Abstract
As more people are paying attention to the issue of environmental protection and biodiversity conservation, an enormous number of diversity measures have been proposed to quantify diversity and assess diversity change across spatial or temporal scales. In addition to the species diversity and the phylogenetic diversity, functional diversity has been increasingly used to take the difference between species traits into account. The higher the functional diversity is, the more stable the ecosystem is, and thus the whole ecosystem is less affected by the change of environment. Most functional diversity measures were derived for a single community, or multiple communities under two-level structure. Nowadays, because of the rapid advances of collecting-data technique, multi-level structures are involved in most data sets, which includes various levels of genes, individuals, species, communities, regions, landscapes, and ecosystems. Therefore, hierarchical analysis across multiple levels is essential to diversity analysis. This thesis includes two parts. The first part focuses on the comparisons between the single community functional diversity measures of Chao et al.（2018） and Gregorius & Kosman （2017）, and discusses the properties, advantages and disadvantages of each measure. The results show that the functional diversity measure of Chao et al.（2018）satisfies more good properties, and can be practically applied to a wide range of ecosystems. For the second part, based on Chao et al.’s（2018）functional diversity measure, hierarchical decomposition of functional diversity based on generalized entropies and addition decomposition is developed under a specified multi-level hierarchical structure. Standardized dissimilarity indices measuring the difference among aggregates (e.g., communities or subregions) at each level are also derived. The proposed decomposition quantifies alpha, beta and gamma diversity of each level under various diversity order q >= 0 and under varying thresholds of functional distinctiveness tau. For both parts, computer simulations are reported to show the performance of the proposed formulas; real data sets are used for illustrating practical application of the proposed hierarchical analysis. In addition, using R language and network package Shiny, an online software hiDIP Online (hierarchical Diversity Partitioning) is developed to facilitate the application of the proposed hierarchical functional analysis for users without R backgrounds.