出現型資料的共同物種數估計

Abstract

兩群落之間的共同物種在群落中所佔的比例，可以做為一種表示Beta多樣性最簡單且直觀的指標之一。文獻中，分別針對不同抽樣方式、調查方法或是資料型態，已提出單一群落物種數和兩群落共同物種數的估計方法。其中，只計錄物種出現與否的出現型資料是生態學家較常收集的資料形式。且在估計方法的推導有母數方法是廣為採用的估計策略。在出現型資料中，通常假設物種出現率服從 一Beta機率分佈，，而相對最大概似估計方法 (Maximum likelihood method)，採用動差法 (moment mothed) 所得到單一群落物種數估計式，有較穩健的統計表現。因此，本文針對出現型之資料，根據取後放回與取後不放回兩種抽樣方式， 分別假設物種出現率服從一Beta 分佈和假設物種存在區塊數服從一零截尾的Beta二項式分佈，並採用動差法推導兩群落共同物種數估計式。並透過電腦模擬，評估估計式的優劣與穩定性。在模擬結果呈現，相較於原有的共同種估計方法，本文所提出的方式有較小的偏誤 (Bias)，較大的變異數 (Variance)，在均方根誤差 (RMSE) 與95%信賴區間涵蓋率 (Cover rate of 95% confidence interval) 兩項評估指標上具更佳的表現。最後，在紅杉國家公園不同海拔棲地的苔蘚實例資料分析中，相較只考慮樣本的共同物種數，透過共同物種數估計值所得到的群落間的Beta 多樣性較符合生態學家的預期。說明在分析或比較生物多樣性時，統計估計有其必要性。

The proportion of shared species between two communities is a simple and intuitive indicator of Beta diversity. Various methods have been proposed to estimate the number of species in a single community and the number of shared species between two communities, tailored to different sampling methods, survey techniques, and data types. Presence-absence data, which records species occurrence, is commonly used by ecologists. Assuming species occurrence rates follow a Beta distribution, Parametric methods are widely adopted. Compared to the maximum likelihood method, the moment method offers a more robust statistical performance for estimating species numbers. This paper focuses on presence-absence data, deriving formulas for estimating shared species between two communities based on with-replacement and without-replacement sampling methods. It assumes species occurrence rates follow a Beta distribution and that the number of species in blocks follows a zero-truncated Beta-binomial distribution, using the moment method for derivation. Computer simulations evaluate the accuracy and stability of these formulas. Results show that the proposed approach has lower bias and higher variance than existing methods, performing better in the root mean square error (RMSE) and the 95% confidence interval cover rate. Analyzing bryophyte data from different altitudes in Sequoia National Park, the estimated Beta diversity aligns more closely with ecologists' expectations than merely counting shared species. This highlights the necessity of statistical estimation in biodiversity analysis and comparison.