標準化物種涵蓋率之Jaccard相異性指標估計方法

Abstract

過去在計算兩群落的Jaccard相異性指標時，研究人員主要根據三種方法進行估計，分別為觀測值估計方法、物種數估計方法及樣本涵蓋率標準化方法。本文主要透過樣本涵蓋率標準化方法進行修正，以往樣本涵蓋率的定義是指樣本中出現物種的總相對豐富度佔整個群落的比例，文獻指出當不同群落的物種相對豐富度有相似的異質性時，兩群落在相同樣本涵蓋率的樣本物種數比例能接近兩群落真正的物種數比例。因為Jaccard相異性指標可視為平均群落物種數佔混合群落物種數比例的轉換，因此可透過標準化樣本涵蓋率來進行Jaccard相異性指標的估計。然而，在兩群落物種豐富度的異質性差異很大時，傳統樣本涵蓋率標準方法的樣本物種數比例無法呈現真實群落物種數的比值。因此，本文提出了一個新的樣本完整性指標Richness coverage來估計Jaccard相異性指標，修正了以往標準化兩地區抽樣資料時，物種豐富度結構所造成的影響，以物種出現與否的角度，重新定義物種樣本涵蓋率。並根據文獻中估計物種數的概念，樣本中的稀有物種佔最多未出現物種的資訊，因此將抽樣資料分為豐富物種及稀有物種，並將樣本中的稀有物種資料作為樣本涵蓋率標準化的基準。為了比較本文提出之估計量與傳統估計方式，本文藉由電腦模擬的方式驗證各估計方法的統計表現，結果呈現相較其它傳統的方法，本文所提出的方法在大部分的母體設定中，在平均偏差、均方根誤差以及 95% 信賴區間涵蓋率都有明顯較佳的表現。最後以兩筆實例資料做應用解說，一筆為伊比利蜘蛛資料集，將此樣本資料視為抽樣母體做模擬研究，以及另一筆資料為巴西兩棲類樣本資料，透過估計去做分析並提出與以往不同的觀點，最後是將本文所推導的新估計方法，透過R軟體寫成互動式網頁以利使用者使用。

In the past, when calculating the Jaccard dissimilarity index of the two communities, researchers mainly estimated based on three methods. They can use the empirical method by observed data, species estimation by estimating unseen species, or the sample coverage standardization method. This paper is mainly corrected by the standardization method of sample coverage. The definition of sample coverage is the total relative abundance of observed species in the entire community. The literature points out that when the relative abundance of species in different communities has similar heterogeneity, the proportion of species with the same sample coverage in the two communities can be close to the true proportion of species in the two communities. Because the Jaccard dissimilarity index can be regarded as the ratio of the average number of species in the two communities to the number of species in the mixed community, the Jaccard dissimilarity index can be estimated by standardized sample coverage. However, when the species richness structure of the two communities is very different, the traditional quantitative method of sample coverage cannot close the true ratio of the number of species in the communities in calculating the ratio of the two communities under each sample coverage. Therefore, this paper redefines the sample coverage from the presence or absence of species and derives its rarefaction estimation methods. Then, according to the concept of estimating the number of species in the literature, the rare species in the sample contain the most unseen species information, so the sampling data are divided into abundant species and rare species, and the rare species data in the sample is used as the standard for the standardization of the sample coverage. In order to compare the proposed estimator in this paper with the traditional estimation method, we use computer simulation to verify. And we found that compared with other traditional methods, the proposed method in this paper has significantly improved which includes bias and a 95% confidence interval coverage rate in most cases. We also applied our proposed method to two real data. One of the datasets is the Iberian spider data set, we use this dataset as a population for simulation, and the other dataset is the Brazilian amphibian data, we use our proposed method for analysis and give different viewpoints. Finally, we develop the interactive website in the R language for the convenience use of users.