生物多樣性在不論是生態學、遺傳學與其他相關學科上都是個關鍵且重要的概念。實際上，生物多樣性的概念橫跨了所有生態系中生物體的變異性，其中包含了從基因、個體、物種、族群、群集、生態系到地景等各種層次的生命型式，因此本質上就是一個多層次的結構，且現今因資料蒐集技術的進步，大多數生態資料會在多層次結構中的不同層次中蒐集，例如一個簡單的三層次結構就是一個整體區域下包含了多個子區域，而每個子區域下又包含了多個群落。因此整合多個層次與多個子區域之間的結構關係來衡量多樣性的方法便顯得更為重要。
本文基於Tsallis (1988) 熵指標族與Hill (1973) 指標族並分別使用加法與乘法分解的概念，以個體數為權重來建立多層次的物種alpha、beta與gamma多樣性，適用在兩種資料形態下：個體抽樣下豐富度資料與區塊抽樣下的出現與否資料，並且定義標準化的相異性指標，以便衡量子區域間或群落間的差異程度。當中利用統計方法估計多層次分解下多樣性指標與相異性指標、以拔靴法估計指標標準差。透過電腦模擬，比較本文推廣估計量與最大概似估計量的優劣，結果顯示本文推廣的估計量不論是在平均偏誤、方均根誤差皆有較佳的表現。接著將本文推廣的架構各以一筆實際資料進行分析並作為實際應用上的範例。最後，透過R語言將本文提及的內容編寫成簡易的互動式網頁，方便無程式背景的使用者分析並擷取分析結果。

Biological diversity (biodiversity) is an essential concept and plays an important role in ecology, genetics and many other disciplines. Biodiversity generally refers to the variety and variability of life at the levels of genes, individuals, species, populations, communities, landscapes, etc, and therefore is inherently under a hierarchical structure. Nowadays, because of rapid advancement of technology, collecting data becomes more convenient and faster, most biological data are typically collected at various levels of multiple-level hierarchical structures, e.g., a simplest 3-level hierarchical structure is that an region includes several subregions and each subregion includes several communities. A unifying framework for the measurement of biodiversity across hierarchical levels is thus required.
Based on two measures (Tsallis entropy and Hill number) and two types of decompositions (additive and multiplicative), this thesis presents a framework for the measurement of species alpha, beta and gamma entropies/diversities across hierarchical levels for both abundance data under individual sampling and incidence data under quadrat sampling. Standardized dissimilarity measures are also derived to quantify differences among multiple regions or communities. Statistical method is developed to estimate the hierarchical entropies/diversities and dissimilarity measures with estimated bootstrap variances. Simulation results are used to show that the proposed estimators outperform the maximum likelihood estimators in terms of bias and root mean squared error (RMSE). The unifying framework is applied to real data sets to illustrate the proposed estimators and interpret the numerical results.
Furthermore, an online application for computing the proposed measures and estimators is developed using R language and Shiny package.

目錄
第一章 緒論 1
第二章 模型與符號說明與相關文獻回顧 6
2.1抽樣方法與模式假設 6
2.1.1個體抽樣 6
2.1.2區塊抽樣 7
2.2符號說明 8
2.2.1單一群落符號 8
2.2.2多群落符號 9
2.2.3物種多層次分解架構符號 11
2.3單一群落物種多樣性文獻回顧 19
2.4多群落物種多樣性相關文獻回顧 24
2.5多層次物種多樣性相關文獻回顧 28
第三章 個體抽樣下物種多層次分解架構 36
3.1個體抽樣下的分解形式與架構 36
3.1.1物種相對豐富度的衡量 36
3.1.2物種絕對豐富度的衡量 41
3.2結構與應用限制 43
3.3相異性指標 44
3.4 乘法分解形式 46
3.4.1物種相對豐富度 46
3.4.2物種絕對豐富度 50
3.5物種多層次多樣性指標估計 55
3.5.1物種相對豐富度下的估計 55
3.5.2物種絕對豐富度下的估計 64
3.6標準差估計方法 68
3.6.1 拔靴母體生成 69
3.6.2修正拔靴法流程說明 72
3.7模擬研究與討論 74
3.7.1模擬設定 74
3.7.2模擬結果 76
3.8實例分析 79
3.8.1 法國羅亞爾河(Loire River) 79
3.8.2 方法比較 87
第四章 區塊抽樣物種多層次分解架構 89
4.1 區塊抽樣下的分解形式與架構 89
4.1.1物種相對出現次數的衡量 89
4.1.2物種絕對出現次數的衡量 91
4.2結構與應用限制 92
4.3相異性指標 92
4.4區塊抽樣資料下物種多層次多樣性指標估計 95
4.4.1物種相對出現次數下的估計 95
4.4.2物種絕對出現次數下的估計 103
4.5標準差估計方法 104
4.5.1拔靴母體生成 104
4.5.2修正拔靴法流程說明 107
4.6模擬研究與討論 108
4.6.1模擬設定 108
4.6.2模擬結果 110
4.7實例分析 113
4.7.1德國巴伐利亞森林國家公園 113
第五章 網頁開發與介紹 120
5.1 簡介 120
5.2使用說明 120
5.3輸出結果 123
第六章 結論與後續研究 128
參考文獻 130
附錄 133
附錄S1 β多樣性指標範圍證明 133
附錄S2 個體抽樣物種多層次分解模擬( B = 200, R = 200, n = 500) 144
附錄S3 個體抽樣物種多層次分解模擬( B = 200, R = 200, n = 1000) 162
附錄S4 區塊抽樣物種多層次分解模擬( B = 200, R = 200, t = 400) 180
附錄S5 區塊抽樣物種多層次分解模擬( B = 200, R = 200, t = 800) 198

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