一般自然資源的分配與管理需透過田野調查 (field study),用以評估
相關的生物多樣性 (biodiversity),做為決策的基礎 。

如何透過統計方法提供精確的多樣性指標估計便是本文的研究主題 。

研究主題主要分成兩大部分,第一部分為評估單一母體的多樣性指標,

主題包括 Shannon 指標與種類預測函數 。第二部分為評估兩個母體的相關指標,

主題包括共同種類數 (the number of shared species) 與重複 (overlap) 指標 。

\vspace{0.5cm}

\noindent

{\mu15 (一)、單一母體的相關主題}

\begin{itemize}

\item[\PaperPortrait] {\mb14 Shannon 指標}:\\%\scriptsize

這個指標是生態上評估生物多樣性常用的指標之一，

但是傳統所使用的估計方法忽略了未出現在樣本中的種類之影響 。

本文所提出的新估計方法結合樣本涵蓋觀念 (sample coverage) 及

Horvitz-Thompson 估計量 (Horvitz and Thompson, 1952) 來修正這個影響，

改善傳統估計方法的低估問題 。

\item[\PaperPortrait] {\mb14 種類預測函數}:\\

在這個研究主題，本文所要解決的問題是%

「利用一組基礎樣本的訊息來預測,未來若多選取一組樣本可能出現的新種類數」,

這個研究主題在評估樣本效益上是一個重要的應用 。本文主要考慮不同的抽樣模式架構下，

透過適當的假設，提出對應不同抽樣模式的估計方法 。整體而言，對於較大的預測樣本，

本文的估計方法相較於文獻回顧中的其他方法，有較佳的表現 。

對於預測樣本小於基礎樣本的情況，

本文的方法也比其他文獻回顧中的方法有較小的變異 。

\end{itemize}

\noindent

{\mu15 (二)、比較兩個母體的相關主題}

\begin{itemize}

\item[\PaperPortrait] {\mb14 共同種類數}:\\

兩個母體的比較是生態上另一個重要的問題，

古典的評估指標， Jaccard 指標,

其定義單純的只與個別母體的種類數及兩個母體的共同種類數有關 。

其中種類數估計是生態上的古典問題，相較於種類數估計方法的蓬勃發展，

文獻上有關共同種類數的估計方法明顯較少,本文因此致力於這個主題的研究 。

在適當的假設條件下，提出對應不同抽樣模式下的共同種類數估計量，

並且提供相對應的漸近標準差估計量 。

\item[\PaperPortrait] {\mb14 重複指標}:\\

相對應於 Jaccard

指標的另一類指標是除了考慮個別母體的種類數及兩個母體的共同種類數外，

並且也考慮種類相對豐富度之重複指標 。

因為一般田野調查研究中，總有某些共同種類未出現於調查結果中，

本文提出一個修正方法解決未出現種類所產生的影響，

因此可以改善重複指標的估計表現 。

\end{itemize}

本文除了理論推導所提出的估計方法外，

並且以電腦模擬比較本文的方法與傳統文獻上的其他方法 。

對於不同的研究主題，本文也附加一些適當的實例分析，

說明相關主題的實際應用 。

由於生態上的評估指標眾多，為了提供使用者一個便利的計算軟體，

本文因此發展了一個整合型的計算軟體---$\mbox{SPADE}\ll{\szero{\textregistered}}$,

內容包含(一)、種類數估計， (二)、共同種類數估計，

(三)、種類預測函數估計及(四)、多樣性指標估計 。

此軟體並將上網供自由下載使用 。

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