Statistical Analysis and Stochastic Modelling of Foraging Bumblebees.

Abstract

In the analysis of movement patterns of animals, stochastic processes play an important role, providing us with a variety of tools to examine, model and simulate their behaviour. In this thesis we focus on the foraging of specific animals - bumblebees - and analyse experimental data to understand the influence of changes in the bumblebees’ environment on their search flights. Starting with a discussion of main classes of stochastic models useful for the description of foraging animals, we then look at a multitude of environmental factors influencing the dynamics of animals in their search for food. With this background we examine flight data of foraging bumblebees obtained from a laboratory experiment by stochastic analyses. The main point of interest of this analysis is the description, modelling and understanding of the data with respect to the influence of predatory threats on the bumblebee’s foraging search flights. After this detail-oriented view on interactions of bumblebees with food sources and predators in the experimental data, we develop a generalized reorientation model. By extracting the necessary information from the data, we arrive at a generalized correlated random walk foraging model for bumblebee flights, which we discuss and compare to the experimental data via simulations. We finish with a discussion of anomalous fluctuation relations and some results on spectral densities of autocorrelation functions. While this part is not directly related to the analysis of foraging, it concerns a closely related class of stochastic processes described by Langevin equations with non- trivial autocorrelation functions analyse experimental data to understand the influence of changes in the bumblebees’ environment on their search flights. Starting with a discussion of main classes of stochastic models useful for the description of foraging animals, we then look at a multitude of environmental factors influencing the dynamics of animals in their search for food. With this background we examine flight data of foraging bumblebees obtained from a laboratory experiment by stochastic analyses. The main point of interest of this analysis is the description, modelling and understanding of the data with respect to the influence of predatory threats on the bumblebee’s foraging search flights. After this detail-oriented view on interactions of bumblebees with food sources and predators in the experimental data, we develop a generalized reorientation model. By extracting the necessary information from the data, we arrive at a generalized correlated random walk foraging model for bumblebee flights, which we discuss and compare to the experimental data via simulations. We finish with a discussion of anomalous fluctuation relations and some results on spectral densities of autocorrelation functions. While this part is not directly related to the analysis of foraging, it concerns a closely related class of stochastic processes described by Langevin equations with nontrivial autocorrelation functions.