Abstract
When it comes to community research, ecologists often measure the similarity by utilizing a similarity index, which is categorized as incidence index or abundance index. Incidence index merely considers the number of species, lacking consideration of the impact of relative abundance. On the other hand, abundance index considers not only the number of species but also the impact of relative abundance. Therefore, this thesis puts more emphasis on the application of an abundance index, namely Bray-Curtis similarity index. Since the observed Bray-Curtis index always underestimates the true parameter especially when sample size is small, this thesis develops new estimators of the Bray-Curtis similarity index based on the abundance data and phylogenetic data. Through the computer simulation study, the proposed Bray-Curtis estimators are compared with the conventional empirical method. Simulation results reveal that - the new proposed estimators exhibit substantial improvement in bias and RMSE. This thesis also applied improved bootstrap methods for two and three communities abundance data and two communities of phylogenetic data, which decrease the overestimates of the mean of the standard deviation of estimators. The new proposed estimators are applied to several real data sets. Relevant softwareis developed to implement the proposer estimators along with other similarity indices. Real data are used for illustration.