生物多樣性是二十一世紀全球重大議題之一，亦是人類永續發展之基礎。我們在瞭解如何定義一生物多樣性的意涵後，藉由數學模型及統計架構來量化成各種指標，透過測量這些指標評估單一群落，亦或在多個群落之間作比較。在實際應用上，生物學家透過先收集樣本再計算多樣性指標，但其指標值通常受到樣本數的影響，因此，使用生態學上之稀釋及預測曲線的概念，使收集到的樣本可以稀釋到相同的樣本數，而互相客觀地比較不同群落的生物多樣性。
本論文架構在多群落下，研究Beta多樣性稀釋及預測曲線，用以比較不同地區群落間的物種組成差異程度。研究內容依抽樣方式分為個體抽樣、區塊抽樣兩個部分，分別推導Beta多樣性稀釋及預測曲線的理論值及估計式、樣本涵蓋率，並用修正拔靴法計算Beta多樣性稀釋及預測曲線估計式的標準差估計量。我們除了利用電腦模擬驗證推導結果；另外，用實例分析加以說明Beta多樣性稀釋及預測曲線的應用。

目錄
論文摘要
第一章 緒論 1
第二章 符號與模式介紹及相關文獻回顧 6
2.1 符號與模式介紹 6
2.1.1 符號介紹 6
2.1.2抽樣方式及模式 7
2.2 物種多樣性的相關文獻回顧 8
2.2.1 單一群落的物種多樣性指標 8
2.2.2 多群落的物種多樣性指標 14
2.2.3 根據Hill數值指標的不同Alpha多樣性形式 21
2.3 稀釋曲線的相關文獻回顧 23
2.4 樣本涵蓋率的相關文獻回顧 27
第三章 個體抽樣的Beta多樣性稀釋及預測曲線 30
3.1 Beta多樣性及統計模型 30
3.2 Beta多樣性的稀釋和預測曲線 31
3.2.1 Beta多樣性的稀釋曲線及其估計 31
3.2.2 Beta多樣性的預測曲線及其估計 36
3.2.3 稀釋曲線標準差估計 41
3.2.4 Beta多樣性的樣本涵蓋率稀釋曲線 43
3.3 模擬研究與討論 44
3.4 實例分析 48
第四章 區塊抽樣的Beta多樣性稀釋及預測曲線 60
4.1 Beta多樣性及統計模型 60
4.2 Beta多樣性的稀釋和預測曲線 62
4.2.1 Beta多樣性的稀釋曲線及其估計 62
4.2.2 Beta多樣性的預測曲線及其估計 67
4.2.3 稀釋曲線標準差估計 68
4.2.4 Beta多樣性的樣本涵蓋率稀釋曲線 70
4.3 模擬研究與討論 71
4.4 實例分析 74
第五章 結論與後續研究 82
附表
附表一：個體抽樣，位階q = 0的Beta多樣性稀釋曲線模擬結果 84
附表二：個體抽樣，位階q = 1的Beta多樣性稀釋曲線模擬結果 91
附表三：個體抽樣，位階q = 2的Beta多樣性稀釋曲線模擬結果 98
附表四：區塊抽樣，位階q = 0的Beta多樣性稀釋曲線模擬結果 105
附表五：區塊抽樣，位階q = 1的Beta多樣性稀釋曲線模擬結果 109
附表六：區塊抽樣，位階q = 2的Beta多樣性稀釋曲線模擬結果 113
附圖
附圖一：個體抽樣，位階q = 0的Beta多樣性稀釋曲線模擬結果 86
附圖二：個體抽樣，位階q = 1的Beta多樣性稀釋曲線模擬結果 93
附圖三：個體抽樣，位階q = 2的Beta多樣性稀釋曲線模擬結果 100
附圖四：區塊抽樣，位階q = 0的Beta多樣性稀釋曲線模擬結果 106
附圖五：區塊抽樣，位階q = 1的Beta多樣性稀釋曲線模擬結果 110
附圖六：區塊抽樣，位階q = 2的Beta多樣性稀釋曲線模擬結果 114
參考文獻 117
附錄 122

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