生物多樣性的量測在生態的研究領域中至關重要，同時也是世界各國進行環境開發的重要評估指標。如何經由抽樣數據來準確的估計多樣性指標一直是生態學家們所關切的問題。Hill數值指標族（即所謂的有效數值）近來被廣泛的應用於刻畫單一地區或者是多地區的生物多樣性。然而，有效數值受到取樣大小所影響，以觀察數據進行不同地區多樣性的比較時，將各地區的數據標準化到相同取樣基準再進行比較是比較公平、客觀的方式。本篇論文主要的研究成果可以分成三個部分：
(1) 對於單一地區的物種多樣性，提出整合抽樣效益、物種豐富度以及系統演化樹結構的多樣性分析曲線及其估計方法，此即系統演化多樣性的稀釋與預測曲線。同時也提出修正傳統拔靴重抽法在進行估計量之變異數估計時產生偏差問題的解決辦法。
(2) 考慮多地區的物種多樣性，延續前一個主題，將系統演化多樣性的稀釋與預測曲線推廣到空間架構下的alpha（平均地區）、beta（地區與地區之間）與gamma（整體地區）的多樣性分析。
(3) 以單一地區和多地區的族群繁衍模型為基礎，進而推導出在繁衍模型趨於平穩時，Hill多樣性指標族的抽樣個體數累積曲線。其結果有助於了解演化因子與基因多樣性的關聯性。
上述研究所提出的曲線估計方法經由電腦模擬驗證為可靠的估計，並採用真實資料進行實例分析。為求研究結果的可重現性以及相關研究者的便利性，以上統計方法可以透過R語言撰寫成統計分析軟體phylo-iNEXT進行測試與分析。

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