功能多樣性 (或特徵多樣性) 是生態學中一個快速發展的研究議題，意指物種特徵的值或範圍的多樣性，對評估生態系統及反應環境壓力或干擾是至關重要的。若功能多樣性愈高，則代表物種間的特徵相異性愈高，整體生態系統更能適應環境的變化，一般而言，我們使用物種豐富度和物種間的特徵值來量化功能多樣性。在文獻中，有許多的功能多樣性量化指標被提出。
本篇論文的研究主題分為兩部分，第一部分探討在單一群落下，將Chao等人 (2018) 提出的應用於豐富度資料的功能多樣性指標，衍生至區塊抽樣下，此方法是根據以位階 與「差異門檻」表示的屬性多樣性 (Hill 指標的衍生) 所推導。針對區塊抽樣下的功能多樣性指標，本文提出適宜的統計估計並且利用拔靴方法估計其變異數。第二部分探討在個體抽樣與區塊抽樣下，多群落功能多樣性指標的分解並利用統計推論估計之，再透過轉換至功能相異(相似)性指標。為比較本文提出之估計量與傳統最大概似估計量，本文藉由電腦模擬驗證所提出之估計量在偏差與均方根差表現均較佳。最後，透過實際資料比較本文提出之功能多樣性指標與功能相異(相似)性指標，並利用R語言與shiny套件發展互動式網頁FunD，將成果一併顯現。

Functional diversity or trait diversity refers to the diversity of the value and range of species traits, and is a rapidly growing research topic in ecology. Functional diversity is essential to assess ecosystem processes and their responses to environmental stress or disturbance. The higher value the functional diversity is, the more dissimilar the characteristics among species are, and as a result the whole ecosystem can better adapt to environmental changes. Functional diversity is typically quantified by using species abundances and species trait values. Many functional diversity measures have been proposed in the literature.
The thesis includes two parts. The first part focuses on modifying Chao et al. (2018) abundance-based functional diversity measures to replicated incidence-based data under quadrat sampling for a single ecosystem. The proposed measures and estimators are formulated based on attribute diversity (a generalization of Hill numbers) in terms of diversity order q  0 and any positive level of threshold of functional distinctiveness. Statistical estimators of the proposed incidence-based measures are proposed and their variances are estimated by a bootstrap method. The second part focuses on the functional diversity decomposition and estimation under multiple communities for both individual-based abundance data and incidence data. Functional (dis)similarity indices are derived as transformations of functional beta diversities. Simulation results are presented to compare the proposed estimators with the conventional empirical diversities; the proposed estimators exhibit substantial improvement in terms of bias and RMSE. Real data sets are used to illustrate the proposed functional diversity measures and related functional dissimilarity indices. To facilitate all computations, online software “FunD” is developed with R language and Shiny package. 

第一章 緒論 9
第二章 模型與符號介紹及相關文獻回顧 13
2.1 模型假設與符號說明 13
2.2 符號定義 13
2.2.1 單一群落符號介紹 13
2.2.2 多群落符號介紹 14
2.3 抽樣方法與模型假設 16
2.3.1豐富度資料 (Abundance data) 16
2.3.2出現與否資料 (Incidence data) 16
2.4 單一地區物種多樣性文獻回顧 17
2.4.1豐富度資料之物種數估計 17
2.4.2豐富度資料之樣本涵蓋率估計 18
2.4.3豐富度資料之Hill指標族介紹即其估計量 20
2.4.4出現與否資料之物種數估計 23
2.4.5出現與否資料之樣本涵蓋率估計 24
2.4.6出現與否資料之Hill指標族介紹即其估計量 25
2.5 單一群落拔靴方法之標準差估計 28
2.5.1豐富度資料 28
2.5.2出現與否資料 30
2.6 多群落物種多樣性文獻回顧 31
2.7 多群落拔靴方法之標準差估計 41
2.7.1豐富度資料 41
2.7.2出現與否資料 42
第三章 功能多樣性 (Functional Diversity) 相關探討 44
3.1 單一群落功能多樣性指標族之介紹與估計 46
3.1.1 豐富度資料 46
3.1.2出現與否資料 53
3.2 單一群落功能多樣性拔靴方法之標準差估計 61
3.2.1 豐富度資料 63
3.2.2 出現與否資料 64
第四章 多群落功能相異性指標族相關探討 68
4.1 功能 多樣性指標族與相異性指標族之介紹與估計 69
4.1.1 豐富度資料 69
4.1.2出現與否資料 84
4.2 多群落功能多樣性拔靴方法之標準差估計 96
第五章 模擬研究與討論 97
5.1 模擬研究設定說明 97
5.1.1 單一群落 97
5.1.2 多群落 99
5.2 單一群落功能多樣性指標族估計之模擬結果 101
5.2.1 豐富度資料 101
5.2.2 出現與否資料 110
5.3 多群落功能相異性指標族估計之模擬結果 118
5.3.1 豐富度資料 118
5.3.2 出現與否資料 126
第六章 實例分析 134
6.1 豐富度資料-義大利沙丘植物資料實例分析 134
6.1.1 義大利沙丘植物資料介紹 134
6.1.2 義大利沙丘植物實例分析 135
6.2 豐富度資料-台灣兩樣區實例分析 146
6.2.1 墾丁樣區三次調查資料介紹 147
6.2.2 福山樣區三次調查資料介紹 149
6.2.3 福山與墾丁樣區調查實例分析 153
6.3 出現與否資料-義大利沙丘植物資料實例分析 175
6.3.1 義大利沙丘植物資料介紹 175
6.3.2 義大利沙丘植物實例分析 176
6.4 出現與否資料-德國巴伐利亞森林國家公園菌類資料實例分析 184
6.4.1 德國巴伐利亞森林國家公園菌類資料介紹 185
6.4.2 砍伐林木前後的菌類資料實例分析 186
第七章 軟體開發 198
7.1 FunD 簡介 198
7.2 FunD使用步驟 199
7.3 FunD輸出結果 202
第八章 結論與後續討論 209
附錄 213
附錄A 單一群落功能多樣性指標族估計之模擬結果 213
A.1 豐富度資料 213
A.2 出現與否資料 225
附錄B 多群落功能多樣性指標族估計之模擬結果 237
B.1 豐富度資料 237
B.2 出現與否資料 255

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