Abstract
Global climate warming and conservation of biodiversity are two major issues in the 21th century. In order to quantify the change of biodiversity, various diversity measures and their sampling properties have been discussed. The traditional species diversity measures only incorporate species richness and species relative abundances without considering the differences between species. The phylogenetic diversity measures which take into account species evolutionary history and their sampling properties have also been discussed in the literature. Recently, using species characteristics or traits to quantify community diversity has become a popular research topics. The associated measures are referred to as “functional diversity index”. However, the sampling issue of functional diversity measures has not been discussed in the literature. This thesis includes two parts. The first part focuses on the estimation of the functional diversity profile on the basis of Hill numbers. Sample-sized- and coverage-based functional rarefaction and extrapolation methods are developed based on abundance data from each community. The second part of this study focuses on the extension of Good-Turing sample coverage to three sample coverage profiles and their estimators: species sample coverage profile, phylogenetic sample coverage profile, and functional sample coverage profile. Simulation results are reported to compare the proposed estimators with the conventional empirical method; the new proposed estimator exhibits substantial improvement in bias and RMSE. The proposed estimators in this study are applied to the analysis of the Brazilian rainforest data. Relevent online software via R code (iNEXT3D) is developed to implement all diversity estimators.