Fig. 1 Four theoretical abundance distributions fitted, using a consistent criterion (see Materials and Methods), to a data set for bats from Los Tuxtlas Biological Research Station (32), which has exceptionally high species richness and is very well sampled. Frequency distribution coverage based on Good’s index [Eq. 8 in (26)] is 0.9990. (A) Double geometric distribution. (B) Lognormal distribution. (C) Geometric series distribution. (D) Log series distribution. The line is jagged at low abundances because predicted values are rounded to the nearest integer.
Fig. 2 Characteristic rank abundance distributions of four disparate taxonomic groups in tropical and temperate zones. Each value is the median proportional abundance at the appropriate position in the rank abundance distribution. Data are truncated at the point where the median falls to 0. Patterns are similar for the remaining groups (fig. S2). Thick lines, tropical zone data; thin lines, temperate zone data. (A) Trees. (B) Bats. (C) Frogs. (D) Dung beetles.
Fig. 3 Predicted and actual dominance (frequency of the most common species) in 1055 ecological samples, including trees (97), bats (159), small terrestrial mammals (161), birds (119), lizards (77), frogs (110), ants (77), dung beetles (115), butterflies (83), and odonates (57). (A) Double geometric distribution. (B) Lognormal distribution. (C) Geometric series distribution. (D) Log series distribution.
- Table 1 Regressions of actual dominance on predicted dominance (Fig. 3) and median offsets between actual and predicted dominance based on the fit of six theoretical abundance distributions to the full data set.
The double geometric outperforms all other models with respect to the slope, intercept, and offset.
Distribution Correlation Slope Intercept Offset Double geometric 0.9497 0.9940 0.0089 −0.0019 Lognormal 0.9732 1.0327 −0.0439 0.0314 Geometric series 0.9045 0.9214 0.0614 −0.0285 Log series 0.9483 1.0144 −0.0286 0.0162 Broken stick 0.6612 1.0392 0.1260 −0.1044 Zipf 0.9124 1.0764 −0.1520 0.1303 - Table 2 Regressions of actual median abundance on predicted median abundance (Fig. 4) and median ratios between actual and predicted median abundance based on the fit of six theoretical abundance distributions to the full data set.
The double geometric outperforms all other models with respect to the slope, intercept, and ratio.
Distribution Correlation Slope Intercept Ratio Double geometric 0.9496 1.0340 −0.0011 0.9783 Lognormal 0.9473 1.0901 −0.0042 1.0931 Geometric series 0.9442 1.2471 −0.0025 0.8604 Log series 0.9339 1.3473 −0.0062 0.9758 Broken stick 0.7801 0.7689 −0.0089 1.9864 Zipf 0.8885 2.1048 −0.0026 0.5615
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/8/e1500082/DC1
Fig. S1. Four theoretical abundance distributions fitted to a data set for birds from Poland (33), which has the highest species richness of any complete sample for this group included in this analysis.
Fig. S2. Characteristic rank abundance distributions of six additional taxonomic groups in tropical and temperate zones based on Fig. 2.
Fig. S3. Predicted and actual dominance in four disparate groups based on the double geometric distribution.
Fig. S4. Predicted and actual dominance in six additional groups based on the double geometric distribution.
Fig. S5. Predicted and actual median relative abundances in four disparate groups based on the double geometric distribution.
Fig. S6. Predicted and actual median relative abundances in six additional groups based on the double geometric distribution.
Fig. S7. Predicted and actual dominance and median relative abundance based on the broken stick and Zipf distributions.
Fig. S8. Mean and median abundances observed in relatively well-sampled distributions.
Table S1. Medians of the fit of the six theoretical abundance distributions to observed frequencies as measured by K-L divergence statistics.
Table S2. Means of the fit of the six theoretical abundance distributions to observed frequencies.
Table S3. Results of tests for differences between distributions of K-L divergence statistics.
Appendix S1. R code used to perform the analyses.
Reference (33)
Additional Files
Supplementary Materials
This PDF file includes:
- Fig. S1. Four theoretical abundance distributions fitted to a data set for birds from Poland (33), which has the highest species richness of any complete sample for this group included in this analysis.
- Fig. S2. Characteristic rank abundance distributions of six additional taxonomic groups in tropical and temperate zones based on Fig. 2.
- Fig. S3. Predicted and actual dominance in four disparate groups based on the double geometric distribution.
- Fig. S4. Predicted and actual dominance in six additional groups based on the double geometric distribution.
- Fig. S5. Predicted and actual median relative abundances in four disparate groups based on the double geometric distribution.
- Fig. S6. Predicted and actual median relative abundances in six additional groups based on the double geometric distribution.
- Fig. S7. Predicted and actual dominance and median relative abundance based on the broken stick and Zipf distributions.
- Fig. S8. Mean and median abundances observed in relatively well-sampled distributions.
- Table S1. Medians of the fit of the six theoretical abundance distributions to observed frequencies as measured by K-L divergence statistics.
- Table S2. Means of the fit of the six theoretical abundance distributions to observed frequencies.
- Table S3. Results of tests for differences between distributions of K-L divergence statistics.
- Appendix S1. R code used to perform the analyses.
- Reference (33)
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