Skellam, 1952

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.”

Skellam, J.G. (1952). Studies in statistical ecology: I. Spatial pattern. Biometrika 39: 346-362.

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4 thoughts on “Skellam, 1952

  1. That’s one of my favorite papers; thanks for highlighting it. Here was an interesting paper describing its influence in the Bulletin of Mathematical Biology that you might find interesting, based upon the subject matter:

    Toft, C.A. and M. Mangel. 1991. From individuals to ecosystems; the papers of Skellam, Hutchinson and Lindeman. Bulletin of Mathematical Biology 53:121-134.

    http://link.springer.com/article/10.1007/BF02464426

    • Wow, I can’t believe I got an actual response to this. And with a link to a paper from a couple of former instructors no less! Thanks seeddispersal, I’m looking forward to reading that!

  2. This is slightly embarrassing–I was thinking the paper is Skellam, Biometrika, 195-ONE, not 195-TWO. Nevertheless, thank you for the paper, and I will have to read it soon. The quote you posted is cogent, and contains what I think to be the ultimate pith of ecological science. It reminded me of reading Hubbell’s monograph (also, in my view, ultimately on spatial patterns) on neutral theory for the first time, specifically akin to part of the introduction:
    “The physicist Heinz Pagels (1982) once observed that there seem to be two kinds of people in the world. There are those who seek and find deterministic order and meaning, if not purpose, in every event. And then there are those who believe events to be influenced, if not dominated, by intrinsically inscrutable, and meaningless, random chance. One of the intellectual triumphs of twentieth-century physics was to prove that both views of physical nature are simultaneously true and correct, but on very different spatial and temporal scales.”

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