Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1996 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Research Abstract 
Attempts were made to determine the frequency of occurrence and the spatial pattern of the plant species composing the vegetation of a seminatural grassland, using the betabinomial distribution and power law. Surveys were carried out in grasslands with two different grazing intensities in the central part of Japan. Assuming that the occurrence of s species was observed, in a zone in each grassland, 100 quadrats with an area of 50 cm x 50 cm (Lquadrat) were used, each of which was divided into n small quadrats with an area of 25 cm x 25 cm (Squadrat). Let the overall proportion of the number of Squadrats containing species i be pi, and the parameter describing spatial heterogeneity of species i be rho i. Then the probability that species i occurs in j of n Squadrats in an Lquadrat is expressed by a betabinomial distribution (j=0,1, ...., n). A large rho i indicates a high heterogeneity. If species i occurs at a random site, the betabinomial distribution converges to a binomial d
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istribution whose parameter is rhoi. Let us consider s species in a community. The power law for species i is given, for i=1,2, ..., s, by the following equation : log [vi/n^2]=A+b log [rhoi(1rhoi)/n], where vi is the observed variance of occurrence of species i among Lquadrats, and A and B are constants. If we put yi=log [vi/n^2] and xi=log [rhoi(1rhoi)/n], the equation, in the population in statistical sense, expresses a usual simple regression as yi=alpha +betaxi +epsiloni, where epsilon i, N(0, sigma^2), and sigma^2 denotes the residual variance of the regression. If alpha>0 and beta>1, the tendency of the distribution of the whole plant community is heterog eneous ; if alpha=0 and beta=1, it is random ; and if alpha<0 and beta>1, the spatial patterns are different among species in the community. For almost all the species dominating in the grasslands, good fits to the betabinomial distribution and power law were obtained in the present surveys. Species which grow stolons, rhizomes and large tillers for propagation such as Potentilla freyniana and Hydrocotyle sibthorpioides exhibited a highly heterogeneous spatial pattern while species which propagate mainly by seeds such as Viola spp.and Polygala japonica exhibited a low heterogeneity. Less
