A more reliable species richness estimator based on the Gamma-Poisson model

Background. Accurately estimating the true richness of a target community is still a statistical challenge, particularly in highly diverse communities. Due to sampling limitations or limited resources, undetected species are present in many surveys and observed richness is an underestimate of true richness. In the literature, methods for estimating the undetected richness of a sample are generally divided into two categories: parametric and nonparametric estimators. Imposing no assumptions on species detection rates, nonparametric methods demonstrate robust statistical performance and are widely used in ecological studies. However, nonparametric estimators may seriously underestimate richness when species composition has a high degree of heterogeneity. Parametric approaches, which reduce the number of parameters by assuming that species-specific detection probabilities follow a given statistical distribution, use traditional statistical inference to calculate species richness estimates. When species detection rates meet the model assumption, the parametric approach could supply a nearly unbiased estimator. However, the infeasibility and inefficiency of solving maximum likelihood functions limit the application of parametric methods in ecological studies when the model assumption is violated, or the collected data is sparse. Method. To overcome these estimating challenges associated with parametric methods, an estimator employing the moment estimation method instead of the maximum likelihood estimation method is proposed to estimate parameters based on a Gamma-Poisson mixture model. Drawing on the concept of the Good-Turing frequency formula, the proposed estimator only uses the number of singletons, doubletons, and tripletons in a sample for undetected richness estimation. Results. The statistical behavior of the new estimator was evaluated by using real and simulated data sets from various species abundance models. Simulation results indicated that the new estimator reduces the bias presented in traditional nonparametric estimators, presents more robust statistical behavior compared to other parametric estimators, and provides confidence intervals with better coverage among the discussed estimators, especially in assemblages with high species composition heterogeneity.