Zur Diskussion über mathematisch‐statistische Modelle

Publisher Website
Google Scholar
Abstract
Reflections on mathematic statistical population models. Mathematic statistical population models are always established for certain, clearly determined purposes. The model of Auer (1968) on the grey larch bud moth should show whether or not single “key factors” are responsible for the observed cyclic population fluctuations. The goodness of fit between calculated and observed population fluctuations is very high (r2 = 0.975). The stability of the observed gradation cycles seems not to be warranted by any single key factor, but by the cooperation of several regulating factors which, however, have different biological and thus mathematical.Varley (1970) criticized our method of mathematical calculation as leading to wrong conclusions and proposed another, much simpler mathematical proceeding. The mathematical and biological meaning of his method is analysed in some detail in the following chapters. These analyses show that Varley's method of calculation, when translated into the really executed operation with the true numerical values, is mathematically inadequate and biologically doubtful. The so called “residual mortality” has no real power of explanation and includes furthermore three single factors which are individually introduced in our model. It explains finally only: there may exist certain factors which have not been measured yet. This we knew without Varley's method. The purpose of our model is exactly contradictory to his conclusions: knowing the incompleteness of our biological data we ask: how much of the observed population dynamics can be explained by our measured biological information?