Mimetic gain in batesian and Müllerian mimicry.

Starting from field investigations and experiments on mimetic butterfly populations a model for two mimetic species is developed. The model comprises various features such as the growth rates and carrying capacities of the two species, their unpalatability to predators, the recruitment and the training of the predators and, most important, the similarity of the two mimetic species. The model ranges from pure Batesian to pure Müllerian mimicry over a spectrum of possible cases. The mimetic gain is introduced as the relative increase in equilibrium density in a mimetic situation as compared to a situation where mimicry is not present. The dependence of this quantity on parameters as growth rate, carrying capacity, unpalatability, and similarity is investigated using numerical methods.

Dynamic models for animal orientation.

The orientation of an animal moving in a plane towards a point-like mark is investigated. The control exerted by the optomotor (tracking) response on the motion of the animal is interpreted as an external force acting on the animal itself, which is modeled as a dipole or as a single point. The optomotor response is assumed as a rather general function of distance and angle. Differential equations governing the motion are derived and analyzed qualitatively and numerically. The role of distance-dependence and of the width of the visual field is investigated in detail and related to some typical kinds of paths in the plane, such as hitting the mark, coming close to the mark within a short distance, circular or undulating motion around the mark.