生物多樣性在不論是生態學、遺傳學與其他相關學科上都是個關鍵且重要的概念。實際上，生物多樣性的概念橫跨了所有生態系中生物體的變異性，其中包含了從基因、個體、物種、族群、群集、生態系到地景等各種層次的生命型式，因此本質上就是一個多層次的結構，且現今因資料蒐集技術的進步，大多數生態資料會在多層次結構中的不同層次中蒐集，例如一個簡單的三層次結構就是一個整體區域下包含了多個子區域，而每個子區域下又包含了多個群落。因此整合多個層次與多個子區域之間的結構關係來衡量多樣性的方法便顯得更為重要。
本文基於Tsallis (1988) 熵指標族與Hill (1973) 指標族並分別使用加法與乘法分解的概念，以個體數為權重來建立多層次的物種alpha、beta與gamma多樣性，適用在兩種資料形態下：個體抽樣下豐富度資料與區塊抽樣下的出現與否資料，並且定義標準化的相異性指標，以便衡量子區域間或群落間的差異程度。當中利用統計方法估計多層次分解下多樣性指標與相異性指標、以拔靴法估計指標標準差。透過電腦模擬，比較本文推廣估計量與最大概似估計量的優劣，結果顯示本文推廣的估計量不論是在平均偏誤、方均根誤差皆有較佳的表現。接著將本文推廣的架構各以一筆實際資料進行分析並作為實際應用上的範例。最後，透過R語言將本文提及的內容編寫成簡易的互動式網頁，方便無程式背景的使用者分析並擷取分析結果。

Biological diversity (biodiversity) is an essential concept and plays an important role in ecology, genetics and many other disciplines. Biodiversity generally refers to the variety and variability of life at the levels of genes, individuals, species, populations, communities, landscapes, etc, and therefore is inherently under a hierarchical structure. Nowadays, because of rapid advancement of technology, collecting data becomes more convenient and faster, most biological data are typically collected at various levels of multiple-level hierarchical structures, e.g., a simplest 3-level hierarchical structure is that an region includes several subregions and each subregion includes several communities. A unifying framework for the measurement of biodiversity across hierarchical levels is thus required.
Based on two measures (Tsallis entropy and Hill number) and two types of decompositions (additive and multiplicative), this thesis presents a framework for the measurement of species alpha, beta and gamma entropies/diversities across hierarchical levels for both abundance data under individual sampling and incidence data under quadrat sampling. Standardized dissimilarity measures are also derived to quantify differences among multiple regions or communities. Statistical method is developed to estimate the hierarchical entropies/diversities and dissimilarity measures with estimated bootstrap variances. Simulation results are used to show that the proposed estimators outperform the maximum likelihood estimators in terms of bias and root mean squared error (RMSE). The unifying framework is applied to real data sets to illustrate the proposed estimators and interpret the numerical results.
Furthermore, an online application for computing the proposed measures and estimators is developed using R language and Shiny package.

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