生物多樣性是指基因、個體、群體、物種、群集等各種層次生物的多樣性和變化性，因此層次架構存在於生物中。生物多樣性包含了三個面向，基因 (遺傳) 多樣性、物種 (分類) 多樣性以及生態系 (功能性) 多樣性。在基因研究領域中，基因學家會使用較複雜的數學模型來表示基因演化過程，並基於選擇的基因模型，推導出其基因多樣性指標及模型參數。其中，在有限島嶼模型框架中的無限突變基因模型 (IAM-FIM) 常被廣泛使用。
在Chao等人 (2015b) 論文中提到，對偶基因在無限突變基因模型假設下，單一群落 (島嶼) 下基因多樣性指標族以及多群落 (島嶼) 下基因多樣性指標族(兩層次架構)。Gaggiotti等人 (2018) 提出了在無基因模型假設下的三層次架構(滿足整體區域包含多個區域，每個區域包含多個島嶼或是群落)基因多樣性指標族，並且基於單調性質，主張使用熵指標及其相異性指標。
本文將Chao等人 (2015b) 論文推廣至在假設IAM-FIM下，在三層次架構中，求得各層次的理論 、 和 基因多樣性熵指標及異質性指標。本文也將與Gaggiotti等人 (2018) 提出了三層次架構物種多樣性指標來比較。經由模擬後，結果顯示當一基因體演化至平衡狀態時，本文理論三層次架構基因多樣性指標接近三層次架構物種多樣性指標，驗證了可將生態多樣性指標工具應用在基因領域中。最後，分析了兩筆實際基因資料，分析理論三層次架構基因多樣性指標和三層次架構物種多樣性指標在真實基因資料的應用。
此外，透過R語言以及其套件Shiny，將本文內容撰寫成簡易且方便的互動式分析網頁軟體，只須依照本文指示即可進行資料分析，方便無程式經驗的使用者使用。

Biodiversity refers to the variety and variability of life at the levels of genes, individuals, species, populations, communities, regions, landscapes, etc, and therefore is inherently under a hierarchical structure. Biodiversity includes three aspects: genetic diversity, species (taxonomic) diversity and ecosystem (functional) diversity. In genetics, researchers often describe the process of genetic evolution by complex mathematical model, and then based on the selected model, some genetic diversity indices in terms of model parameters are derived. The most widely used model is the infinite allele model (IAM) for mutation under the finite island model (FIM) framework.
Chao et al. (2015b) derived the formulas for the expected values of various gene diversity indices under the assumption of IAM model for an isolated population and for multiple subdivided populations (i.e., two-level hierarchy). Gaggiotti et al. (2018) developed allelic diversities under a three-level hierarchy (i.e., an entire area includes several regions and each region includes several islands/communities) without using any genetic models; they advocated the use of Shannon entropy and its corresponding dissimilarity index because of their good monotonicity properties. This thesis extends Chao et al.’s formulas to three-level hierarchical structure under the IAM-FIM framework. The theoretical formulas for genetic alpha, beta and gamma diversities at each level are derived in terms of model parameters for Shannon entropy-based and hetrozygosity-based measures. The resulting formulas are also compared with the results obtained from Gaggiotti et al. (2018). Simulation results show that when a gene pool is at equilibrium, the proposed three-level theoretical formulas match well with the simulated diversities. Two real genetic data were analyzed to illustrate the application of the proposed formulas. In addition, an online software with simple interactive interface using R language and network package Shiny is developed to facilitate the computations of the proposed formulas in this paper for users without R background.

第一章 緒論 1
第二章 相關文獻回顧 1
2.1 多樣性指標相關文獻回顧 1
2.2 單一群落基因頻率分布介紹及相關文獻回顧 3
2.2.1 無限突變基因模型基因演化介紹 4
2.2.2 符號介紹 4
2.2.3 單一群落基因頻率分布介紹 4
2.2.4 單一群落基因頻率相關期望指標 5
2.3 多群落基因頻率分布介紹及相關文獻回顧 7
2.3.1 有限島嶼-無限突變基因模型基因演化介紹與假設 7
2.3.2 符號介紹 8
2.3.3 多群落基因頻率分布介紹 9
2.3.4 多群落基因相關期望指標 11
2.4 理論三層次多群落物種多樣性介紹及相關文獻回顧 15
2.4.1 理論三層次多群落架構及符號介紹 17
2.4.2 理論三層次多群落物種多樣性指標 19
第三章 三層次架構多群落(有限島嶼)基因島嶼分布架構 21
3.1 三層次有限島嶼基因模型介紹與假設 21
3.2 符號介紹 21
3.3 三層次有限島嶼基因頻率分布介紹 23
3.4 三層次有限島嶼基因相關指標 27
3.5 模擬結果與探討 31
3.6 實例分析與討論 37
3.6.1 澳洲椋鳥(Australia sturnus vulgaris) 37
3.6.2 夏威夷珊瑚礁群島魚類 (Hawaiian archipelago fish) 42
第四章 應用網頁軟體開發與介紹 48
4.1 簡介 48
4.2 介面簡介與使用解說 48
4.3 介面分析輸出 50
第五章 結論與未來研究方向 53
參考文獻 55
附錄 58
附錄A 三層次架構下，各層次基因頻率分布詳細推導 58
附錄B 三層次架構下，各層次基因頻率熵指標、異質性指標詳細推導 61
附錄C 三層次單一群落物種多樣性指標估計式 65
附錄D 三層次多群落物種多樣性指標估計式 68
附錄E 其他模擬結果 73
附錄F 澳洲椋鳥資料 86

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