物種辨識錯誤下物種數之估計

Abstract

對於一個地區進行物種數的估計一直是個相當大的統計挑戰。過去的文獻中已發展相當多的統計估計方法來解決小樣本容易低估的情況，但是對於進行物種調查時，物種辨識錯誤造成物種數的估計偏差問題，在文獻中卻很少被提及。為了解決此問題，本文採取兩階段抽樣方法，分別針對單組與多組調查人員的區塊抽樣資料提出物種數估計修正的方法，同時以Chao2物種數估計式與一階摺刀法物種數估計式作為我們修正式的理論基礎。為取得物種辨識錯誤率的資訊，首先必須讓調查人員先進行一小區域的物種普查工作，再利用此資訊對樣本中觀測到的物種數、樣本中記錄一次的物種數和記錄兩次的物種數進行修正。同時為了修正因校正Chao2物種數估計式所造成的較大偏差與變異數過大的情形，因此本文中也提出了物種數估計式的修正式以解決此困境。為了檢測此修正估計式的表現情況，本文根據不同物種辨識錯誤率及物種機率模型下的設定，透過模擬來檢測其統計表現。結果顯示修正後的估計式有較佳的均方根誤差。最後分別於單組與多組調查人員的狀況下各提出一筆實例資料進行分析。

Estimation of species richness in an area is always challenging statisticians regard to small sample units or the presence of species identity error. In the literatures, most richness estimators were only proposed to deal with the underestimation of the size-limited sample. However, species identity error almost exists in species surveys and seriously causes the inaccuracy of richness estimation. Therefore, the biased collected data due to species identity error should be adjusted to estimate the true richness. In the manuscript, we proposed a method to adjust the richness estimation with the existence of species identity error for single or multiple investigators. We choose Chao2 and first-order Jackknife richness estimator as the theoretical foundation of deriving the adjusted method. First, census of a subplot should be done by investigators in order to get the information of species identity error among investigators, so we can use the information of species identity error to adjust the observed, singleton, and doubleton richness in order to get the corrected Chao2 estimator. Nonetheless, the estimation will be inaccurate due to the increased variance of adjusted singleton, and doubleton richness. Then the adjusted estimator is proposed to tackle with the problem mentioned above. To investigate the performance of the adjusted estimator, we do several simulation studies and find out the estimation has the smallest root mean square error (RMSE) in most cases. In the end, we demonstrate an estimation of species richness by a weed survey data from Soft Bridge County in Taiwan for single investigator and a plant cover survey data from the Grand St. Bernard Pass in Switzerland for multiple investigators.