多樣性研究中反應變數選擇之研究

Abstract

生態中群落之物種組成可能會受到氣候因子的影響，進而造成群落多樣性的變化。而在全球暖化的影響下，生物多樣性也可能隨之改變。為了解物種多樣性與環境因子的關聯性，研究者會透過物種數多樣性分析建立氣候因子與估計物種數的統計模型，來探討氣候與物種數之間的關係及模型表現。然而，將估計物種數作為反應變數於多樣性分析中的適用性在過去研究中鮮少有系統性的探討。本文首先比較不同物種數估計式的變異數估計方法，選出在不同異質性的群落與不同抽樣大小下，估計表現最準確且穩定的變異數估計方法。接著，將物種數估計之變異數估計應用於物種數多樣性分析中。利用加權最小平方法(Weighted Least Square; WLS)建立解釋變數為氣候因子，反應變數為估計物種數的多元線性迴歸模型。同時，利用最大概似估計法(Maximum Likelihood Estimation; MLE)估計真實模型的誤差變異，並將物種數估計的估計變異與估計誤差變異作為WLS模型的權重。最後，透過模型參數的估計值、檢定統計量以及解釋因子顯著率，作為物種數多樣性之反應變數的選擇依據。模擬結果顯示，無論在出現型或豐富型資料下，對於群落物種數的估計方法，根據δ-method的變異數估計方法在不同異質性的模型設定下的表現最為穩定；而對於標準化物種數的估計方法，重抽拔靴法則具有較佳的估計表現。在模型參數估計方面，考量較小偏誤的條件下，以有母數為依據的物種數估計方法：Gamma-Poisson-based (GP)以及Beta-Binomial-based (BB)估計式分別為較適合作為豐富型以及出現型資料的物種數多樣性之反應變數；而在模型檢定統計量方面，以樣本涵蓋率為標準化依據的物種數估計方法與真值表現較為接近，適合作為真實群落物種數的代理統計量。此外，在物種數多樣性分析模擬結果顯示，相較於一般最小平方法(Ordinary Least Square; OLS)，WLS方法在迴歸參數估計的變異性及顯著率具有較佳的表現，顯示出其在多樣性分析中具有較穩定的估計優勢。

The species composition of communities in ecosystem can be influenced by environmental or climatic factors. Biodiversity may also change due to the impact of global warming. To understand the relationship between species diversity and climatic factors, researchers often use species diversity analysis to construct statistical model between climatic factors and species richness estimates, aiming to explore the relationship between variables, and to evaluate model performance. However, the suitability of using estimated species richness as the response variable in diversity analysis has rarely been systematically discussed in previous studies. This study first compares various variance estimation methods for species richness estimation and identifies the most accurate and stable method under different community heterogeneity and different sample sizes. These variance estimates are then applied to diversity analysis. Using Weighted Least Squares(WLS), a multiple linear regression model is constructed with climatic factors as explanatory variables and species richness estimates as response variable. Meanwhile, Maximum Likelihood Estimation(MLE) is employed to estimate the error variance of the true regression model. Both estimated variance of species richness estimator and the estimated error variance are used as weights for the WLS regression model. Finally, the methods for estimating species richness as response variables are evaluated and compared based on regression coefficient estimates, test statistics, and the significance rate of explanatory variables. The simulation results show that, for estimating species richness in community, the variance estimation method based on the δ-method performs the most consistently across different model settings with varying heterogeneity, regardless of whether incidence or abundance data are used. In contrast, for standardized estimation of species richness, the bootstrap resampling method demonstrates better estimation performance. For regression coefficient estimation, under the condition of minimizing bias, the parametric species richness estimators, Gamma-Poisson-based(GP)and Beta-Binomial-based(BB), are considered more suitable as response variables for species richness diversity analysis in abundance data and presence-absence data respectively. For model test statistics, the standardized species richness estimation method based on sample coverage, yields test statistics closer to the true model, making it more suitable as a proxy for the test statistics of number of species in communities. Furthermore, the simulation results also show that, compared to the Ordinary Least Squares(OLS) method, the WLS method performs better in terms of variability and significance of regression parameter estimates, highlighting its more stable estimation advantages in diversity analysis.