生態學家在做兩群落或多群落研究時，常考慮相似性指標(similarity index)，可依照考慮的資料型態分為「出現指標」(incidence index)與「豐富指標」(abundance index)。「出現指標」只考慮物種樹的訊息，而忽略了相對豐富度的影響；因此促成了第二類指標「豐富指標」的發展，此指標除了物種數之外，亦考量了物種相對豐富度的影響，其中本文著墨最多的Bray-Curtis指標便屬於此類。
對於多樣性的估計，當樣本數小時，傳統的最大概似估計法在估計Bray-Curtis相似性指標時，有嚴重低估的現象，為了改善此一問題，本文針對物種多樣性與系統演化多樣性資料提出新的估計Bray-Curtis相似性指標的方法，並藉由電腦模擬與傳統的最大概似估計法做比較，而比較結果發現，新的估計方法明顯在偏差、均方根誤差與最大概似估計法相比都有較良好的表現。
除此之外，本文也針對物種多樣性兩群落的拔靴法做修正，改善了過去平均估計標準差高估樣本標準差的情況，並用類似的方法建構出物種多樣性下三群落的拔靴法，以及系統演化多樣性資料下兩群落的拔靴法，用上述的拔靴法架構藉此求得各估計量所對應的估計標準差，而不論是哪一種拔靴法架構，其所得之估計標準差都會與樣本標準差相去不遠。
此外，分別將物種多樣性與系統演化多樣性資料的新估計法應用到台灣三溪河口鳥類觀察資料，以及棲息於四種不同區域的蝙蝠資料，觀察新估計法在真實資料上的應用。
最後將物種多樣性下常用的相似性指標統整在一起發展一套線上程式，並選一個原始雨林所收集的樹冠資料為範例做線上程式的使用說明。

When it comes to community research, ecologists often measure the similarity by utilizing a similarity index, which is categorized as incidence index or abundance index. Incidence index merely considers the number of species, lacking consideration of the impact of relative abundance. On the other hand, abundance index considers not only the number of species but also the impact of relative abundance. Therefore, this thesis puts more emphasis on the application of an abundance index, namely Bray-Curtis similarity index.
Since the observed Bray-Curtis index always underestimates the true parameter especially when sample size is small, this thesis develops new estimators of the Bray-Curtis similarity index based on the abundance data and phylogenetic data. Through the computer simulation study, the proposed Bray-Curtis estimators are compared with the conventional empirical method. Simulation results reveal that - the new proposed estimators exhibit substantial improvement in bias and RMSE.
This thesis also applied improved bootstrap methods for two and three communities abundance data and two communities of phylogenetic data, which decrease the overestimates of the mean of the standard deviation of estimators.
The new proposed estimators are applied to several real data sets. Relevant softwareis developed to implement the proposer estimators along with other similarity indices. Real data are used for illustration.

第一章 緒論 1
第二章 模型符號介紹及相關文獻回顧 5
2.1 符號說明 5
2.1.1 物種多樣性符號說明 5
2.1.2 系統演化多樣性符號說明 7
2.2 物種多樣性相關文獻回顧 8
2.2.1 物種數下界估計 8
2.2.2 多群落共同種下界估計 9
2.2.3 樣本涵蓋率 (Sample Coverage) 12
2.2.4 單群落拔靴 14
2.3 系統演化多樣性相關文獻回顧 16
2.3.1 未觀察到節點之支脈長下界估計 17
2.3.2 兩群落共同節點之支脈長下界估計 18
2.3.3 單群落拔靴 20
第三章 物種多樣性Bray-Curtis指標之探討 22
3.1 兩群落的 多樣性指標 22
3.1.1 出現指標 23
3.1.2 豐富指標 24
3.1.3 相似指標與 多樣性指標族的關係 29
3.2 多群落Bray-Curtis相似性指標 30
3.2.1 多群落Bray-Curtis指標估計式推導 30
3.2.2 兩群落Bray-Curtis指標估計式推導 33
3.3 拔靴法之標準差估計與其修正 35
3.3.1 兩群落拔靴法介紹與修正 35
3.3.2 三群落拔靴法介紹 42
3.3.3 拔靴估計變異數流程介紹 55
3.4 Bray-Curtis指標電腦模擬研究與討論 56
3.4.1 模擬條件與結構介紹 56
3.4.2 模擬結果中的符號定義 58
3.4.3 兩群落Bray-Curtis指標表現情形 58
3.4.4 三群落Bray-Curtis指標表現情形 61
3.5 實例分析 63
3.5.1 資料介紹 63
3.5.2 資料分析 64
第四章 系統演化多樣性Bray-Curtis指標之探討 68
4.1 兩群落Bray-Curtis指標估計式推導 68
4.2兩群落拔靴法之標準差估計 71
4.2.1拔靴法介紹 71
4.2.2拔靴法估計變異數流程介紹 75
4.3 Bray-Curtis指標電腦模擬研究與討論 76
4.3.1 模擬條件與架構介紹與模擬演化樹生成 76
4.3.2 模擬結果中的符號定義 77
4.3.3 Bray-Curtis指標表現情形 77
4.4實例分析 80
4.4.1 資料介紹 80
4.4.2 資料分析 80
第五章 軟體開發 84
5.1 研究動機 84
5.2 軟體使用說明 84
5.3 範本資料實例分析 86
5.3.1 資料介紹 86
5.3.2 程式輸出結果 86
5.3.3 輸出結果解釋 88
第六章 結論與後續研究 91
參考文獻 93
附錄(模擬試驗) 96
附錄A 相同權重下兩群落Bray-Curtis指標表現 96
附錄B 不同權重下兩群落Bray-Curtis指標表現 100
附錄C 相同權重下三群落Bray-Curtis指標表現 104
附錄D 不同權重下三群落Bray-Curtis指標表現 118
附錄E 系統演化下相同權重兩群落Bray-Curtis指標表現 131
附錄F 系統演化下不同權重兩群落Bray-Curtis指標表現 135

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