Appendix A. Supporting information for model comparisons.
FIG. A1. Structural equation models tested for combinations of functional diversity (FD), phylogenetic diversity (PD), and functional group richness (FGR) in combination with species richness (S) as predictors of the biodiversity effect on aboveground biomass accumulation (LRmean). Models were constructed to represent the effect of PD, FD, or FGR on the biodiversity effect as functions of S, since the indices used here are inherently dependent on S to some extent. That is, the PD and FD indices used here can only remain flat or increase as a species is added to a community. Model 5 shows one of many alternatives where PD and FD do not depend on S; note that this model is consistently the poorest-fitting of the candidate models (Table 3). These models were chosen to test the degree to which PD and FD predict the biodiversity effect, taking into account the correlations between these metrics and species richness.
FIG. A2. Relationship between PD (based on the molecular phylogeny) and FD (based on leaf %N, mean height at maturity, and N-fixing ability) within species richness levels. For species richnesses greater than 8 for this data set, there is no variation in species composition and thus FD and PD do not vary within a species richness level.
FIG. A3. Residuals of linear models of PD (based on the molecular phylogeny) and FD (N, height, N-fixation) as a function of S. After removing the effect of species richness, a statistically significant (P < 0.001) but quite minor relationship can be found between PD and FD (R2 = 0.024).
FIG. A4. Phylogeny extracted from the angiosperm supertree of Davies et al. (2004), showing variation in trait values for the functional traits used in this study. White boxes indicate no data were available. Major families for the 121 species used in this study are indicated at the right.
TABLE A1. Sources of grassland biodiversity and aboveground biomass production data. "Used polycultures" refers to polycultures for which LRmean could be calculated (1,433 out of 1,593 polycultures).
Study | Experiment |
Total polycultures |
Used polycultures |
BioCON / Reich et al. 2001 | +C +N | 57 | 57 |
BioCON / Reich et al. 2001 | +C N | 57 | 57 |
BioCON / Reich et al. 2001 | C +N | 58 | 58 |
BioCON / Reich et al. 2001 | C N | 59 | 59 |
Biodepth / Spehn et al. 2005 | Germany | 30 | 16 |
Biodepth / Spehn et al. 2005 | Greece | 6 | 6 |
Biodepth / Spehn et al. 2005 | Ireland | 50 | 46 |
Biodepth / Spehn et al. 2005 | Portugal | 28 | 23 |
Biodepth / Spehn et al. 2005 | Sheffield | 30 | 30 |
Biodepth / Spehn et al. 2005 | Silwood | 32 | 30 |
Biodepth / Spehn et al. 2005 | Sweden | 34 | 34 |
Biodepth / Spehn et al. 2005 | Switzerland | 28 | 14 |
Dimitrakopoulos and Schmid 2004 | Large pot size | 20 | 20 |
Dimitrakopoulos and Schmid 2004 | Medium pot size | 20 | 20 |
Dimitrakopoulos and Schmid 2004 | Small pot size | 20 | 20 |
Dukes 2001 | - | 40 | 16 |
Fridley 2002 | Amb. nut. | 50 | 50 |
Fridley 2002 | High nut. | 49 | 49 |
Fridley 2002 | Low nut. | 47 | 47 |
Fridley 2003 | High nut./High light | 42 | 42 |
Fridley 2003 | High nut./low light | 42 | 42 |
Fridley 2003 | Low nut./High light | 42 | 42 |
Fridley 2003 | Low nut./low light | 42 | 42 |
Lanta and Leps 2006 | High nut. | 58 | 58 |
Lanta and Leps 2006 | Low nut. | 58 | 58 |
Naeem et al. 1996 | - | 330 | 117 |
Naeem et al. 1999 | - | 117 | 330 |
Tilman et al. 1996 | - | 127 | 6 |
Tilman et al. 1997 | - | 148 | 44 |
TABLE A2. Summary of the best-fit structural equation models for each of the three subsets of data examined, when using PD values based on the highly-resolved molecular phylogeny which covered most species, or based on the supertree which covered all species. Model M8 includes a correlation between PD and FD, and was the most parsimonious model across all plots when PD was calculated from either phylogeny. Model M3 is identical to M8 except for the correlation between PD and FD.
