Abstract

The Langevin equation is a cornerstone of statistical physics, employing Newton’s Second Law to formulate a stochastic process for modelling Brownian motion. It explains the origin of diffusion for a tracer particle in a fluid as being passively driven by molecular collisions. A century ago Pearson proposed to apply related random walk models for understanding the movements of biological organisms. However, biological agents move actively by themselves, not passively driven by the environment. This raises the question of how to properly formulate stochastic models for describing active biological movements. I will briefly review ordinary Langevin dynamics, as well as more recent active Brownian particle models. I will then show how to construct generalised stochastic Langevin equations from experimental data analysis of biological motion. As an example, I will analyse bumblebee flights tracked in a laboratory experiment with and without predation threat. Both a fixed laboratory frame and comoving coordinates will be considered for obtaining stochastic models. The comoving model features three different types of active Brownian motion as special cases. This suggests to formulate a generalised Langevin dynamics in the comoving frame for describing the movements of biological organisms. I will discuss the promise and the open problems of this Langevin-type approach, fusing movement ecology with active Brownian motion, especially in view of providing a non-Markovian framework for modelling biological motion.