通常評估生物多樣性的要素之一是「某群落或地區的物種數有多少」。而如何藉由統計方法的輔助，提供一精確的物種豐富度之估計量，以便相關研究領域的學者有更詳盡的資料來做保育決策是一個很重要的課題，而本論文的研究主題主要是探討在多群落下的共同種類數估計問題。有關單一群落的種類數估計方面，此課題是生態學的傳統問題，其相關的研究也非常的熱絡，但是關於兩群落以上共同種類數的估計方法之相關研究卻是十分的缺乏。本論文致力於此方面的研究，主要是利用拉普拉斯邊界形式近似法(Laplace’s Boundary-Mode Approximations)和柯西-史瓦茲不等式(Cauchy -Schwarz Inequality)來處理共同種類數估計問題。在適當的假設條件下，提出在多項式抽樣模式下的共同種類數估計量，和其相對應的漸近標準差估計量及相關的漸近性質。

本文中所提及的多個群落是針對兩個群落以上（包含三、四、五個群落等等）的情形來討論；兩群落的共同種類數定義，是「在兩群落中都存在的共同種類數」，然而三個群落以上的共同種類數卻不像兩群落的共同種類數，那麼容易且有明確的定義。本文將根據不同的定義方法，將共同種類數分成狹義和廣義這兩種共同種類數來討論，所謂的狹義共同種類數是「在每一群落中均存在的共同種類數」，而廣義共同種類數是「只要在任意兩個或兩個以上之群落中存在的共同種類數」。在多群落的狹義共同種類數部分，分別用拉普拉斯近似法和柯西-史瓦茲不等式，提出此兩種不同方法的共同種類數估計量及其相關的偏差校正估計量，並理論推導出這些估計量的統計性質，也以電腦模擬的結果來比較本文中所提出的方法之優劣，有關標準差估計量方面，則是利用 -method來求得。而有關廣義共同種類數部分，則是利用集合論的方法且將狹義共同種類數代入，而求得廣義共同種類數估計量。有關標準差估計量方面，也是利用 -method來求得。

此外亦將文中所提出的共同種類數估計量運用至美國康乃迪克大學Chazdon教授所收集的六座熱帶雨林資料與奧地利薩爾斯堡大學Foissner教授所收集的五大區域（澳洲、南美洲、非洲、歐洲、亞洲）之原生物種，做進一步的資料分析，以佐證本文所提之方法的實際應用效果。同時亦藉由一些模擬研究來瞭解本文所提出之估計方法的表現。

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