|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)
Attempts were made to determine the frequency of occurrence and the spatial pattern of the plant species composing the vegetation of a semi-natural grassland, using the beta-binomial 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 (L-quadrat) were used, each of which was divided into n small quadrats with an area of 25 cm x 25 cm (S-quadrat). Let the overall proportion of the number of S-quadrats 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 S-quadrats in an L-quadrat is expressed by a beta-binomial distribution (j=0,1, ...., n). A large rho i indicates a high heterogeneity. If species i occurs at a random site, the beta-binomial distribution converges to a binomial d
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(1-rhoi)/n], where vi is the observed variance of occurrence of species i among L-quadrats, and A and B are constants. If we put yi=log [vi/n^2] and xi=log [rhoi(1-rhoi)/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 beta-binomial 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.