A species richness estimator for sample-based incidence data sampled without replacement

1. The accurate estimation of species richness in a target region is still a statistical challenge, especially in a highly heterogeneous community. Most richness estimators have been developed based on the assumption that data are randomly sampled with replacement or that data are sampled from an infinite population. However, in reality, most sampling schemes in the field are implemented as sampling without replacement (SWOR). As such, estimators derived based on sampling with replacement may cause overestimation as the sampling fraction increases and not converge to the true richness as the sampling fraction approaches one. Sample-based incidence data, in which the sampling unit is a plot, and only the presence or absence of a species in each chosen plot is recorded, is one of the most commonly used data types for assessing species diversity in ecological studies. 2. In this manuscript, according to sample-based incidence data collected through SWOR, a new richness estimator is proposed using a truncated beta-binomial mixture model. The new estimator was obtained through the moment approach, which avoids using iterative numerical algorithms for parameter estimation and presents a closed-form estimator as an alternative to the maximum likelihood method. Although the newly proposed method is a parametric-based richness estimator, similar to nonparametric estimators, only the rare species in the sample (i.e. the frequencies of uniques and duplicates) are required to estimate undetected richness. 3. Based on the hypothetical models, the statistical performances of the proposed estimator are evaluated under varying degrees of heterogeneity and different mean species detection rates. Compared to other widely used nonparametric and parametric estimators, the simulation results indicate that the proposed estimator has a smaller bias and lower root mean square error when the sampling fraction is greater than 10%, particularly in highly heterogeneous communities. 4. In addition, one ForestGEO permanent forest plot dataset is used to evaluate and compare the proposed approach with other estimators discussed in the study. The results demonstrate that the proposed estimator, in comparison to other widely used estimators, produces less biased estimate of true richness, along with more accurate 95% confidence interval.