Using PD from molecular phylogeny (110 species) | Using PD from angiosperm supertree (121 species) | ||||||||
All: M8 | All: M8 | ||||||||
Path | Estimate | S.E. | z | P | Path | Estimate | S.E. | z | P |
S → PD | 0.920 | 0.012 | 77.34 | < 0.001 | S → PD | 0.914 | 0.011 | 84.98 | < 0.001 |
S → FD | 0.471 | 0.027 | 17.60 | < 0.001 | S → FD | 0.627 | 0.021 | 30.47 | < 0.001 |
PD → B | 0.194 | 0.034 | 5.79 | < 0.001 | PD → B | 0.191 | 0.032 | 5.98 | < 0.001 |
FD → B | 0.096 | 0.034 | 2.87 | 0.004 | FD → B | 0.141 | 0.032 | 4.42 | < 0.001 |
S ↔ S | 1.000 | 0.043 | 23.31 | < 0.001 | S ↔ S | 1.000 | 0.037 | 26.75 | < 0.001 |
B ↔ B | 0.935 | 0.040 | 23.31 | < 0.001 | B ↔ B | 0.911 | 0.034 | 26.75 | < 0.001 |
PD ↔ PD | 0.154 | 0.007 | 23.28 | < 0.001 | PD ↔ PD | 0.165 | 0.006 | 26.72 | < 0.001 |
FD ↔ FD | 0.778 | 0.033 | 23.30 | < 0.001 | FD ↔ FD | 0.607 | 0.023 | 26.75 | < 0.001 |
PD ↔ FD | 0.053 | 0.011 | 5.02 | < 0.001 | PD ↔ FD | 0.038 | 0.008 | 4.52 | < 0.001 |
No legumes: M3 | No legumes: M8 | ||||||||
Path | Estimate | S.E. | z | P | Path | Estimate | S.E. | z | P |
S → PD | 0.927 | 0.016 | 59.63 | < 0.001 | S → PD | 0.904 | 0.016 | 56.80 | < 0.001 |
S → FD | 0.718 | 0.029 | 24.90 | < 0.001 | S → FD | 0.704 | 0.026 | 26.67 | < 0.001 |
PD → B | 0.099 | 0.055 | 1.79 | 0.074 | PD → B | 0.102 | 0.049 | 2.07 | 0.039 |
FD → B | 0.110 | 0.055 | 1.98 | 0.048 | FD → B | 0.117 | 0.049 | 2.37 | 0.018 |
S ↔ S | 1.000 | 0.059 | 17.07 | < 0.001 | S ↔ S | 1.000 | 0.052 | 19.05 | < 0.001 |
B ↔ B | 0.964 | 0.056 | 17.07 | < 0.001 | B ↔ B | 0.959 | 0.050 | 19.05 | < 0.001 |
PD ↔ PD | 0.141 | 0.008 | 17.05 | < 0.001 | PD ↔ PD | 0.184 | 0.010 | 19.03 | < 0.001 |
FD ↔ FD | 0.485 | 0.028 | 17.07 | < 0.001 | FD ↔ FD | 0.505 | 0.027 | 19.04 | < 0.001 |
PD ↔ FD | 0.042 | 0.011 | 3.67 | < 0.001 | |||||
Fertilized: M3 | Fertilized: M3 | ||||||||
Path | Estimate | S.E. | z | P | Path | Estimate | S.E. | z | P |
S → PD | 0.930 | 0.025 | 36.82 | < 0.001 | S → PD | 0.914 | 0.023 | 39.45 | < 0.001 |
S → FD | 0.800 | 0.041 | 19.35 | < 0.001 | S → FD | 0.870 | 0.028 | 30.76 | < 0.001 |
PD → B | 0.187 | 0.094 | 1.99 | 0.047 | PD → B | 0.159 | 0.089 | 1.80 | 0.072 |
FD → B | 0.233 | 0.094 | 2.48 | 0.013 | FD → B | 0.201 | 0.089 | 2.27 | 0.023 |
S ↔ S | 1.000 | 0.097 | 10.27 | < 0.001 | S ↔ S | 1.000 | 0.081 | 12.35 | < 0.001 |
B ↔ B | 0.847 | 0.082 | 10.27 | < 0.001 | B ↔ B | 0.883 | 0.072 | 12.35 | < 0.001 |
PD ↔ PD | 0.135 | 0.013 | 10.26 | < 0.001 | PD ↔ PD | 0.164 | 0.013 | 12.33 | < 0.001 |
FD ↔ FD | 0.361 | 0.035 | 10.27 | < 0.001 | FD ↔ FD | 0.244 | 0.020 | 12.34 | < 0.001 |
LITERATURE CITED
Davies, T. J., T. G. Barraclough, M. W. Chase, P. S. Soltis, D. E. Soltis, and V. Savolainen. 2004. Darwin's abominable mystery: Insights from a supertree of the angiosperms. Proceedings of the National Academy of Sciences of the United States of America 101:1904–1909.