生物多樣性在生態研究與保育政策的制定上佔有重要角色。在傳統上，多樣性指標僅在探討單一群落或群落間的關係，即以單一層次的觀點來描述生態系，然而多樣性的衡量並不能僅侷限在區域性的群落中，必須整合各區域的資訊，才能了解整個生態系統的關係與狀態。現今因科技快速進步，巨量數據的時代已經來臨，因此以結構關係來衡量多樣性勢在必行，多層次架構將扮演衡量生態系統的重要角色，以宏觀的角度來建構指標，利用層次結構間來了解生態系中層次的關係與差異。
本文基於 Hill 指標族以及乘法分解的概念，加入個體數權重的資訊來建構多層次多樣性分解（hierarchical decomposition），並且定義標準化的相異性指標，來衡量層次間的差異程度。文中分為兩個部份進行討論，第一部分以物種多樣性、第二部分則是以系統演化多樣性來建立多層次架構。兩部分均介紹多層次架構、指標分解形式以及應用限制，並以統計方法來估計指標、提出利用拔靴法來估計指標標準差。經由電腦模擬，驗證本文推廣估計量與最大概似估計量的優劣，模擬結果顯示本文推廣估計量不論在偏誤（Bias）及均方根誤差（RMSE）都有較好的表現。並於兩章節後各分析一筆真實資料，介紹多層次生物多樣性分解架構的實際應用。
此外，透過 R 語言以及其網路套件 Shiny，將本文的內容編寫成簡易且方便的互動式分析網頁軟體，只須依照指示建立並上傳資料即可進行計算，方便無程式背景的使用者使用此網頁軟體進行分析。

Biodiversity measures plays a very important role in ecological research and conservation studies. Traditionally, biodiversity measures are used to quantify variability among organisms in a single community, i.e. only a single-level of ecological system is considered. However, natural systems often includes multiple-level hierarchical structure. In order to quantify diversity across different levels, diversity partitioning in multiple-level structure is needed. Nowadays, because of the rapid progress of science and technology, big data have become prevalent in biodiversity studies; most such data involve multiple-level structures. Therefore, hierarchical analyses across multiple levels is essential to understand the relationship and the differences among natural systems.
Based on Hill number and multiplicative decomposition, this thesis deals with hierarchical decomposition of species diversity and phylogenetic diversity under a specified multi-level hierarchical structure. Standardized dissimilarity indices to measure the difference among units at each level are also derived. Statistical estimation of the hierarchical diversity measures is discussed and their variances are assessed by using the Bootstrapping method. Simulation results are used to show that the proposed estimators have better performance than the maximum likelihood estimator in terms of bias and root mean square error (RMSE). Real data sets are used for illustrating practical application of the proposed hierarchical analyses and estimation.
In addition, using R language and its network package Shiny, an online software with simple interactive interface is developed to facilitate the application of the proposed estimation methods for users without R.

目錄

第一章 緒論 1
第二章 抽樣方法、模式假設、符號說明與文獻回顧 5
2.1 抽樣方法與模式假設 5
2.2 符號說明 7
2.2.1 單一群落符號 7
2.2.2 多群落符號 8
2.2.3 物種多層次分解架構符號 11
2.2.4 系統演化多層次分解架構符號 15
2.3 單一群落多樣性文獻回顧 18
2.3.1 單一群落物種多樣性 18
2.3.2 系統演化多樣性 23
2.4 多群落多樣性相關文獻回顧 28
2.4.1 多群落物種多樣性 30
2.4.2 多群落系統演化多樣性 35
第三章 物種多層次分解架構 37
3.1 分解形式與架構建立 37
3.2 結構與應用限制 45
3.3 相異性指標轉換與定義 48
3.4 物種多層次多樣性指標估計 51
3.5 標準差估計方法 58
3.5.1 拔靴母體生成 59
3.5.2 拔靴法流程介紹 62
3.6 模擬研究與討論 64
3.6.1 模擬設定說明 64
3.6.2 模擬結果 67
3.7 實例分析 68
3.7.1 哥斯大黎加熱帶雨林 69
第四章 系統演化多層次分解架構 75
4.1 分解形式與架構建立 75
4.2 結構與應用限制 82
4.3 相異性指標轉換與定義 83
4.4 物種多層次多樣性指標估計 86
4.5 標準差估計方法 94
4.5.1 拔靴母體生成 94
4.5.2 拔靴法流程 97
4.6 模擬研究與討論 98
4.6.1 模擬設定說明 98
4.6.2 模擬結果 100
4.7 實例分析 102
4.7.1 墨西哥蝙蝠資料 102
第五章 網頁開發與介紹 107
5.1 簡介 107
5.2 介面介紹與使用說明 107
5.3 介面輸出 109
第六章 結論與後續研究 112
參考文獻 114
附錄 117
附錄A 平衡架構b多樣性指標範圍之證明 117
附錄B 物種多層次架構模擬 121
附錄C 物種多層次架構模擬 133
附錄D 系統演化多層次架構模擬 145
附錄E 系統演化多層次架構模擬 157

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