Been reading the old distance-based density estimation literature recently. I love how they under-stated things back in the day, including article titles. For example, a 1952 paper by J.G. Skellam goes into great mathematical detail on the theory of spatial patterns and their analysis, and unless I’m mistaken, was the first to translate Poisson’s distribution into a point-to-object framework, a significant achievement. Yet it is titled simply Studies in statistical ecology: I. Spatial pattern.
Anyway, here’s an interesting comment therein regarding the power of mathematically-based theory versus empirical analyses:
“In the world of organic nature there seems to exist an uneasy balance between the factors which increase randomness and those that oppose it. This is particularly true of the distribution in space of animals and plants. The broad outlines of the pattern are determined by the main structural features of the physical environment. But even under constant conditions neither uniformity nor complete randomness prevail.
On the one hand the reproduction of organisms and the interactions between them tend to develop a closely knit pattern; whilst on the other, locomotory movements and dispersive processes bring about an ever-increasing randomness. An ecological complex of interacting species is a dynamical system, which may not only display a regular seasonal rhythm, but also appears liable by reason of its intrinsic nature to undergo oscillations (Volterra, 1931) or cyclical changes (Watt, 1947), all of which are liable to be disturbed in an irregular manner by apparently unpredictable fluctuations in weather conditions or by the spasmodic arrival of additional components to the system from outside.
It is unfortunate however that the use of probability generating functions should not have featured more prominently in the literature on these and related topics, for by means of them the subject under consideration [the distribution of individuals in census sample units] can be given greater unity and understanding. Many statistical results already deduced with much labour by the pioneers of quantitative ecology can be immediately derived by this method, and the way opened for further generalization and development.”