This PDF file includes:

• section S1. Upscaling biodiversity
  
• section S2. Limitation of the LS methods
  
• section S3. Flexibility of NB distribution
  
• section S4. Test on computer-simulated forests
  
• section S5. Comparison with other popular estimators
  
• section S6. Data set
  
• section S7. Self-consistency and estimation of the critical p*: How much remains to be sampled?
  
• section S8. RSA parameters maximize relative fluctuation in abundances
  
• fig. S1. Assuming that the global RSA is distributed according to an NB, we can compute the probability that a species comprises a single individual at the scale p by using eq. S31.
  
• fig. S2. Fisher’s α for three different rainforests: Amazonia, Barro Colorado Nature Monument, and Caxiuana.
  
• fig. S3. Fit of an RSA consisting of a combination of an LS and a log-normal distribution.
  
• fig. S4. We have generated synthetic data from a combination of discrete distributions (a binomial distribution of parameters r = 40 and ξ = 0.8, a geometric distribution of parameter μ = 0.15, and a Poisson distribution with parameter λ = 15) and fit these data with one, three, and six NBs, respectively.
  
• fig. S5. Robustness of the method.
  
• fig. S6. Comparison between biodiversity estimators for Amazonia and BCI forests.
  
• fig. S7. Self-consistency test of our framework.
  
• fig. S8. Plot, in logarithmic scale, of the percentage p_pred% that one ought to sample to have a precision estimate of around 5% for the predicted percentage of hyper-rare species, that is, species with fewer than 1000 individuals at the global
  scale.
  
• table S1. Predicted number of singletons in the whole area of each tropical forest obtained by applying our method (NB method).
  
• table S2. Prediction of the total number of species obtained by applying both NB and LS methods to the forest generated according to an NB and distributed in 8900 × 8900 units according to two different modified Thomas processes with the
  same density of clusters ρ = 6 × 10⁻⁵ and different clump sizes σ = 15 and 200.
  
• table S3. Summary table of the most popular biodiversity estimators.
  
• table S4. Comparison between NB, LS, Chao_wor, and the Harte methods on empirical data.
  
• table S5. Comparison between the NB, LS, Chao_wor, and Harte methods on BCI empirical data.
  
• table S6. Number of species and singletons in 15 forests in our data set with the percentage p% (last column of the table) of surveyed area.
  
• Reference (54)

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