Data-directed modelling of Daphnia dynamics in a long-term micro-ecosystem experiment

The micro-ecosystem under consideration consists of three compartments forming a closed chain in which water circulates. Three trophic levels are represented in different compartments: autotrophs (algae, mainly Chlorella vulgaris), herbivores (Daphnia magna) and microbial decomposers. From a 20 years experiment with this system, data has been selected for this study. The dynamics of algae and Daphnia magna in only one of the compartments were modeled by different systems of differential and difference equations. We describe the successive steps in the process of model development, and the fitting of parameters using a Nelder-Mead simplex calibration method. Identification problems were overcome by taking values for physiological parameters in agreement with the literature. It turned out that a logistic type of model gives the best result for the structured Daphnia population because of the set up of the experiment: algae grow and reproduce in the upstream compartment. For this reason well-known plant–herbivore models did not comply with the data. The results of the parameter estimation procedure are discussed. The estimated grazing rate by Daphnia was smaller than expected. Possibly the Daphnia fed also on detritus and decomposing algae which were not measured.