在生態學中衡量群落間的相異性時， β 多樣性指標是最廣泛使用的相異性指標之一。為了公平地比較不同區域的 β 多樣性，本文提出 β 多樣性指標的稀釋與預測函數，將每個地區的資料標準化至相同的比較基礎。
過去的 β 多樣性稀釋與預測函數估計，是由標準化到相同個體數的 γ 多樣性（混合群落中的多樣性）與 α 多樣性（各群落的平均多樣性）相除得到，但此方法通常會有高估 β 多樣性的問題。因此本文將標準化的基礎改為樣本涵蓋率，以此改善高估問題。
本文分別對於考慮物種分類的物種多樣性、考慮物種演化歷史的系統演化多樣性與考慮物種功能特徵的功能多樣性，定義對應的 β 多樣性稀釋與預測函數，並利用統計推論得到其估計量。同時也針對出現與否資料，提出功能多樣性的稀釋與預測函數及其估計量。拔靴方法被用來評估本文提出之 β 多樣性估計量的變異性。
接著藉由電腦模擬，驗證本文建議的樣本涵蓋率基礎，比起舊有的個體數基礎，更能客觀反映 β 多樣性。並實際應用此方法於英國魚群資料以及香港螞蟻資料，展示其在真實資料上的分析結果。最後利用R語言的shiny套件將本文提出之方法製作成互動式網頁iNEXT Beta (iNterpolation and EXTrapolation of Beta diversity)以供生態學家使用。

In ecology, β diversity is one of the most common measurements of dissimilarity among assemblages. In order to fairly compare dissimilarity of different regions, this thesis introduces the rarefaction and extrapolation of β diversity to standardize the data with different sampling effort.
The past estimators of rarefaction and extrapolation of β diversity are calculated from γ diversity (i.e. diversity in the pooled assemblage) and α diversity (i.e. average diversity within each assemblage). Both γ and α diversity are standardized to the same sample size. However, this often results in an overestimated β diversity. Hence, this thesis standardizes γ and α diversity to the same sample coverage to solve the problem of overestimation.
This thesis derives rarefaction and extrapolation of β diversity for taxonomic, phylogenetic and functional level. The rarefaction and extrapolation of functional diversity based on incidence data are also proposed. The bootstrap method is used to assess the uncertainty of the proposed β diversity.
With computer simulation results, the proposed β diversity estimators are proven to be more accurate than the traditional estimators that standardize data to the same sample size. The proposed estimators are also applied to the analysis of fish data from the UK and ant data from Hong Kong. The online software iNEXT Beta (iNterpolation and EXTrapolation of Beta diversity) is developed with R language and the shiny package to implement the proposed method.

摘要
目錄
第1章 緒論 1
第2章 模型與符號介紹及相關文獻回顧 5
2.1 模型假設與符號介紹 5
2.1.1 物種多樣性符號介紹 5
2.1.2 系統演化多樣性符號介紹 8
2.1.3 功能多樣性符號介紹 10
2.2 模型假設與抽樣方法 10
2.3 單一群落物種多樣性相關文獻回顧 11
2.3.1 物種數估計 11
2.3.2 樣本涵蓋率介紹及其估計 12
2.3.3 樣本涵蓋率稀釋與預測函數介紹及其估計 14
2.3.4 Hill指標族介紹及其估計 15
2.3.5 Hill指標族稀釋與預測函數介紹及其估計 20
2.3.6 單一群落拔靴方法之標準差估計 23
2.4 單一群落系統演化多樣性相關文獻回顧 25
2.4.1 系統演化多樣性指標族介紹及其估計 26
2.4.2 系統演化多樣性指標族稀釋與預測函數介紹及其估計 29
2.4.3 單一群落拔靴演化樹生成 33
2.5 單一群落功能多樣性相關文獻回顧 33
2.5.1 個體抽樣功能多樣性指標族介紹及其估計 33
2.5.2 個體抽樣功能多樣性指標族稀釋與預測函數介紹及其估計 36
2.5.3 單一群落拔靴方法之功能距離矩陣生成－個體抽樣 38
第3章 單一群落出現與否資料功能多樣性指標族之探討 40
3.1 出現與否資料功能多樣性指標族介紹 40
3.1.1 出現與否資料功能多樣性指標族稀釋與預測函數介紹及其估計 41
3.1.2 出現與否資料功能多樣性指標族稀釋函數之估計 42
3.1.3 出現與否資料功能多樣性指標族預測函數之估計 43
3.1.4 單一群落拔靴方法之功能距離矩陣生成－出現與否資料 47
第4章 多群落β多樣性稀釋與預測函數之探討 50
4.1 物種 γ、α 多樣性稀釋與預測函數之估計 53
4.2 系統演化 γ、α 多樣性稀釋與預測函數之估計 57
4.3 功能 γ、α 多樣性稀釋與預測函數之估計 62
4.4 物種、系統演化與功能β多樣性指標族稀釋與預測函數之估計 68
4.5 多群落拔靴方法之標準差估計 70
4.5.1 物種多樣性多群落拔靴方法之標準差估計 70
4.5.2 系統演化多樣性多群落拔靴方法之標準差估計 71
4.5.3 功能多樣性多群落拔靴方法之標準差估計 72
第5章 模擬研究 73
5.1 模擬研究與討論 73
5.1.1 模擬研究設定說明 73
5.1.2 物種β多樣性稀釋與預測函數估計之模擬結果（個體抽樣） 81
5.1.3 物種β多樣性稀釋與預測函數估計之模擬結果（出現與否資料） 83
5.1.4 系統演化β多樣性稀釋與預測函數估計之模擬結果（個體抽樣） 85
5.1.5 系統演化β多樣性稀釋與預測函數估計之模擬結果（出現與否資料） 87
5.1.6 功能β多樣性稀釋與預測函數估計之模擬結果（個體抽樣） 89
5.1.7 功能β多樣性稀釋與預測函數估計之模擬結果（出現與否資料） 90
第6章 實例分析 93
6.1 英國魚群資料分析 93
6.1.1 個體抽樣資料 93
6.1.2 出現與否資料 98
6.2 香港螞蟻資料分析－以個體抽樣方法處理出現與否資料 103
6.2.1 時間相異性 104
6.2.2 空間相異性 108
第7章 軟體開發 113
第8章 結論與後續研究 121
參考文獻 122
附錄：第五章之電腦模擬實驗結果 124

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