在單一地區的生態環境研究主題中，種類數與母體總數的研究是發展已久的主題。當研究地區推廣到多地區的研究之後，除了相關的種類數總和研究、共同種類數研究或特有種類數研究，還有描述兩地區生物組成是否相同的相似性指標。無論是單一地區或是多地區的生態研究，學者們都期盼藉由資料的不斷收集，能夠對研究母體或群落的數量、豐富度或者區域間的相似性能有更精確的瞭解。藉由統計方法的協助，可以提供各領域學者一個可靠且精確的參數估計方法，以便相關研究學者得以對研究主題有更深一步的認識。本論文的研究主題主要著重於區塊抽樣（quadrat sampling）在種類數估計與兩地區相似性指標的應用。在種類數估計的領域，探討區塊抽樣的樣本涵蓋種類數估計如何運用至多地區所收集的資料，提出新的模式符合多地區資料的架構，並在此架構之下，提出多地區合併種類數、共同種類數與特有種類數的樣本涵蓋估計量。在兩地區相似性指標的研究中，提出在區塊抽樣之下，描述兩地區的相似性指標。此二主題分述如下：
（一）多地區區塊抽樣的種類數估計
區塊抽樣為生態調查中一個普遍常用的抽樣方法，其方法為針對調查區域隨機抽取 個區塊，觀察物種出現在區塊的情形。若只記錄物種在區塊出現與否，則稱出現與否資料（incidence based），若記錄物種在區塊中出現的個體數，則稱豐富度資料（abundance based）。多地區的區塊抽樣則為在多個地區同時或先後利用區塊抽樣方法來調查物種在各地區出現的情形。一般方法所使用的架構（Chao, Lee, and Jeng, 1992）並無法符合多地區區塊抽樣的實際情形，因此無法處理多地區區塊抽樣的種類數估計問題。本文則利用隨機效應方法提出新的架構，利用四種隨機效應來描述物種在各地區的分佈情形，藉此新的架構來處理多地區區塊抽樣的種類數估計問題。在此隨機效應的架構之下，證明樣本涵蓋的多地區種類數總和估計與單一地區區塊抽樣的樣本涵蓋種類數估計（Chao, Lee, and Jeng, 1992）形式相同，並藉由可以處理多地區種類數總和的問題，更進一步提出多地區區塊抽樣資料中，單一地區的特有種類數估計與任意多個區域的共有種類數估計。利用所提出的多地區種類數總和估計、特定地區特有種類數估計與多地區共有種類數估計運用至奧地利薩爾斯堡大學Foissner教授所收集的一組世界各地原生纖毛類物種的資料，估計Foissner教授所收集資料的四大區域（澳洲、南美洲、非洲、歐洲）的原生物種種類數總和、各地區特有種類數以及兩兩地區的共有種類數，並利用相關的估計結果，檢定原生物種學家所爭論的原生物種分佈為共有性（ubiquity）的假設，相關檢定的結果顯示證據足以拒絕原生物種的分佈為共有性的假設。
（二）區塊抽樣的兩地區相似性指標
在兩地區的生態研究中，描述其生態的相似性指標尤其重要。一般方法著重於個體抽樣，在個體抽樣之下可以得到兩地區相似指標的估計。但是在實際的抽樣方法中，很多情形使用的抽樣方法並非個體抽樣（如本文所附之原生纖毛類物種資料的抽樣方法為區塊抽樣），因此提出區塊抽樣方法的兩地區相似性指標估計有其必要性。藉由此方法的修正可以補足兩地區相似性指標的估計在不同抽樣方法的應用。本文將以奧地利薩爾斯堡大學Foissner教授利用區塊抽樣所收集的一組世界各地原生纖毛類物種的資料來說明所提出的方法在實際領域的應用。
本論文所提出的內容除了可以運用至區塊抽樣的種類數估計與兩地區相似性指標外，相關隨機效應模式亦可以運用至封閉型重複捕取模式（closed capture-recapture model）的樣本涵蓋母體總數估計，藉此處理個體在調查區域內分佈不均的母體總數估計問題。除此之外，也可以運用至多樣本系統（multiple samples system）中，處理不同時間點或不同地區所收集的多樣本系統的總數總和估計。
除了估計量的理論導證之外，對於新模式運用在多地區區塊抽樣的種類數估計上，也利用了電腦模擬方法來模擬不同的隨機效應狀況，藉此比較各個估計量的優劣表現。同時兩地區相似性也有類似的電腦模擬部分。除此之外加上了Foissner教授所收集的資料的分析結果，解釋本文所提出的方法的實際應用，在Foissner教授所收集的資料中，本文提出的方法可以得到適當的應用。論文最後一章為結論，說明隨機效應應用在多地區區塊抽樣的使用情形與兩地區相似性指標在區塊抽樣方法的推廣。

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