A Bayesian-weighted approach to predicting the number of newly discovered rare species

In natural ecological communities, most species are rare and thus susceptible to extinction. Consequently, the prediction and identification of rare species are of enormous value for conservation purposes. How many newly found species will be rare in the next field survey? We took a Bayesian viewpoint and used observed species abundance information in an ecological sample to develop an accurate way to estimate the number of new rare species (e.g., singletons, doubletons, and tripletons) in an additional unknown sample. A similar method has been developed for incidence-based data sets. Five seminumerical tests (3 abundance cases and 2 incidence cases) showed that our proposed Bayesian-weight estimator accurately predicted the number of new rare species with low relative bias and low relative root mean squared error and, accordingly, high accuracy. Finally, we applied the proposed estimator to 6 conservation-directed empirical data sets (3 abundance cases and 3 incidence cases) and found the prediction of new rare species was quite accurate; the 95% CI covered the true observed value very well in most cases. Our estimator performed similarly to or better than an unweighted estimator derived from Chao et al. and performed consistently better than the naïve unweighted estimator. We recommend our Bayesian-weight estimator for conservation applications, although the unweighted estimator of Chao et al. may be better under some circumstances. We provide an R package RSE (rare species estimation) at https://github.com/ecomol/RSE for implementation of the estimators.