[Cybernetical approach to enemy-prey systems]

The interactions between one enemy and one prey population are described by the aid of cybernetic concepts, including plants as prey.By their numerical responses the populations of enemy and prey together constitute a feedback control system (Fig.1). Both of them can be interpreted either as regulator or as controlled system. The negative feedback is made possible by limitation of the enemy's searching ability. The difference between (the logarithms of) density independent fertility and mortality of both populations can be regarded as disturbance or as command variable. The encounter of both populations has the effect of a detecting element or of an correcting element (Fig. 2).To a first approximation, both populations react like integrating elements with dead time. Their interactions in the feedback control system can be described appropriately by these means. Thus there is no need for interpreting the enemies as temporarily defective regulator.If the individual prey organisms cannot be utilized by different enemies as often as they are found, there exists a competition for prey. Its intensity depends on enemy density. In the mode of a second regulator the competition reacts negatively upon the enemy population. In the information flow diagram it can be represented by an additional element (Fig. 3). Together with the prey it composes a PI-regulator of the enemy (Fig.4).The limited feeding capacity of the enemy often causes a relative decrease of the enemy's activity with increasing prey density. This decrease can be taken into account by a further element (Fig. 5), that reacts positively upon the prey population.Considering only numerial responses the enemy-prey system is composed of two integrating elements. Consequently both densities oscillate after every change of disturbance with amplitudes that increase because of the dead time in each element. The competition for prey among enemies is probably able to damp the oscillations in certain cases. On the other hand, the relative decrease of activity caused by the limited feeding capacity favours instability. If the system is not damped sufficiently by itself quenching is possible only by the proportional effects of additional regulators.By the cybernetical approach the complex system is divided into simple components. With that cybernetics provides a model of structure which, among others, facilitates insight into kind and degree of density dependence of different factors. When the effects of the single elements are characterized by mathematical functions a dynamic model will arise.On principle the cybernetical model can be extended by adding further components.