論文摘要

生態學田野調查中的樣本往往無法包含全部的物種，因此在估計生物多樣性的過程中，「樣本涵蓋率」(sample coverage) 的概念扮演重要的腳色。正確的估計樣本涵蓋率有助於建構更精確的生物多樣性估計量。目前有關於樣本涵蓋率估計量的文獻都只限於單一群落產生的樣本，因此只能處理 alpha 多樣性的估計問題，對於用樣本涵蓋率處理多群落的 gamma多樣性的估計問題的文獻則十分缺乏。本論文將單一群落的樣本涵蓋率估計量推廣到多群落，因此對於估計 Shannon 指標的問題，在群落權數和樣本數成比例的條件下，得以將具有 Horvitz-Thompson 估計型式的 Chao & Shen (2003) 的 alpha 多樣性估計量推廣到 gamma 多樣性估計量。同時因為在 Shannon 指標之下，beta 多樣性即為 gamma 多樣性的自然指數除以 alpha 多樣性的自然指數，因此亦得到 beta 多樣性的估計量。不僅對於 Shannon 指標，對於具統合性的 Hill 指標，也得以藉著多群落的樣本涵蓋率估計量得到 gamma多樣性的適當估計。

本篇論文提出的 beta 多樣性估計量需要假設群落的真權數和樣本數成比例，才會具有小偏誤 (bias)。 本文並證明在此假設下，提出的 beta 估計量具有一致性 (consistency)。至於 beta 多樣性估計量標準差的估計，則是利用拔靴法 (bootstrapping) 求得。由模擬比較顯示，在小樣本時，本文提出的 beta 多樣性估計量比摺刀法 (Jackknife) 具有更小的偏誤；在大樣本時，則反過來，摺刀法的偏誤較小。

在實例分析方面，分別分析來自中美洲的 6 座森林演替資料、6 大洲原生纖毛類資料和熱帶雨林樹冠層及樹底層蝴蝶群落資料。藉著估計兩兩群落或三群落的 Shannon 指標的beta 多樣性，分別了解雨林演替和樹種大小的關係、原生纖毛類多樣性差異和地緣的關係、及樹冠層和樹底層蝴蝶群落的差異性，以驗證本文提出的 beta多樣性估計量的實際應用效果。

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