Regensburg 2025 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications I

DY 4.7: Hauptvortrag

Montag, 17. März 2025, 11:30–12:00, H43

Modelling the movements of organisms: Movement ecology meets active particles and anomalous diffusion — •Rainer Klages — Centre for Complex Systems, School of Mathematical Sciences, Queen Mary University of London

Organisms living at very different spatio-temporal scales, from migrating in the microworld to foraging at the surface of the earth, typically all display random-looking movement patterns. Understanding these complex patterns by constructing mathematical models from data provides a fundamental challenge. In this talk I first review fundamental stochastic models for understanding movement data, like random walks, Langevin equations and active Brownian particles. On this basis experimental data for the movement paths of foraging sea turtles, migrating cells and bumblee flights is analysed. For all three examples generalised overdamped Langevin equations are constructed from data revealing active and anomalous diffusive properties. I then put forward a generalised underdamped Langevin equation for modelling organismic movements, which blends key ingredients of the three fields of movement ecology, active particles and anomalous diffusion. I illustrate the application of this equation for constructing a stochastic model of bumblebee flights from experimental data and outline its theoretical foundation.

Keywords: movement ecology; active particles; anomalous diffusion; Langevin equation; random walk