Abstract
With the surge of the concept of sustainable development, much attention has been paid to environment protection and biodiversity conservation. In order to quantify the change of biodiversity and compare the difference between two or more areas, a wide range of diversity measures has been proposed. Traditional species diversity measures only consider species relative abundances without taking the differences among species into account. Phylogenetic diversity measures take species evolutionary history and species relative abundances into account. However, species traits have been increasingly used to quantify diversity and the associated measured are called “functional diversity index”. Functional diversity index can reflect the stability of ecosystem. The higher this index is, the more difference of traits between species is, and the whole ecosystem has less effects by the change of environment. This thesis includes two parts. The first part focuses on the estimation of the functional diversity profile on the basis of Hill numbers under a single ecosystem. The second part focuses on biodiversity data analysis of three sampling plots in Taiwan (Kenting, Fushan and Lianhuachi). An issue is that ecologists think that there exists significant change of ecosystem caused by the massive invasion of Cervus nippon taiouanus (silka deer), and hope to find sufficient evidence based on species and functional diversity index to develop proper management plan. Our statistical approach provides a resolution to this issue. Simulation results are reported to compare the proposed estimators with the conventional empirical method; the proposed estimator exhibits substantial improvement in terms of bias and RMSE. Online software is developed via R language. An interactive platform which demonstrates the analyses of the three sampling plots in Taiwan is also developed to implement all diversity estimators for users without R backgrounds.