A Horvitz–Thompson‐type estimator of species richness

A Horvitz–Thompson‐type estimator of species richness for plot (cluster) sampling is constructed by considering species sampling as sampling with an unequal probability. Inclusion probabilities are estimated from sample‐based estimates of relative species incidence. Bias is addressed by adding, to each observed species, the expected number of unseen species with the same relative incidence. A Hansen–Hurwitz estimator of variance is adopted and augmented by the anticipated variance from sample‐based inclusion probabilities and the number of observed species. In Monte Carlo simulation of simple random plot (cluster) sampling from 11 large finite populations of forest trees and three sample sizes, the proposed estimator achieved the best overall ranking in terms of relative root mean square error efficiency when compared to 12 alternative estimators. The proposed estimator ranked third in terms of bias. The augmented Hansen–Hurwitz estimator of variance was liberal (median −13%). No richness estimator was uniformly best across populations and sample sizes. Across all settings, the performance of the best four estimators was similar, both in terms of bias and relative root mean square error efficiency.