在生態學研究領域上，探討不同地區 (或稱群落) 物種組成之相似 (或差異) 的原因一直是生態學中的核心問題，因此如何客觀地定量不同群落物種組成的相似，在此領域變得至為重要。雖然文獻中已有大量的相似性指標被發表出來，但其中只有Horn (1966) 依據訊息理論所建構的Horn熵指標滿足“單調性公設”性質。本研究將首先利用不同地區的取樣資料，透過Good-Turing頻度方程式探討任意群落權重比例混合群落熵指標及Horn熵指標之估計。

再者，因為取樣問題，在有限的樣本下，對於相似性指標之估計通常會有較高估或低估之現象，本文引用Sanders (1968) 物種數的累積曲線之概念至相似性指標，包含Sørensen指標 (Sørensen 1948)、Horn熵指標 (Horn 1966) 及Morisita指標 (Morisita 1959)，將各地區樣本之個體數或樣本涵蓋率標準化至相同下，再計算相似性指標之稀釋與外插曲線估計，以便比較與瞭解群落間物種組成之相似性。

一般進行野外抽樣時，可分為歸還及不歸還抽樣方式，對於文獻上常用的三個生物多樣性指標，包含物種數指標、Shannon熵指標及Simpson指標，除了物種數指標已發展出於歸還及不歸還抽樣下之估計，對於Shannon熵指標及Simpson指標之估計皆架構於歸還抽樣下之討論。本研究將應用統計方法，提供架構於不歸還抽樣下之Shannon熵指標及Simpson指標之估計。再者，為了比較不同群落之物種多樣性，本文亦將Chao et al. (2014) 架構於歸還抽樣下，對於物種數指標、Shannon多樣性指標、Simpson多樣性指標及樣本涵蓋率，其稀釋與預測曲線之估計討論，推廣至不歸還抽樣下。

本文除了詳細理論推導上述提出的各個生物多樣性指標之估計式外，並且以電腦模擬方式驗證各個估計式之表現，亦附加一些實例說明其應用。在混合群落熵指標及Horn熵指標之估計主題，應用哥斯大黎加的原始林資料及西非的蝙蝠資料作實例分析; 在相似性指標之稀釋與外插曲線估計主題，應用西非的蝙蝠資料作實例分析；在Shannon熵指標、Simpson指標、物種多樣性指標的稀釋與預測，及樣本涵蓋率之估計主題，應用哥斯大黎加奧薩地區的甲蟲資料及巴拿馬的鳥類資料作實例分析。

How to assess and quantify species compositional (dis)similarity among communities has been a central objective in ecology. Although a large number of (dis)similarity measures have been published, only the Horn index (Horn 1966), or normalized mutual information, satisfies the essential monotonicity property. Empirical estimate of the Horn index depends strongly on sample sizes and may be subject to large bias. Based on sampling data, this thesis applies Good-Turing frequency formula to derive an analytic estimator of the Horn index under any community weight proportions. Simulations results show that the proposed estimator reduces the bias associated with the empirical estimator. As the sample size increases, the proposed estimator coverages quickly to the true value.

This thesis also extends the previous rarefaction and extrapolation for species richness to (dis)similarity measures which include the Sørensen index (Sørensen 1948), Horn index (Horn 1966) and Morisita index (Morisita 1959). In order to compare the (dis)similarity measures across multiple assemblages, rarefaction and extrapolation methods are proposed based on standardized sample size or sample completeness. From simulations studies, our estimated rarefaction and extrapolation curve of (dis)similarity measures can accurately quantify the species compositional (dis)similarity among assemblages up to double the sample size in each community.

Biological sampling can be conducted by sampling with replacement or sampling without replacement. For the three most commonly used indices of biological diversity, including species richness, Shannon diversity, and Simpson diversity, estimators were developed for both types of sampling schemes only for species richness. In this thesis, we derive estimators of Shannon and Simpson diversities under sampling without replacement. The corresponding sample-size-based and sample-coverage-based rarefaction and extrapolation sampling curves are also developed. From simulations studies, the proposed rarefaction and extrapolation method works well up to double the sample size in each community.

Real data examples are used to illustrate all proposed estimators and to demonstrate various applications.

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