全球環境的變遷和劣化與暖化效應造成前所未有的生物多樣性改變與全球對生物多樣性消失的關注。許多珍貴的大自然資源由於人類需求的劇增以驚人的速度被消耗，環境與生態系受到嚴重的破壞，對大多數的物種造成很大的威脅。為了讓地球的生態得以永續發展，生物多樣性數據與分析逐漸受到重視，量化多樣性的指標也相繼被提出，除了有考慮物種豐富度的「物種多樣性」以及考慮到演化歷程的「系統演化多樣性」指標之外，「功能多樣性」指標是透過生物特徵來衡量一地區或生態系受環境變化或干擾的適應能力，是近年來生態學中重視的研究議題。另一方面，現今多層次結構的資料越來越常見，以單一群落或多群落的指標已無法完善的分析多樣性，因此許多研究者以多群落中的 多樣性為概念，相繼提出多層次生物多樣性的架構與量化指標。
本文的研究主題接續林依靜碩士論文 ( 2018 ) 的功能多層次架構，以及結合程麒任碩士論文 ( 2018 ) 的功能多樣性指標估計， 推廣到功能多層次指標估計，同時也進一步推導區塊抽樣下出現與否資料 ( incidence data ) 的功能多層次分解架構和估計式，並透過電腦模擬的方式比較本文推廣的估計量與最大概似估計量在各項指標的表現，結果顯示本文推廣的估計量在平均偏誤和方均根誤差的表現上優於最大概似估計量。本文最後分析羅亞河無脊動物資料 ( abundance data ) 和台灣墾丁與福山動態樣區資料 ( incidence data ) 作為實際資料分析的示範，並藉由R語言與Shiny 新增和修改互動式網頁 hiDIP ( hierarchical DIversity Partitioning ) Online中Functional Diversity的估計功能和介面，讓使用者能以簡易的方式進行資料分析。

Global warming and environmental change/degradation have led to an unprecedented threat to the world’s biodiversity and widespread concern about the loss of biodiversity. Many precious natural resources have been consumed at an alarming rate due to the rapid increase in human activities/disturbances. The environment and ecosystem have been severely damaged, posing a great threat to most rare species. In order to achieve the sustainable development of the earth system, researchers are paying more attention to the issue of biodiversity data and relevant statistical analysis. An enormous number of diversity measures have been proposed to quantify diversity. In addition to the species/taxonomic diversity and phylogenetic diversity, functional diversity takes the difference between species traits into account and measure the capability of a region or ecosystem to adapt to environmental changes or disturbances. Functional diversity is a rapidly growing research topic in ecology recently. In addition to the commonly used data for single/multiple communities, hierarchical structure data have become more prevalent in many functional studies. Thus, many researchers have proposed hierarchical structure and measurement via the concept of diversity decomposition ( diversity).
This thesis integrates the hierarchical functional diversity structure proposed in Yi-Ching Lin’s thesis ( 2018 ) and the functional diversity estimator proposed in Qi-Ren Cheng’s thesis ( 2018 ) and develops the framework and estimator for hierarchical functional diversity. The hierarchical functional diversity structure and estimator for the incidence data under quadrat sampling are also proposed. Simulation results are reported to show that the proposed estimators outperform the maximum likelihood estimators in terms of bias and root mean squared error (RMSE). Loire River macroinvertebrate data and woody plant data of two Taiwan dynamics plots are used for illustrating the application of the proposed hierarchical functional analysis and estimation. In addition, the Functional Diversity online application hiDIP ( hierarchical Diversity Partitioning ) which is developed with R language and Shiny package is expanded and implemented to facilitate all computation for the proposed estimators and graphics.

摘要
目錄
第一章 緒論 1
第二章 模型與相關文獻回顧 4
2.1 模式假設與符號定義 4
2.1.1 個體抽樣之符號介紹與模型假設 4
2.1.2 區塊抽樣之符號介紹與模型假設 5
2.2 單一群落多樣性符號介紹與相關文獻回顧 5
2.2.1 物種多樣性指標介紹及其估計 5
2.2.2 系統演化多樣性指標介紹及其估計 10
2.2.3 功能多樣性指標介紹及其估計 14
2.3 多群落多樣性符號介紹與相關文獻回顧 17
2.3.1物種多樣性 18
2.3.2系統演化多樣性 22
2.3.3功能多樣性 25
2.3.4 多樣性指標極大值與相異性指標 28
2.4 多層次多樣性符號介紹與相關文獻回顧 31
2.4.1多層次架構與應用限制 31
2.4.2相對豐富度與絕對豐富度衡量 33
2.4.3多層次物種多樣性符號介紹與分解形式 34
2.4.4多層次系統演化多樣性符號介紹與分解形式 40
2.4.5多層次功能多樣性符號介紹與分解形式 46
第三章 個體抽樣資料功能多層次多樣性架構與估計 52
3.1加法分解形式 52
3.1.1相對豐富度衡量 52
3.1.2 絕對豐富度衡量 56
3.2乘法分解形式 58
3.2.1 相對豐富度衡量 59
3.2.2 絕對豐富度衡量 60
3.3 相異性指標定義 62
3.3.1 相對豐富度下的相異性指標 63
3.3.2 絕對豐富度下的相異性指標 67
3.4 功能多層次多樣性的估計 70
3.4.1 相對豐富度下的衡量 70
3.4.2 相對豐富度下的衡量 85
3.5 拔靴方法與標準差估計 93
3.5.1物種相對豐富度修正估計 93
3.5.2 未觀察到物種功能距離之估計 97
3.5.3 標準差估計流程說明 100
3.6 模擬研究與討論 101
3.6.1架構與機率模型設定 101
3.6.2 模擬結果 104
3.7 實例分析 111
第四章 區塊抽樣資料功能多層次多樣性架構與估計 123
4.1加法分解形式 127
4.1.1相對豐富度衡量 127
4.1.2 絕對豐富度衡量 131
4.2乘法分解形式 133
4.2.1 相對豐富度衡量 133
4.2.2 絕對豐富度衡量 134
4.3 相異性指標定義 136
4.3.1 相對豐富度下的相異性指標 136
4.3.2 絕對豐富度下的相異性指標 139
4.4 功能多層次多樣性的估計 141
4.4.1 相對豐富度下的衡量 141
4.4.2 絕對豐富度下的衡量 156
4.5 拔靴方法與標準差估計 164
4.5.1物種相對豐富度修正估計 164
4.5.2 未觀察到物種功能距離之估計 168
4.5.3 標準差估計流程說明 171
4.6 模擬研究與討論 172
4.6.1架構與機率模型設定 172
4.6.2 模擬結果 173
4.7 實例分析 180
第五章 網頁開發與介紹 190
5.1 網頁簡介 190
5.2 使用說明 190
5.3輸出結果 194
第六章 結論與後續研究 198
參考文獻 200
附錄 202
附錄S1 個體抽樣多層次功能分解模擬 ( B = 200, R = 200, n = 400 ) 202
附錄S2區塊抽樣多層次功能分解模擬 ( B = 200, R = 200, t = 400) 238

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