根據Hill 數值指標及空間資料，Whittaker (1960)將地區多樣性 (gamma多樣性) 分解為兩部分：alpha及beta多樣性。一般而言，當一地區有多個群落時，gamma多樣性為混合群落的多樣性，alpha多樣性為平均群落的多樣性，而beta多樣性為衡量群落間物種組成的不同。因此，透過beta多樣性的轉換，可用來定量群落間物種組成的相似度或分化程度；其中較常使用根據熵指標建立的Horn相似指標為其一特例。
對於多樣性的估計，當樣本數小時，傳統的做大概似估計方法幾乎都會有嚴重低估的現象，Chao et al. (2013) 根據Good-Turing 方程式，推導得到群落內熵指標的近似不偏估計量。然而文獻中，對於對於多群落的gamma熵指標的估計幾乎不曾被討論。因此，本文的目的為在個別群落的區塊抽樣資料下發展一個新的估計方法來估計gamma熵指標。藉由電腦模擬的研究與傳統最大概似估計法比較，新的估計方法明顯在偏誤、均方根誤差以及95%信賴區間涵蓋率都有較佳的表現。
最後將新的估計方法及相似度指標應用到生態學家Foissner et al. (2002)在位於非洲西南部的納米比亞的三個地區收集共51個土壤泥塊的纖毛蟲物種資料。

Based on Hill numbers and spatial data, Whittaker (1960) used multiplicative decomposition approach to partition regional diversity (gamma diversity) into two components: alpha and beta components. Generally, when there are multiple communities, gamma diversity is the diversity of the pooled community, alpha diversity is the mean diversity of individual communities, and beta diversity measures the extent of compositional difference among communities Therefore, differentiation or similarity among communities can be quantified through transforming beta diversity; the traditional widely used entropy-based Horn-similarity index is a special case.
Since the observed diversity always underestimates the true diversity especially when sample size is small, Chao et al. (2013) developed a nearly unbiased estimator of within-community Shannon diversity based on Good-Turing frequency formulas. However, when there are multiple communities, the estimation of gamma Shannon has not been discussed in the literatures. A new estimator is proposed to estimate the gamma Shannon diversity based on the sampling data from each community. Through the computer simulation study, when compared with the traditional empirical method, the new proposed estimator exhibits substantial improvement in bias, RMSE and the coverage probability of 95% confidence interval. Finally, I apply the new proposed estimator and related similarity measure to the analysis of 51 soil ciliates quadrat sampling data collected by Foissner et al. (2002) from three areas in Namibia (Southwest Africa).

第一章 緒論 1
第二章 模型與符號介紹及相關文獻回顧 4
2.1 模型假設與符號說明 4
2.1.1 區塊抽樣下之抽樣方式與模型假設 4
2.1.2 兩群落區塊抽樣之符號介紹 6
2.1.3 模擬研究符號介紹 7
2.2 相關文獻回顧 8
單群落相關文獻回顧 8
2.2.1 物種數估計 8
2.2.2 樣本涵蓋率 10
2.2.3 Shannon熵指標介紹與估計 13
多群落相關文獻回顧 23
2.2.4 多樣性指標分解 24
2.2.5 多群落共同種數下界估計 27
2.2.6 Horn指標 30
第三章 兩群落多樣性指標之估計量 36
3.1 混合群落熵指標之估計量 36
3.2 廣義權重相似性Horn 指標之估計量 41
3.3 兩群落拔靴方法之標準差估計與其修正 44
3.3.1 拔靴法與修證拔靴法介紹 44
3.3.2 拔靴法估計變異數流程介紹 51
第四章 模擬研究 53
4.1 模擬研究設定說明 53
4.2 混合群落熵指標的模擬結果 55
4.3 廣義權重相似性Horn 指標的模擬結果 58
第五章 實例分析 60
第六章 結論與後續研究 65
附錄 67
附錄 A 模擬試驗之估計量表現－混合群落熵指標 67
附錄 B 模擬試驗之估計量表現－廣義權重相似性Horn指標 102
附錄 C 實例資料的頻率個數 138
參考文獻 140

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