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CPS1255 Tsung-Jen Shen et al.
8. Magurran, A., and P. Henderson. 2003. Explaining the excees of rare
species in natural species abundance distributions. Nature 422:714–716.
9. Preston, F. 1948. The commonness and rarity of species. Ecology 29:254–
283.
10. Shen, T., A. Chao, and J. Lin. 2003. Predicting the number of new species
in further taxonomic sampling. Ecology 84:798–804.
11. Shen, T. & Chen, Y. (2018) A Bayesian weighted approach to predicting
the number of newly discovered rare species. Conservation Biology,
10.1111/cobi.13253.

Table 1. Estimate of newly found rare species (singletons, doubletons, and tripletons) in the
Malaysian butterfly data set. F (m) is the true value for rare species with abundance k in an
k
addition sample size m. Avg denotes the average of estimates using 2000 replicates.
Performance of each estimator was evaluated using relative bias (Rbias) and relative root mean
square error (Rrmse).

() Proposed: ̂ () Naive: ̃ ()

Avg Rbias Rrmse Avg Rbias Rrmse
100 50 1 27.950 28.868 0.033 0.131 8.026 −0.713 0.713
2 2.164 1.928 −0.109 0.225 2.154 −0.005 0.056
3 0.191 0.179 −0.061 0.237 0.407 1.131 1.134
100 1 48.159 50.519 0.049 0.171 9.420 −0.804 0.805
2 6.750 6.246 −0.075 0.192 4.942 −0.268 0.273
3 1.080 0.936 −0.134 0.276 1.792 0.658 0.664
150 1 63.150 65.778 0.042 0.200 8.358 −0.868 0.868
2 12.084 11.905 −0.015 0.152 6.475 −0.464 0.466
3 2.6411 2.257 −0.145 0.290 3.418 0.294 0.306
200 1 74.487 76.307 0.024 0.241 6.654 −0.911 0.911
2 17.423 18.222 0.046 0.139 6.806 −0.609 0.610
3 4.662 4.092 −0.122 0.291 4.699 0.008 0.076

200 100 1 37.244 39.138 0.051 0.128 12.314 −0.669 0.670
2 4.334 4.021 −0.072 0.132 3.483 −0.196 0.201
3 0.574 0.516 −0.101 0.167 0.727 0.267 0.272
200 1 59.976 62.743 0.046 0.161 14.092 −0.765 0.765
2 11.983 11.969 −0.001 0.087 7.614 −0.365 0.367
3 2.755 2.435 −0.116 0.186 2.930 0.064 0.084
300 1 74.624 76.033 0.019 0.185 12.386 −0.834 0.834
2 19.505 21.090 0.081 0.111 9.748 −0.500 0.502
3 5.924 5.403 −0.088 0.170 5.328 −0.101 0.115
400 1 84.446 82.425 −0.024 0.207 9.849 −0.883 0.883
2 26.026 30.213 0.161 0.180 10.153 −0.610 0.611
3 9.396 9.209 −0.020 0.139 7.152 −0.239 0.244

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