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.

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