Acta Botanica 22. (1976)

1976 / 1-2. szám - JUHÁSZ-NAGY PÁL: Spatial dependence of plant populations. Part I.: Equivalence analysis. (An outline for a new model)

Acta Botanica Academiae Scientiarum Hungaricae, Tomus 22 (1—2), pp. 61—78 (1976) SPATIAL DEPENDENCE OF PLANT POPULATIONS PART I. EQUIVALENCE ANALYSIS (AN OUTLINE FOR A NEW MODEL) P. Juhász-Nagy D EPARTMENT OF PLANT TAXONOMY AND ECOLOGY, EÖTVÖS L. UNIVERSITY, BUDAPEST (Received February 1, 1976) Traditional terms and methods cannot cover many aspects of spatial dependence of natural populations. (Spatial dependence includes such old terms as “association between species’*, “interspecific correlation”, “sample similarity” as well.) This series of papers is aimed at presenting a number of new models which may provide a better insight into some neglected problems. Special emphasis is put on a space-dynamic approach (i.e. on some spatial processes). Our first model is concerned with a certain generalization of the attribute duality principle. 0. Primary discussion 0.1 In an excellent review, Goodall has recently summed up a huge number of studies on “sample similarity and species correlation”. This im­portant paper (Goodall, 1973) makes quite unnecessary to repeat here many established results, and makes possible to pay more attention to certain future tasks. Goodall, in one of his main concluding remarks (p. 141), wrote that “. . . there is nothing absolute about correlation between species — it is entirely context-dependent”. Indeed, after too long a period of pioneering work, it is high time to study the manyfold sources and problems of context­­dependence. This, to say the least, is not going to be an easy job. 0.2 In the first place, our terminology is quite inadequate to the com­parative work that must be performed. Even our most fundamental terms are vague and ambiguous, in praxi. 0.2.1 “Correlation”, for instance, cannot be such a central concept as it is suggested by the title and wording of Goodall’s paper. As it is well known, two random variables, X and Y, may be dependent and yet un­correlated [p(X, Y) — 0], because correlation is restricted to the linear de­pendence of X and У (cf. e.g. Feller, 1957, p. 222). This restriction has the heuristic implication that “interspecific correlation” is somehow a subcase of “association between species” (a non-parametric measure of local dependence). Association, however, has a number of serious restrictions of other types. Disregarding at the moment either the controversial usage of this term in statistics (Kendall—Stuart, 1963—67; Maxwell, 1961), or some rather special meaning attached to it (e.g. Volterra, 1926, p. 33—), we may Acta Botanica Academiae Scientiarum Hungaricae 22, 1976

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