Przegląd metod oceny typu rozkładu przestrzennego populacji roślinnych

Kwiatkowska, Anna Justyna; Symonides, Ewa

doi:ISSN 0013-2969

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Title: Przegląd metod oceny typu rozkładu przestrzennego populacji roślinnych

Abstract:

Methods for determining the type of population spatial structure belong to two main categories: methods of statistical analyses and methods of cartographic analysis. The former are an attempt to reduce empirical distribution density to the theoretical model of random distribution. Theoretical distributions have in common the assumption about independent occurrence of individuals (models of Bernoullie, Poisson and normal model) or their agglomerations (models of Cole, Thomas, Neyman and negatively binomial) in space. If in empirical studies it is only ascertained whether the species is absent or present in a determined length of series of sample areas or sectors (in point centered quarter method, Cottam and Curtis 1956) then Bernoullie’s model is used as a theoretical distribution. The probability Pi that the random variable will assume values 0, 1, 2, ... x is calculated according to equation (2), and expected theoretical numbers — as products of probability values and totals of empirical frequencies nt for the variable equal 0, 1, 2, ... x.Models of Bernoullie and Poisson are for step variable, whereas the theoretical model for continuous variable is normal distribution. Analysis of the type of distribution is connected in this case either with measurement of cover (Vasilevic 1969) or with measurement of density by means of non-surface methods (Kwiatkowska and Symonides 1978b). Empirical frequencies are compared with theoretical numbers according to generally accepted rules (Oktaba 1966).Cole’s distribution (1946) is of limited use in studies of the type of distribution of natural plant populations. Elaboration of data using this method is especially troublesome if agglomerations consist of large, varying numbers of individuals. ; Thomas’s model (1949) assumes that agglomerations of individuals are distributed at random and the number of agglomerations per unit area is consistent with numbers in Poisson’s distribution. Thus in the situation described, around paternal plants distributed at random their progeny colonize forming with each paternal plant spatially separate agglomerations. Probability P(X) of finding x individuals on the surface area is illustrated by equation (35).Neyman’s model (1939) in relation to population spatial structure assumes that: (a) individuals occur in groups distributed at random on the surface area and (b) random numbers of individuals in particular agglomerations; thus it is a form of complex Poisson’s distribution. Probability P of finding sample surface with x individuals is calculated using equation (45).It can be expected that the empirical distribution will be consistent with negatively binomial theoretical distribution if the assumptions of Bernouillie’s scheme (Platt 1974) are fulfilled except the one about constant conditions under which the experiment is being carried out. Probability P(X) of finding x individuals on sample surface in the distribution discussed is illustrated by equation (49).In all theoretical models the consistence of empirical distribution with corresponding model of theoretical distribution is checked using test X2 (3). This consistency proves about random distribution of individuals or their agglomerations only in the scale of sample surface area. In order to obtain a true spatial differentiation of population structure it is indispensable to use sample surface of different size when analysing the same object.In studies of spatial sequence of density values good results are obtained using a nonparametric series test for samples taken by means of transect method (Kwiatkowska 1972, Weber 1972).As opposed to statistical methods, for which the most correct is the random sampling scheme, cartographical methods are based on systematical arrangement of samples. Depending on the size of investigated area either the ,,lattice” method is used, where each basic unit is characterized by a determined character value, or the „grid” method (Kwiatkowska and Symonides 1978b). In the first case the place of occurrence of individuals can be shown according to the principle of topographical distribution obtaining the so-called one weight or muiti- weight pointed map (Figs. 1, 2), or according to the principle of cartogramic distribution obtaining the so-called cartogram (Fig. 3). In the grid method only chosen „points” of space forming a system of regular sexpartites, or more frequently shifted squares, are taken into consideration (Fig. 4a) and the final effect of cartographic elaboration is the so-called interpolation map (Fig. 4b). The extent to what this map is detailed depends on the density of measurement points and also on the number of intervals into which the range of variable is divided.Cartographical methods illustrate spatial relations between individuals and their agglomerations and frequently allow to estimate the type of spatial structure of population. In doubtful cases the nonparametric series test should be additionally applied.

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