生態學家探討多群落生物多樣性研究時，常常會考慮各種相似(相異)性指標來探討群落間的相似(相異)性，β多樣性指標則是最常被用來討論群落之間的相似(相異)性指標之一。一般的β多樣性指標僅考慮各群落中各物種的相對豐富度，為了將物種與物種之間的差異納入考量，本文也將討論以考慮物種間的演化歷史的系統演化β多樣性指標族之相關議題。
傳統的最大概似估計法在估計物種和系統演化β多樣性指標族常常會有高估的情況產生。為了改善此問題，本文利用分別估計γ和α多樣性指標族提出了此兩指標族新的估計方法，使得其高估的情況有所改善。此外，為了將各地區的數據標準化到相同的取樣基準來進行比較，本文提出物種與系統演化β多樣性指標族之稀釋與預測函數，並且利用統計推論提出此兩指標族之稀釋與預測函數的估計量。
為比較本文提出的估計方法與傳統的最大概似估計量，本文藉由電腦模擬進行驗證，結果顯示本文建議的估計量不管在平均偏誤、樣本均方根誤差皆有較佳的表現，可以驗證本文提出的估計方法為可靠的估計。最後利用哥斯大黎加雨林和義大利沙丘植披資料進行實例分析並分別展示本文提出之估計量在真實資料上的實際應用，並透過R語言將本文所提及的系統演化多樣性指標寫成互動式網頁PhD Online。

When there are multiple communities, ecologists often measure similarity or dissimilarity among communities by utilizing various similarity or dissimilarity measures. Beta diversity quantifies dissimilarity among communities. Species beta diversity only considers species relative abundances. In order to take species evolutionary history into account, this thesis also consider phylogenetic beta diversity.
Since the observed species and phylogenetic beta diversity always overestimates the theoretical true value, this thesis develops new estimators by estimating species and phylogenetic gamma and alpha diversity respectively. On the other hand, in order to compare dissimilarity based on the different sampling effort, the thesis derives both theoretical formulas and analytic estimators for rarefaction and extrapolation of species and phylogenetic beta diversity.
In order to compare the proposed new beta diversity estimators with traditional empirical method, computer simulation results are reported. The proposed estimators exhibit substantial improvement in terms of bias and RMSE. The proposed estimators are also applied to the analysis of rain forest data of Costa Rica, and to Italian dunes data. Online software Phylogenetic Diversity (PhD Online) is developed to implement all proposed measures and estimators.

第一章 緒論 1
第二章 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 單一群落符號介紹 5
2.1.2多群落符號介紹 6
2.1.3 模型假設與抽樣方法 8
2.2 單一群落物種多樣性相關文獻回顧 11
2.2.1 物種數估計 11
2.2.2 樣本涵蓋率介紹及其估計 12
2.2.3 樣本涵蓋率稀釋與預測函數介紹及其估計 13
2.2.4 Hill指標族介紹及其估計量 14
2.2.5 Hill指標族稀釋與預測函數介紹及其估計 17
2.2.6 單一群落拔靴方法之標準差估計 21
2.3單一群落系統演化多樣性相關文獻回顧 24
2.3.1 系統演化指標族介紹及其估計 24
2.3.2 系統演化指標族稀釋與預測函數介紹及其估計 28
2.3.3 單一群落拔靴演化樹生成 32
第三章 多群落物種β多樣性指標族之探討 34
3.1 物種β多樣性指標族介紹及其估計 34
3.2 物種β多樣性指標族稀釋與預測函數介紹及其估計 43
3.2.1 物種β多樣性指標族稀釋函數之估計 45
3.2.2 物種β多樣性指標族預測函數之估計 49
3.3 多群落拔靴方法之標準差估計 53
3.3.1 多群落拔靴方法之標準差估計 53
3.3.2 拔靴法估計標準差之流程介紹 55
3.4 模擬研究與討論 56
3.4.1 模擬研究設定說明 57
3.4.2 物種β多樣性指標族估計之模擬結果 60
3.4.3 物種β多樣性稀釋與預測函數之模擬結果 62
第四章 多群落系統演化β多樣性指標族之探討 66
4.1 系統演化β多樣性指標族介紹及其估計 66
4.2 系統演化β多樣性指標族稀釋與預測函數 73
4.2.1 系統演化β多樣性指標族稀釋函數之估計 75
4.2.2 系統演化β多樣性指標族預測函數之估計 78
4.3 多群落拔靴演化樹生成 82
4.4 模擬研究與討論 84
4.4.1 模擬研究設定說明 84
4.4.2 系統演化β多樣性指標族估計之模擬結果 85
4.4.3 系統演化β多樣性稀釋與預測函數之模擬結果 87
第五章 實例分析 91
5.1 哥斯大黎加雨林資料分析 91
5.2 義大利沙丘植物資料分析 97
第六章 軟體開發 108
6.1 簡介 108
6.2 使用步驟 109
6.3 輸出結果 113
第七章 結論與後續研究 118
參考文獻 120
附錄 122
附錄A 物種β多樣性指標族估計之模擬研究 122
附錄B 物種β多樣性的稀釋與預測函數估計之模擬研究 134
附錄C系統演化β多樣性的指標族估計之模擬研究 146
附錄D系統演化β多樣性的稀釋與預測函數估計之模擬研究 158

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