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CPS1255 Tsung-Jen Shen et al.
a) The proposed Bayesian-weight estimator predicted the
number of singletons, doubletons, and tripletons accurately, as
supported by the direct comparison of true and estimated
values in the two empirical data sets (Tables 1).
b) The proposed Bayesian-weight estimator had lower relative
bias and lower relative root mean squared error (thus
indicating higher accuracy) in comparison to the naïve
estimator (Tables 1).

4. Discussion and Conclusion
Natural species abundance distributions observed in the real world show
a pattern of only a few species being common while most species are rare
(Magurran & Henderson 2003). Our studies showed that this was also true for
newly discovered species in our simulated new samples (Tables 1). Expected
and true values for doubleton new species were much smaller than for
singleton new species, while the values for tripleton new species were much
smaller than for doubleton new species.
In conclusion, in this study we developed a novel Bayesian-weight
estimator for predicting rare new species in potential additional ecological
samples. The method we developed was nonparametric and accurate. In
addition to rare species, our statistical model was equally powerful for
predicting the number of common species, which are important drivers of
many ecosystem functions (Gaston 2011; Houadria & Menzel 2017)

References
1. Chao, A., T. Hsieh, R. Chazdon, R. Colwell, and N. Gotelli. 2015. Unveiling
the species-rank abundance distribution by generalizing the Good-
Turing sample coverage theory. Ecology 96:1189–1201.
2. Chen, Y., and T. Shen. 2017. A general framework for predicting delayed
responses of ecological communities to habitat loss. Scientific Reports
7:998.
3. Fisher, R., A. Corbet, and C. Williams. 1943. The relation between the
number of species and the number of individuals in a random sample of
an animal population. Journal of Animal Ecology 12:42–58.
4. Gaston, K. 2011. Common ecology. BioScience 61:354–362.
5. Houadria, M., and F. Menzel. 2017. What determines the importance of a
species for ecosystem processes? Insights from tropical ant
assemblages. Oecologia 184:885–899.
6. Kunin, W., and K. Gaston. 1993. The bioogy of rarity: patterns, causes and
consequences. Trends in Ecology and Evolution 8:298–301.
7. Magurran, A. 2004. Measuring biological diversity. Blackwell, Oxford.

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