植物群落と等比級數法則 : 生物集団の基本構造第1報

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1) Professor MOTOMURA (1932) advocated "the law of geometrical progression of the population density". That is, the number of individuals of each species of a sample area in some animal populations approximately forms a geometrical progression, when it is arranged from commonest to rarest. The empirical formula for MOTOMURA's law is [numerical formula] where y is the number of individuals of each species and x is the rank of the species according to the number of individuals. Thereafter, many reports of Japanese zoologists were printed concerning the fitness or non-fitness for the law. A theoretical and mathematical interpretation of this law was attempted by UTIDA (1943) and MOTOMURA himself (1947) with the assumption in terms of the struggle for existence of animals in a habitat. 2) In plant populations, NUMATA (1950,1952) discussed the law from the viewpoint of the homogeneity of vegetation and estmiated that a lognormal universe (PRESTON, 1948) was approximated by the law of geometrical progression when the number of species in the modal octave and the sampling ratio or sample size were very small. SUZUKI (1951a, b) reported several cases fitting for the law and theoretical considerations for such a fitness. 3) Suppose that there are the 1st, 2nd, ......, and nth species according the rank of biotic potential of each species ; there is a bare area A ; the remaining area for the nth species is BI ; and the area occupied by the nth species against the weaker species is BIX pI. Then, [numerical formula] The cover of each species is [numerical formula] Now, assume [numerical formula] If the cover of each individuals is almost equal to Q the number of individuals of the nth species is, [numerical formula] These formulae(1)and(2)express the geometrical progression where the initial term is Ar or Ar/Q and the equal ratio is(1-p). The assumptions for this theory to be valid are that the probability of occurence of each species is equal, that there is an interspecies struggle for existence, and that the life-forms in a wide sense, of constituents, are similar. In fact, the law of geometrical progression was adequate approximately to the data only when the sample size was considerably small, namely to a very small part of a community. Its state of affairs was estimated also theoretically(NUMATA, 1952). Then a wide stand is to be the mosaic of small patches to which the law are adequate. 4) The goodness of fitting for this law to a few samples were tested by means of the Z^2-test. (Table 1). And also, an example tested by the comparison of the acutal values and the confidence intervals of theoretical values was indicated (Table 2). There are a few cases which were not adequate even to those confidence intervals(Table 3). The phytosociological meaning of such cases of the fitting or non-fitting for the law will be discussed later.
日本生態学会の論文
1954-03-25

植物群落と等比級數法則 : 生物集団の基本構造第1報

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植物群落と等比級數法則 : 生物集団の基本構造 第1報

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植物群落と等比級數法則 : 生物集団の基本構造第1報