區塊抽樣之兩群落γ熵指標估計

Estimation of Gamma Entropy of Two Assemblages in Quadrat Sampling

陳禹含(Chen, Yu Han)

指導教授 ： 趙蓮菊

國立清華大學/理學院/統計學研究所/碩士(2015年)

摘要

根據Hill 數值指標及空間資料，Whittaker (1960)將地區多樣性 (gamma多樣性) 分解為兩部分：alpha及beta多樣性。一般而言，當一地區有多個群落時，gamma多樣性為混合群落的多樣性，alpha多樣性為平均群落的多樣性，而beta多樣性為衡量群落間物種組成的不同。因此，透過beta多樣性的轉換，可用來定量群落間物種組成的相似度或分化程度；其中較常使用根據熵指標建立的Horn相似指標為其一特例。
對於多樣性的估計，當樣本數小時，傳統的做大概似估計方法幾乎都會有嚴重低估的現象，Chao et al. (2013) 根據Good-Turing 方程式，推導得到群落內熵指標的近似不偏估計量。然而文獻中，對於對於多群落的gamma熵指標的估計幾乎不曾被討論。因此，本文的目的為在個別群落的區塊抽樣資料下發展一個新的估計方法來估計gamma熵指標。藉由電腦模擬的研究與傳統最大概似估計法比較，新的估計方法明顯在偏誤、均方根誤差以及95%信賴區間涵蓋率都有較佳的表現。
最後將新的估計方法及相似度指標應用到生態學家Foissner et al. (2002)在位於非洲西南部的納米比亞的三個地區收集共51個土壤泥塊的纖毛蟲物種資料。

關鍵字

熵 ； 兩群落 ； 區塊

並列摘要

Based on Hill numbers and spatial data, Whittaker (1960) used multiplicative decomposition approach to partition regional diversity (gamma diversity) into two components: alpha and beta components. Generally, when there are multiple communities, gamma diversity is the diversity of the pooled community, alpha diversity is the mean diversity of individual communities, and beta diversity measures the extent of compositional difference among communities Therefore, differentiation or similarity among communities can be quantified through transforming beta diversity; the traditional widely used entropy-based Horn-similarity index is a special case.
Since the observed diversity always underestimates the true diversity especially when sample size is small, Chao et al. (2013) developed a nearly unbiased estimator of within-community Shannon diversity based on Good-Turing frequency formulas. However, when there are multiple communities, the estimation of gamma Shannon has not been discussed in the literatures. A new estimator is proposed to estimate the gamma Shannon diversity based on the sampling data from each community. Through the computer simulation study, when compared with the traditional empirical method, the new proposed estimator exhibits substantial improvement in bias, RMSE and the coverage probability of 95% confidence interval. Finally, I apply the new proposed estimator and related similarity measure to the analysis of 51 soil ciliates quadrat sampling data collected by Foissner et al. (2002) from three areas in Namibia (Southwest Africa).

參考文獻

[23] 周三童 (民 102). 區塊抽樣之熵指標估計 趙蓮菊指導 新竹市國立清華大學統計學研究所碩士論文

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[4] Chao, A. and Jost, L. (2014). Estimating diversity and entropy profiles via discovery rates of new species. Manuscript.