Statistical ecology of spatial heterogeneity in grass Land commin

1997 Fiscal Year Final Research Report Summary

• Project/Area Number: 08640797
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: 生態
• Research Institution: Ibaraki University
• Principal Investigator: SHIOMI Masae Ibaraki Univ.Faculty Science, Prof., 理学部, 教授 (80250976)
• Co-Investigator(Kenkyū-buntansha): YAMAMURA Y. Ibaraki Univ.Faculty Science, Ass.Prof, 理学部, 助教授 (50202388) ; HORI Y. Ibaraki Univ.Faculty Science, Ass.Prof, 理学部, 助教授 (30125801)
• Project Period (FY): 1996 – 1997
• Keywords: Beta-binomial / Frequency / Grassland / Occurrence data / Spatial pattern / Power law

Research Abstract

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.