A Richness Estimator Based on Integrated Data

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in a small-sized sample or highly heterogeneous assemblage. To estimate the number of different species (species richness) present across several different sites (communities), researchers often use a combined collection of data (an integrated dataset). This dataset is created by collecting samples from each site individually and independently. However, the pooled sample of integrated data is no longer a random sample from the entire area, and the use of different sampling schemes results in different collected data formats. Consequently, employing a single sampling distribution to model the pooled sample becomes unfeasible, rendering existing richness estimators inadequate. This study provides a theoretical explanation for the applicability of Chao's lower bound estimator in assessing species richness across multiple sites based on the pooled sample. Additionally, a new non-parametric estimator is introduced, which adjusts the bias of Chao's lower bound estimator by leveraging the Good-Turing frequency formula. This proposed estimator only utilizes the richness of singletons, doubletons, and tripletons in the pooled sample to estimate undetected richness. Simulated datasets across various models are employed to demonstrate the statistical performance of the estimator, showcasing its ability to reduce the bias of observed richness and provide accurate 95% confidence intervals. Real datasets are also utilized to illustrate the practical application of the proposed approach.