Abstract
Based on Hill numbers and spatial data, Whittaker (1960) used multiplicative decomposition approach to partition regional diversity (gamma diversity) into two components: alpha and beta components. Generally, when there are multiple communities, gamma diversity is the diversity of the pooled community, alpha diversity is the mean diversity of individual communities, and beta diversity measures the extent of compositional difference among communities Therefore, differentiation or similarity among communities can be quantified through transforming beta diversity; the traditional widely used entropy-based Horn-similarity index is a special case. Since the observed diversity always underestimates the true diversity especially when sample size is small, Chao et al. (2013) developed a nearly unbiased estimator of within-community Shannon diversity based on Good-Turing frequency formulas. However, when there are multiple communities, the estimation of gamma Shannon has not been discussed in the literatures. A new estimator is proposed to estimate the gamma Shannon diversity based on the sampling data from each community. Through the computer simulation study, when compared with the traditional empirical method, the new proposed estimator exhibits substantial improvement in bias, RMSE and the coverage probability of 95% confidence interval. Finally, I apply the new proposed estimator and related similarity measure to the analysis of 51 soil ciliates quadrat sampling data collected by Foissner et al. (2002) from three areas in Namibia (Southwest Africa).