the second case, they describe a self-regulation of the population coming for instance from a competition for resources. They are also harder to analyse: in the latter case, they are typically not "monotone" systems, since adding additional individuals at some time point can diminish the population at a later time. We focus on (1) extinction versus survival regimes, (2) the linear speed of the front, and the corresponding fluctuations, (3) genealogies and interfaces. A common connecting tool is the study of the spatial embedding of ancestral lines. They are random walks in a dynamic random environment, and the study of such random walks has an independent interest.

Description Phase 1

We consider spatial population models with local (self-)interactions. The interaction can be either induced by a common random (spatial) environment in which the individuals live or it can be modelled explicitly by a local feed-back mechanism which regulates an individual’s offspring law depending on the configuration in a certain neighbourhood around it. These models are more realistic than classical branching random walks, where particles move and branch completely independently; they are also harder to analyse because of this lack of independence and also because they typically are not “monotone” systems, since adding additional individuals can be actually harmful for the present population.

We focus on (1) extinction versus survival regimes, (2) in an equilibrium, when including neutraltypes: growth of clusters versus local diversity, (3) front speed and fluctuations in expanding populations in a random environment. A common connecting tool is the study of the spatial embedding of ancestral lines, which are random walks in a dynamic random environment.

Preprints/Publications

Matthias Birkner, Andrej Depperschmidt, Timo Schlüter: Pair coalescence times of ancestral lineages of two-dimensional logistic branching random walks (05/2024)

Pascal Oswald: Ancestral lineages for a branching annihilating random walk (03/2024) published

Matthias Birkner, Andrej Depperschmidt, Timo Schlüter: Quenched CLT for ancestral lineages of logistic branching random walks (03/2024)

Matthias Birkner, Alice Callegaro, Jiří Černý, Nina Gantert, Pascal Oswald: Survival and complete convergence for a branching annihilating random walk (04/2023) published

Jiří Černý, Alexander Drewitz, Pascal Oswald: On the tightness of the maximum of branching Brownian motion in random environment (12/2022) published

Stein Andreas Bethuelsen, Matthias Birkner, Andrej Depperschmidt, Timo Schlüter: Local limit theorems for a directed random walk on the backbone of a supercritical oriented percolation cluster (05/2021) published

Members

  • member's portrait

    Prof. Dr. Matthias Birkner

    Johannes Gutenberg-Universität Mainz
    Principal Investigator
  • member's portrait

    Prof. Dr. Nina Jael Gantert

    Technische Universität München
    Principal Investigator
  • member's portrait

    Dr. Alice Callegaro

    Technische Universität München
    Associated Scientist
  • member's portrait

    Prof. Dr. Jiří Černý

    Universität Basel
    Associated Scientist
  • member's portrait

    B. Sc. Gideon R. Chiusole

    Technische Universität München
    Associated Scientist
  • member's portrait

    M. Sc. Eszter Couillard

    Technische Universität München
    Associated Scientist
  • member's portrait

    M. Sc. Flavio Dalessi

    Universität Basel
    Associated Scientist
  • member's portrait

    M. Sc. Jan Lukas Igelbrink

    Johannes Gutenberg-Universität Mainz
    Associated Scientist
  • member's portrait

    Dr. Pascal Oswald


    Associated Scientist
  • member's portrait

    M. Sc. Janine Piesold

    Johannes Gutenberg-Universität Mainz
    Associated Scientist

Project Related News