全球環境的變遷和劣化與暖化效應造成前所未有的生物多樣性改變與全球對生物多樣性消失的關注。許多珍貴的大自然資源由於人類需求的劇增以驚人的速度被消耗，環境與生態系受到嚴重的破壞，對大多數的物種造成很大的威脅。為了讓地球的生態得以永續發展，生物多樣性數據與分析逐漸受到重視，量化多樣性的指標也相繼被提出，除了有考慮物種豐富度的「物種多樣性」以及考慮到演化歷程的「系統演化多樣性」指標之外，「功能多樣性」指標是透過生物特徵來衡量一地區或生態系受環境變化或干擾的適應能力，是近年來生態學中重視的研究議題。另一方面，現今多層次結構的資料越來越常見，以單一群落或多群落的指標已無法完善的分析多樣性，因此許多研究者以多群落中的 多樣性為概念，相繼提出多層次生物多樣性的架構與量化指標。
本文的研究主題接續林依靜碩士論文 ( 2018 ) 的功能多層次架構，以及結合程麒任碩士論文 ( 2018 ) 的功能多樣性指標估計， 推廣到功能多層次指標估計，同時也進一步推導區塊抽樣下出現與否資料 ( incidence data ) 的功能多層次分解架構和估計式，並透過電腦模擬的方式比較本文推廣的估計量與最大概似估計量在各項指標的表現，結果顯示本文推廣的估計量在平均偏誤和方均根誤差的表現上優於最大概似估計量。本文最後分析羅亞河無脊動物資料 ( abundance data ) 和台灣墾丁與福山動態樣區資料 ( incidence data ) 作為實際資料分析的示範，並藉由R語言與Shiny 新增和修改互動式網頁 hiDIP ( hierarchical DIversity Partitioning ) Online中Functional Diversity的估計功能和介面，讓使用者能以簡易的方式進行資料分析。

Global warming and environmental change/degradation have led to an unprecedented threat to the world’s biodiversity and widespread concern about the loss of biodiversity. Many precious natural resources have been consumed at an alarming rate due to the rapid increase in human activities/disturbances. The environment and ecosystem have been severely damaged, posing a great threat to most rare species. In order to achieve the sustainable development of the earth system, researchers are paying more attention to the issue of biodiversity data and relevant statistical analysis. An enormous number of diversity measures have been proposed to quantify diversity. In addition to the species/taxonomic diversity and phylogenetic diversity, functional diversity takes the difference between species traits into account and measure the capability of a region or ecosystem to adapt to environmental changes or disturbances. Functional diversity is a rapidly growing research topic in ecology recently. In addition to the commonly used data for single/multiple communities, hierarchical structure data have become more prevalent in many functional studies. Thus, many researchers have proposed hierarchical structure and measurement via the concept of diversity decomposition ( diversity).
This thesis integrates the hierarchical functional diversity structure proposed in Yi-Ching Lin’s thesis ( 2018 ) and the functional diversity estimator proposed in Qi-Ren Cheng’s thesis ( 2018 ) and develops the framework and estimator for hierarchical functional diversity. The hierarchical functional diversity structure and estimator for the incidence data under quadrat sampling are also proposed. Simulation results are reported to show that the proposed estimators outperform the maximum likelihood estimators in terms of bias and root mean squared error (RMSE). Loire River macroinvertebrate data and woody plant data of two Taiwan dynamics plots are used for illustrating the application of the proposed hierarchical functional analysis and estimation. In addition, the Functional Diversity online application hiDIP ( hierarchical Diversity Partitioning ) which is developed with R language and Shiny package is expanded and implemented to facilitate all computation for the proposed estimators and graphics.

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