隨著永續發展的概念抬頭，環境保育與生物多樣性的概念逐漸受到重視，為了解生態系的變化與不同生態系的比較，許多量化多樣性的指標被提出，從傳統僅考慮物種相對豐富度的物種多樣性 (species diversity) 到加入物種演化歷史的系統演化多樣性指標 (phylogenetic diversity)，都已廣為發展與應用。然而，考慮物種的特徵與特徵來量化多樣性逐漸受到重視，稱為功能多樣性指標 (functional diversity)。功能多樣性指標透過考慮物種不同特徵的方式，能夠詮釋一地區生態系統的穩定程度，功能多樣性指標越高代表物種彼此特徵的差異越大，整個地區對於外在環境的變化 (天災、人類干擾等) 有較小的影響。
本篇論文的研究主題分為兩部分，第一部分為在個體抽樣下，利用統計推論估計單一群落下功能多樣性指標族以及稀釋與預測函數。第二部分為針對臺灣三個樣區 (墾丁、福山、蓮華池) 的資料分析，其中生態學家認為梅花鹿大量入侵墾丁樣區造成原本生態系的破壞，希望可以透過物種多樣性與功能多樣性的比較找出充足的證據，以利相關單位擬定管理方案。
為比較本文提出之估計量與傳統最大概似估計量，藉由電腦模擬驗證顯示本文所提出之估計量在偏差與均方根差表現較佳。並透過R語言將兩種功能多樣性指標：FD、FAD撰寫成互動式網頁Functional Diversity-Online，以及針對臺灣樣區資料建立互動平臺Taiwan Database，使不擅於程式語言的學者也可以針對自己的資料分析。

With the surge of the concept of sustainable development, much attention has been paid to environment protection and biodiversity conservation. In order to quantify the change of biodiversity and compare the difference between two or more areas, a wide range of diversity measures has been proposed. Traditional species diversity measures only consider species relative abundances without taking the differences among species into account. Phylogenetic diversity measures take species evolutionary history and species relative abundances into account. However, species traits have been increasingly used to quantify diversity and the associated measured are called “functional diversity index”. Functional diversity index can reflect the stability of ecosystem. The higher this index is, the more difference of traits between species is, and the whole ecosystem has less effects by the change of environment.
This thesis includes two parts. The first part focuses on the estimation of the functional diversity profile on the basis of Hill numbers under a single ecosystem. The second part focuses on biodiversity data analysis of three sampling plots in Taiwan (Kenting, Fushan and Lianhuachi). An issue is that ecologists think that there exists significant change of ecosystem caused by the massive invasion of Cervus nippon taiouanus (silka deer), and hope to find sufficient evidence based on species and functional diversity index to develop proper management plan. Our statistical approach provides a resolution to this issue.
Simulation results are reported to compare the proposed estimators with the conventional empirical method; the proposed estimator exhibits substantial improvement in terms of bias and RMSE. Online software is developed via R language. An interactive platform which demonstrates the analyses of the three sampling plots in Taiwan is also developed to implement all diversity estimators for users without R backgrounds.

第一章 緒論 1
第二章 相關文獻探討 5
2.1 模型假設與符號定義 5
2.1.1符號定義 5
2.1.2抽樣方法與模型假設 6
2.2 單一地區物種多樣性文獻回顧 7
2.2.1物種數估計 7
2.2.2樣本涵蓋率估計 8
2.2.3 樣本涵蓋率稀釋與預測函數估計式 10
2.2.4 Shannon熵指標與Simpson指標 11
2.2.5 Hill指標族介紹與估計 12
2.2.6 Hill指標的稀釋與預測函數及其估計式 16
2.2.7拔靴方法 (Bootstrap) 之標準差估計與其修正 20
2.3 單一地區功能多樣性相關文獻回顧 22
2.3.1功能性指標族介紹及其估計式 22
2.3.2功能性稀釋與預測函數及其估計式 27
第三章 功能多樣性 (Functional Diversity) 相關探討 32
3.1功能多樣性指標族的介紹與估計 34
3.2 功能多樣性稀釋與預測函數介紹即其估計 42
3.3功能多樣性拔靴方法之標準差估計 47
第四章 模擬研究與討論 51
4.1模擬研究設定說明 51
4.2 Binomial近似分配假設模擬驗證 52
4.3功能多樣性 指標族估計之模擬結果 55
4.4功能多樣性 指標族估計之模擬結果 59
4.5功能多樣性指標族稀釋與外插估計之模擬結果 64
第五章 臺灣三樣區實例分析 71
5.1墾丁樣區三次調查實例分析 72
5.1.1物種多樣性墾丁樣區分析 78
5.1.2功能多樣性墾丁樣區分析 81
5.2福山樣區兩次調查實例分析 92
5.2.1物種多樣性福山樣區分析 97
5.2.2功能多樣性福山樣區分析 99
5.3蓮華池樣區一次調查實例分析 104
5.3.1一般物種多樣性蓮華池樣區分析 108
5.3.2功能多樣性蓮華池樣區分析 109
5.4三樣區多群落相異性指標比較 111
第六章 軟體開發 117
6.1.1 Functional Diversity-Online簡介 117
6.1.2 Functional Diversity-Online使用步驟 118
6.1.3 Functional Diversity-Online輸出結果 121
6.2.1 Taiwan Database簡介 125
6.2.2 Taiwan Database使用步驟 125
6.2.3 Taiwan Database輸出結果 127
第七章 結論與後續討論 130
附錄 135
附錄A：功能多樣性q指標族估計之模擬結果 135
附錄B：功能多樣性τ指標族估計之模擬結果 145

