The number of detected species varied strongly between samples (fig. S1, B and C). To infer robust species richness patterns directly from raw observations (figs. S4 and S5), we split raw data into coarse environmental or geographic strata and repeatedly selected a certain number of samples at random, from each stratum. Determining the integral richness from the pooled samples, per stratum, served to depict richness patterns in the observational data. This approach, in part, ameliorates the problem of severe undersampling of richness by traditionally small sampling volumes (20).

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