自20世紀邁入21世紀以來，環境保育的意識逐漸地抬頭，人們對於生態環境維持的重要性也有一定程度的理解，為了保護生態系的完整，必須定義合適的生物多樣性指標 ( biodiversity index )，如此才能衡量生態系中的多樣性高低，並藉由多樣性指標進行生態系的保育。

在過往的文獻中，關於多樣性指標的定義，大多落在單一群落和多群落的結構上討論，譬如：單一群落下的物種數、Shannon熵指標 ( Shannon 1948) 和Gini-Simpson指標 ( Simpson 1949 )，多群落下的Jaccard出現指標 ( Jaccard 1908 )、Sørensen出現指標 ( Sørensen 1948 )、Jaccard與Sørensen豐富指標 ( Chao et. al. 2005, 2006 )、Horn指標 ( Horn 1966 ) 和Morisita-Horn指標 ( Morisita 1959 ) 等等。隨著資料收集方式的進步，資料型態不再單純侷限於單一群落或多群落的型態。因此就不同結構型態的生物多樣性探討而言，本論文的研究主題可分為兩個主要的部份。

第一部分主要研究多層次架構 ( hierarchical structure )，而該主題是基於Hill指標族 ( Hill 1973 ) 和乘法分解 ( Whittaker 1960, Jost 2006, 2007 ) 的概念，並結合訊息理論中共有訊息 ( mutual information ) 來構造多層次下的多樣性分解。同時定義合適的相似性指標來衡量各層次內的相似程度，且給予直觀的解釋意義。此外，關於現有建構在多層次上的加法分解，將其適切地轉換至較為適當的相似度指標，並證明該指標與乘法分解下的相似度指標定義相同，如此一來，便可得到一個整合性的相似度指標，因此不論是在加法或是乘法分解下，皆可採用該指標來一致地描述該架構的生態結構情況。

第二部份主要研究空間與時間架構 ( space-time structure )，該主題藉由乘法分解、條件共有訊息 ( conditional mutual information ) 與交互訊息 ( interaction information ) 來建構，首先定義時空架構下的多樣性分解，並構造交互項指標，用以說明時空變換時物種轉換的情形和程度大小。此外也說明如何藉由排列檢定 ( permutation test ) 的方法來對有興趣的物種組成結構進行檢定。由於交互指標較為適切的解釋意義和排列檢定的方便性，可以清楚地解釋空間與時間兩個因子對於生態系所造成的影響，進而反推是否有特殊的環境因素來形成如此的結果。

關於這兩個主題的指標估計，均透過五種不同的估計方式來進行，分別為最大概似估計量、條件期望不偏估計量、分段樣本涵蓋率估計量、分段樣本涵蓋率調整估計量和二階不偏估計量，在不同的模擬設定之下，配合電腦模擬的結果，評估各估計量的表現優劣，且說明各種情況下估計量的選擇。最後各自以兩筆資料來介紹這兩種不同架構下的指標使用，並解釋資料於生態系上說明的現象。

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