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Figure S1 Bias and variability of parameter estimates from fitting Pareto and power function distributions to data from a truncated Pareto distribution.

Figure S2 Bias, standard deviation, and mean squared error of the MLE of the exponent &lgr;tp of the truncated Pareto distribution (left) and the bias-corrected MLE of the same exponent (right).

Figure S3 Bias, standard deviation, and mean squared error of an estimate of the exponent &lgr;tp of the truncated Pareto distribution, using 10 bins uniform on a logarithmic scale.

Figure S4 A straightforward adaptation of cdf fitting to the case where only taxon means &Mmacr; and population densities N are available (left), compared to a generalized method (right).

Figure S5 ISDE+1 as estimated by the generalized-cdf fitting method of Appendix S5 versus as estimated by the bin-based method of Methods.

Figure S6 (Left) Same as Fig. 3A, C, E but using the generalized-cdf estimator of ISDE.

Table S1 ISDE estimates for the 149 webs of this study.

Table S2 SMSDE and LSDRE estimates for the 149 webs of this study.

Appendix S1 Details of the derivation of the theory.

Appendix S2 Fitting the truncated Pareto distribution.

Appendix S3 Fitting a generalized truncated Pareto distribution.

Appendix S4 Pareto vs. truncated Pareto distributions.

Appendix S5 Estimating the individual size distribution exponent.

Appendix S6 Data.

Appendix S7 Other theories and mechanisms.

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Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.