Processes in the dynamics of insect populations and their analysis by mathematical models 1, 2

The complex nature of the system of components affecting reproduction, mortality, and migration of insects has long been emphasized by Schwerdt‐feger (1941) in his original description of “das Gradocön”. Notwithstanding the large number of variable factors involved and the erratic nature of the dynamics of populations of many insects, definite patterns are repeatable and can be recognized. This confirms the conception that non‐random processes are basic to the determination of numbers in populations. In principle, the analysis of population processes proceeds along the classic paths of the natural sciences: observations, formulation of hypotheses, and testing the hypotheses by experimentation. This approach, however, meets two barriers which are inherent to the system under study: the field population of insects. Firstly, the acquisition of the observations required for formulating hypotheses is generally hampered by the complexity of the system, and secondly, if hypotheses can be formulated, their effective testing under field conditions mostly meets practical difficulties. To overcome the first barrier, mathematical models may be introduced, the structure of which mimics the natural system to be analysed. If there is agreement between the output of the model and the observations on the natural system, it can be hypothesized that the structure of the latter equals the structure of the model. This hypothesis should be tested by experimental intervention in the field system, the outcome of which is predicted by the structure and manipulation of the model. This test has to overcome the second barrier, but the practical difficulties attended with it have prevented many workers from taking this logical and final step in their research program. The problems raised here have been amplified in Klomp (1973), to which the reader is referred for the sake of brevity. Zusammenfassung Populationsdynamische Prozesse und ihre Analyse mit Hilfe mathematischer Modelle Der Analyse populationsdynamischer Prozesse stehen zwei Hindernisse entgegen: 1. Die Erlangung von Beobachtungsergebnissen wird durch die Komplexität des Systems sehr er‐schwert und 2. die Überprüfung aufgestellter Hypothesen stößt unter Freilandbedingungen auf große Schwierigkeiten. Zur Überwindung dieser Hindernisse kann die Schaffung mathe‐matischer Modelle dienen, deren Struktur jene des zu analysierenden Systems nachahmen. Die hierbei auftretenden Probleme wurden von Klomp 1973, näher behandelt.