Daphnicle dynamics based on kinetic theory: An analogue-modelling of swarming and behaviour of Daphnia

Abstract

Attempts are presented of an analogue modelling of Daphnia responses to various influences and stimuli, as distribution of food and of predators. An aim of the study is to examine to what extent a statistical-mechanical approach may be useful as a tool in modelling of Daphnia swarms behaviour. In the modelling we follow a line close to test particle studies in physical sciences. A generalized kinetic equation of what we shall call daphnicles is derived. The modelling incorporates individual characteristics of daphnicles, as position, velocity, degree of food saturation and responses daphnicles have to outside influences. Each daphnicle we assume responds to some stimuli in ordered ways and to others in stochastic ways, and the degree or strength of reactions depends on the density of all daphnicles, the density 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, including a food distribution equation, in some particular cases that show peculiarities in reactions of daphnicles to food, degree of saturation and to threat, when these are acting alone, and in combination. The modelling results may be compared to results of laboratory experiments of Daphnia behaviour that soon will be performed.