物種組成之估計

Abstract

文獻中，大部分生態學家幾乎都是根據物種相對組成（即物種個體數占群落總個體數的比例）來量化群落的多樣性，而物種等級豐富度分佈（Species-rank abundance distribution; RAD）即是一種描述該地區物種相對豐富度的方式。傳統上，生態學家常會根據物種在樣本中出現的個體數比例來估計其真實的相對豐富度，但這種估計方式會高估被觀測到物種的相對豐富度，且未考慮樣本中未出現的物種及其相對豐富度。因此，現有估計方法大多根據古德-圖靈（Good–Turing）樣本涵蓋率的概念，對已觀測到物種之個體數在樣本中的佔比進行校正，並結合物種數估計和樣本覆蓋不足的概念估計未觀測物種的相對豐富度。此外，當物種數已知且對各物種觀測到個體數進行分佈假設時，可將物種相對豐富度的估計問題，視為分佈的參數估計問題。 本文依照上述架構將樣本涵蓋率當作校正依據，在個體抽樣且抽後放回的豐富型資料下，將各物種於樣本中的個體數比例加入兩個參數，並以最小化差異平方和之期望值的方式建立單一群落RAD估計方法。接著考量不同物種豐富度模型和物種數未知及已知的情境，進行電腦模擬，以絕對誤差和和誤差平方和的評量方式比較不同估計方法的表現。此外，本文也進行了將真實資料視為母體的模擬。模擬結果顯示，本文提出的估計方法在大多數模型下，估計表現與現有文獻中的方法差異不大，而在同質性模型及負二項模型下則是有明顯的進步。

In the literature, ecologists have almost universally quantified community diversity based on species relative composition (i.e., the proportion of individuals of each species within the total number of individuals in the community). The species-rank abundance distribution (RAD) is a method used to describe the relative abundance of species in the community. Traditionally, ecologists estimate the true relative abundance of species based on their observed proportion in a sample. However, previous studies have shown that this approach tends to overestimate the relative abundance of observed species, while neglecting the relative abundance of unobserved species. Consequently, existing estimation methods often apply corrections to the observed species' abundance using the concept of Good-Turing sample coverage and incorporate species number estimates to account for unobserved species and their relative abundance. Furthermore, when the number of species is known, the problem of estimating relative abundance can be framed as estimating the parameters of its distribution. This paper follows this framework, using sample coverage as the basis for correction, and establishes a community RAD estimation method under the condition of individual sampling with replacement. The study considers different species abundance models and scenarios where the number of species is unknown or known. Computer simulations are conducted to compare the performance of different estimation methods using sum of absolute error and sum of squared errors as evaluation metrics. Additionally, this paper also conducts simulations treating real data as the population. The simulation results show that the proposed estimation method performs similarly to Chao et al.'s method under most models, with significant improvements in homogeneity models and negative binomial models.