[1] Basharin, G. P. (1959). On a statistical estimate for the entropy of a sequence of independent random variables. Theory of Probability & Its Applications, 4, 333-336.
[2] Chao, A. (1984). Nonparametric estimation of the number of classes in a population. Scandinavian Journal of Statistics, 11, 265-270.
[3] Chao, A. (2005). Species estimation and applications. Encyclopedia of Statistical Sciences, 12, 7907-7916.
[4] Chao, A. and Jost, L. (2012). Coverage-based rarefaction: standardizing samples by completeness rather than by size. Ecology, 93, 2533-2547.
[5] Chao, A., Wang, Y. T. and Jost, L. (2013). Entropy and the species accumulation curve: a novel estimator of entropy via discovery rates of new species. Methods in Ecology and Evolution, 4, 1091-1110.
[6] Chao, A., Gotelli, N. G., Hsieh, T. C., Sander, E. L., Ma, K. H., Colwell, R. K. and Ellison, A. M. (2014). Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species biodiversity studies. Ecological Monographs, 84, 45-67.
[7] Chao, A. and Jost, L. (2015). Estimating diversity and entropy profiles via discovery rates of new species. Methods in Ecology and Evolution, 6, 873-882.
[8] Chao, A. (2016). Quantifying sample completeness of a biological survey: a generalization of Good-Turing’s concept of sample coverage. Under review.
[9] Chao. A., Chiu, C. H., Colwell, R. K., Chazdon, R. L. and Gotelli, N. J. (2017). Deciphering the enigma of undetected biodiversity: The Good-Turing frequency formula and its generalizations. Under revision.
[10] Chiu, C. H., Wang, Y. T., Walther, B. A. and Chao, A. (2014). An improved non-parametric lower bound of species richness via the Good-Turing frequency formulas. Biometrics, 70, 671-682.
[11] Chiu, C. H. and Chao, A. (2014). Distance-based functional diversity measures and their decomposition: a framework based on Hill numbers. PloS one, 9, e100014.
[12] Colwell, R. K., Chao, A., Gotelli, N. J., Lin, S. Y., Mao, C. X., Chazdon, R. L. and Longino, J. T. (2012). Models and estimators linking individual-based and sample-based rarefaction, extrapolation and comparison of assemblages. Journal of Plant Ecology, 5, 3–21.
[13] Efron, B. (1979). Bootstrap Methods: Another look at the jackknife. The Annals of Statistics, 1-26.
[14] Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40, 237-264.
[15] Gower, J. C. (1971). A general coefficient of similarity and some of it property. Biometrika, 27, 857-74.
[16] Hill, M. O. (1973). Diversity and evenness: A unifying notation and its consequences. Ecology, 54, 427-432.
[17] Magnago, L. F. S., Edwards, D. P., Edwards, F. A., Magrach, A., Martins, S. V. and Laurance, W. F. (2014). Functional attributes change but functional richness is unchanged after fragmentation of Brazilian Atlantic forests. Journal of ecology, 102, 475-485.
[18] Pielou, E. C. (1975). Ecology Diversity. J. Wiley and Sons, New York.
[19] Rao, C. R. (1982). Diversity and dissimilarity coefficients: a unified approach. Theoretical population biology, 21, 24-43.
[20] Shannon, C. E. (1948). The mathematical theory of communication. Bell System Technical Journal, 27, 379-423.
[21] Shen, T, J., Chao, A. and Lin, J. F. (2003). Predicting the number of new species in a further taxonomic sampling. Ecology, 84, 798-804.
[22] Simpson, E. H. (1949). Measurement of diversity. Nature, 163, 688-688.
[23] Walker B, Kinzig A & Langridge J (1999). Plant attribute diversity, resilience, and ecosystem function: The nature and significance of dominant and minor species. Ecosystems 2: 95–113.
[24] 趙蓮菊, 邱春火, 王怡婷, 謝宗震, 馬光輝 (2013). 仰觀宇宙之大, 俯察品類之盛：如何量化生物多樣性. Journal of the Chinese Statistical Association, 51, 8-53.
[25] 許曉雯 (2016). 功能多樣性曲面估計與軟體開發 趙蓮菊指導 新竹市國立清華大學統計學研究所碩士論文
[26] 王相華 (2015) 墾丁高位珊瑚礁森林之幼齡稚樹在2001至2013年間急遽減少 國家公園學報二○一五年第二十五卷第一期
[27] 墾丁高位珊瑚礁森林動態樣區樹種特徵及分布模式 林業叢刊第220號