一般野外調查可分為歸還及不歸還抽樣模式，過去的文獻主要都是架
構在歸還取樣模式下估計群落的種類數，對於不歸還取樣模式下之種
類數估計文獻較少且估計亦較複雜。如何透過統計方法，提供不歸還
取樣模式下之生物多樣性估計便是本文的研究主題。本論文主要分成
兩大部分，第一部份為單一群落之多樣性探討，主題包括種類數、樣
本數及種類預測函數估計。第二部分為多群落之多樣性探討，主題包
含二群及三群落以上之共同種類數估計。
（一） 單一群落的多樣性探討
種類數估計
種類數是單一群落最直覺的多樣性指標，過去文獻主要是架
構在歸還取樣模式下進行估計，對於不歸還抽樣模式下之文
獻則並不多，並且估計量也較複雜。本文主要是利用科西-史
瓦滋不等式，提出不歸還取樣模式下之種類數估計及其變異
數估計，此估計量形式簡潔可更易於生態學家所使用。
樣本數估計
樣本數估計一直是生態學家所感興趣的問題，大多數的統計
方法只求得了種類數的估計及變異數，但極少指出需要再抽
多少的樣本才能看到原先樣本所估計的種類數。關於此類的
問題相關文獻並不多，本文則是架構在不歸還取樣模式下，
提供樣本數之估計量及其變異數估計。
種類預測函數估計
種類預測函數可評估再次取樣之效益，主要問題是利用第一
次基礎樣本的訊息來預測第二次抽樣可能出現的新種類數。
過去文獻主要都是架構在歸還取樣的方式下推導其估計量，
本文主要是架構在不歸還取樣模式下，將過去表現較佳的種
類預測函數估計量推廣至此模式下，並提供其變異數估計。
（二） 多群落之多樣性探討
多群落的比較亦是生態上另一個重要的課題，包含探討同一個地
區不同時間點的變化或同一座森林不同緯度物種的變化，亦可探
討不同地區的群落差異。早期的文獻，有關共同種類數的估計方
法較少深入探討，傳統作法都是直接以出現在樣本中的共同種類
數當作估計值，此種估計明顯嚴重低估。對於架構在不歸還取樣
模式下，至目前為止對於多群落之共同種類數估計方法尚無相關
文獻，本文主要提供二群落及三群落以上之共同種類數估計及其
變異數估計。
本文除了理論推導所提出之種類數估計量外，並且以電腦模擬比較本
文的方法與過去文獻上的其它方法。對於樣本數、種類預測函數及多
群落共同種類數主題，亦提供電腦模擬以瞭解其估計量的表現。對於
不同主題，本文亦附加一些合適的實例分析，以說明其應用方式。

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