針對單一群落所定義的物種累積曲線(species accumulation curve，簡稱為 SAC)，描述出在樣本中期望觀察到的物種數如何隨著抽樣個體數而改變，而此主題已被許多生態學的文獻廣泛討論。本文將SAC推廣至兩群落共同種累積曲線，此參數描述出在樣本中期望觀察到的共同種數如何隨著兩群落的抽樣個體數而改變。如同兩群落的共同種數，此參數在度量兩群落之間的相似性(或相異性) 上扮演著重要的角色。另外本文也針對此參數提出了一套估計的方法。
生物多樣性包含了三個層面，分別為物種多樣性(species diversity)、系統演化多樣性(phylogenetic diverstiy)和功能多樣性(functional diversity)。共同種累積曲線僅考慮各群落中各物種的相對豐富度以及共同種的相對豐富度，為了將物種與物種之間的差異也納入考量，本文以Faith (1992)提出的PD指標(定義為連結該群落所有物種之演化樹總支脈長)為基礎將其推廣至系統演化多樣性，即共同支脈長累積曲線。此外本文還以Walker等人(1999)提出的FAD指標(定義為所有物種配對之物種距離總和)為基礎將其推廣至功能多樣性，即共同功能多樣性累積曲線。
為比較本文提出之估計量與傳統最大概似估計量，本文藉由電腦模擬的方式驗證，並發現比起傳統的方法，本文所提出的方法在偏誤、均方根誤差以及95%信賴區間涵蓋率都有明顯較佳的表現。最後本文以一筆墨西哥的葉鼻蝠資料和一筆巴西雨林的樹木資料分別展示本文估計量的實際應用。

The formulation and estimation of species accumulation curve (SAC) for a single community have been extensively discussed in ecological literature. The expected SAC describes how the expected number of observed species changes when the number of sampling individuals is increased. This thesis focuses on extending SAC to shared species accumulation curve in two communities as shared species richness plays an important role to quantify the similarity and dissimilarity among multiple communities. This thesis focuses on two communities case, an estimator for the shared species accumulation curve including rarefaction and extrapolation is proposed, that is, the focus is on how the estimated expected number of shared species changes when the number of sampling individuals changes.
Biological diversity includes three aspects: species diversity, phylogenetic diversity and functional diversity. The shared species accumulation curve only considers species abundance distributions within each community and species abundances for shared species. This thesis also extends this framework to the phylogenetic diversity, that is, shared PD accumulation curve based on the Faith’s (1992) phylogenetic diversity (the sum of all branch lengths connecting all species in an assemblage). In addition, the thesis also extends the framework to the functional diversity, that is, shared FAD accumulation curve based on the functional attributed diversity (the total species pairwise distances) defined by Walker et al. (1999).
To compare the estimator proposed in this thesis to the traditional empirical method, computer simulation results are reported, when compared with the traditional empirical method, the new proposed estimator exhibits substantial improvement in bias, RMSE and the coverage probability of 95% confidence interval. Finally, the estimators proposed in this thesis are illustrated with a dataset for Mexican Phyllostomid bat and a dataset for Brazilian rain forest trees.

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 模型假設與符號說明 5
2.1.1 符號定義 5
2.1.2 抽樣方法及模型假設 9
2.2 物種多樣性之相關文獻回顧 10
2.2.1 物種數估計 10
2.2.2 樣本涵蓋率估計 12
2.2.3 物種累積曲線估計 14
2.2.4 樣本涵蓋率累積曲線估計 14
2.2.5 兩群落共同種數估計 15
2.3 系統演化多樣性之相關文獻回顧 17
2.3.1 支脈長(Faith’s PD)估計 18
2.3.2 兩群落共同支脈長(shared PD)估計 19
2.4 功能多樣性之相關文獻回顧 21
2.4.1 功能多樣性(FAD)估計 22
2.4.2 兩群落共同功能多樣性(shared FAD)估計 23
第三章 兩群落共同種累積曲線之估計 27
3.1 兩群落共同種累積曲線之估計 27
3.1.1 兩群落共同種之稀釋曲線估計 28
3.1.2 兩群落共同種之外插曲線估計 28
3.1.3 兩群落共同種之一稀釋一外插曲線估計 32
3.2 拔靴法之標準差估計 33
3.2.1 單一群落之拔靴母體生成 34
3.2.2 兩群落之拔靴母體生成 35
3.2.3 拔靴法估計標準差之流程介紹 39
3.3 模擬研究與討論 40
3.3.1 模擬研究設定說明 40
3.3.2 兩群落共同種累積曲線估計之模擬結果 41
3.4 實例分析 44
第四章 兩群落共同支脈長累積曲線之估計 52
4.1 兩群落共同支脈長累積曲線之估計 52
4.1.1 兩群落共同支脈長之稀釋曲線估計 52
4.1.2 兩群落共同支脈長之外插曲線估計 53
4.1.3 兩群落共同支脈長之一稀釋一外插曲線估計 57
4.2 拔靴法之標準差估計 58
4.2.1 單一群落之拔靴演化樹生成 59
4.2.2 兩群落之拔靴演化樹生成 60
4.3 模擬研究與討論 62
4.3.1 模擬研究設定說明 62
4.3.2 兩群落共同支脈長累積曲線估計之模擬結果 63
4.4 實例分析 66
第五章 兩群落共同功能多樣性累積曲線之估計 73
5.1 兩群落共同功能多樣性累積曲線之估計 73
5.1.1 兩群落共同功能多樣性之稀釋曲線估計 74
5.1.2 群落共同功能多樣性之外插曲線估計 74
5.1.3 兩群落共同功能多樣性之一稀釋一外插曲線估計 77
5.2 拔靴法之標準差估計 78
5.2.1 單一群落之拔靴距離矩陣生成 78
5.2.2 兩群落之拔靴距離矩陣生成 80
5.3 模擬研究與討論 83
5.3.1 模擬研究設定說明 83
5.3.2 兩群落共同功能多樣性累積曲線估計之模擬結果 85
5.4 實例分析 88
第六章 結論與後續研究 95
參考文獻 97
附錄 100

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