《生物多樣性公約》已有193個國家簽署，可見世界各國已正視生物多樣性之重要，因此研究生物間的交互行為亦是個重要的議題。互資訊 (mutual information) 是用來衡量兩隨機變數之間的關聯性，在生態上可以使用互資訊來量化物種之間的交互作用或是專一程度。互資訊可由熵 (entropy) 指標來表示，Chao, A., Wang, Y. T. and Jost, L. (2013) 將熵指標表示成發現新物種速率的一個函數，提出近乎不偏的熵指標估計量。本文研究Chao et al. (2013) 熵指標估計量套用在估計互資訊上的表現情形，亦即本文建議之估計量，並與其他五個估計量作比較，以及提出修正兩維度資料下拔靴方法之標準差估計。藉由電腦模擬的方式探討各個估計量的表現，結果顯示本文建議之估計量在所有實驗中有接近最小的偏差，可接受的變異程度，以及近乎一致的具有最小的均方根誤差，其收斂速度相較於其他估計量也更為迅速；當抽取個體數較少時，即可有非常出色的估計表現。同時搭配實例分析，更能了解互資訊對於生態上的實務應用。
此外介紹以R語言開發的互動式網頁ChaoEntropy Online，此軟體包含兩大部分「Shannon entropy」與「Mutual Information」，經由簡單地點選即可得到估計值、拔靴標準差與信賴區間。亦能在本機端執行，資料不外洩，希望對熵指標或互資訊估計有需求的人士，能藉由此軟體輕鬆分析。

致謝詞 i
摘要 ii
第一章 緒論 1
第二章 介紹模型與符號及相關文獻回顧 5
2.1 模型假設與符號說明 5
2.1.1 抽樣方法與模型假設 5
2.1.2 符號說明 8
2.2 相關文獻回顧 11
2.2.1 物種數估計 11
2.2.2 樣本涵蓋率 (Sample Coverage) 估計 14
2.2.3 拔靴 (Bootstrapping) 方法之標準差估計與其修正 16
第三章 Shannon熵指標與互資訊及其估計量 20
3.1 熵指標介紹 20
3.2 聯合熵、條件熵與相對熵介紹 22
3.2.1 聯合熵 (joint entropy) 23
3.2.2 條件熵 (conditional entropy) 23
3.2.3 相對熵 (relative entropy) 24
3.3 互資訊介紹 25
3.4 互資訊估計量 28
3.4.1 最大概似估計 29
3.4.2 最大概似估計量之修正偏差 30
3.4.3 摺刀法估計量 32
3.4.4 Chao and Shen 估計量 33
3.4.5 本文建議之估計量 35
3.5 兩維度拔靴方法之標準差估計與其修正 38
第四章 模擬研究 40
4.1 模擬實驗設定說明 40
4.2 模擬實驗的結果與討論 44
4.3 檢驗互資訊估計量使用常態假設之合理性 47
4.4 最大概似估計量之低估情形 48
第五章 實例分析 51
第六章 軟體開發 55
6.1 簡介 55
6.2 第一部分、Shannon 熵指標 (Shannon entropy) 56
6.2.1 個體資料 (Abundance data) 57
6.2.2 區塊資料 (Incidence data) 61
6.3 第二部分、互資訊 (Mutual Information) 65
第七章 結論與後續研究 71
附錄 74
附錄A: 五種實驗下的模擬結果 74
附錄B: 五種實驗下偏差情形與均方根誤差之表現 81
參考文獻 84

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