by

Alf H. Øien

Abstract:

Attempts are presented of an analogue modelling of Daphnia responses to various influences and stimuli, as distribution of food and of predators. The aim with the study is to examine to what extent a statistical-mechanical approach of swarms may be useful as a tool in modelling of Daphnia behaviour. In the modelling we follow a line close to test particle studies in physical sciences. A generalised kinetic equation of what we shall call daphnicles is derived. The modelling incorporates individual characteristics of daphnicles, as position, velocity and degree of food saturation and responses daphnicles have to say food- concentration and to threat. The daphnicles we model respond to some stimuli in ordered ways and to others in stochastic ways, and the degree or strength of reactions generally depends on the density and distribution of food available, the saturation level of daphnicles and the threat level in the environment, or background, the daphnicles are living on. Some fluid equations of daphnicle swarms are subsequently derived from the basic equation, and solutions are given of the model-equations in some particular cases and show peculiarities in reactions of daphnicles to food and to threat, when these are acting alone, and in combination. The results may have some relevance to certain laboratory experiments of Daphnia behaviour.

Report no. 156, Department of Applied Mathematics, June 2001.