Ecological Archives E094067A1
Kevin E. Mueller, David Tilman, Dario A. Fornara, Sarah E. Hobbie. 2013. Root depth distribution and the diversity–productivity relationship in a longterm grassland experiment. Ecology 94:787–793. http://dx.doi.org/10.1890/121399.1
Appendix A. Below we report the results from statistical models of root biomass (Table A1), the deeproot proportion (Table A2), and the difference between observed and expected deeproot proportions (Table A4). The deeproot proportions for monocultures of each focal species are given in Table A3. Figure A1 shows the median root biomass in each depth increment for each level of planted species richness. Figure A2 shows the correlations of deeproot proportion and the difference between observed and expected deeproot proportion with the abundance of legumes and C_{4} grasses (for plots planted with 16 species).
Table A1. Effects of plant functional composition and species richness on root biomass in two depth increments.

ROOT BIOMASS 0–30 cm 
ROOT BIOMASS 30–100 cm 


without no. of sp. as covariate 
with no. of sp. as covariate 
without no. of sp. as covariate 
with no. of sp. as covariate 

Factor 
% SS* 
P 
Sign# 
% SS* 
P 
Sign# 
% SS* 
P 
Sign# 
% SS* 
P 
Sign# 
C_{3} 
4 
0.0002 
+ 
1 
0.15 

0 
0.91 

2 
0.01 
 
C_{4} 
17 
<.0001 
+ 
10 
<.0001 
+ 
4 
0.0007 
+ 
1 
0.10 
+ 
Forb 
0 
0.33 

0 
0.27 

0 
0.52 

1 
0.05 
 
Legume 
9 
<.0001 
+ 
3 
0.0007 
+ 
26 
<.0001 
+ 
10 
<.0001 
+ 
C_{3} × C_{4} 
0 
0.69 

0 
0.36 

0 
0.65 

0 
0.85 

C_{3} × Forb 
1 
0.17 

0 
0.75 

0 
0.29 

0 
0.76 

C_{3} × Legume 
0 
0.23 

1 
0.05 
+ 
1 
0.22 

0 
0.78 

C_{4} × Forb 
1 
0.17 

1 
0.04 
 
0 
0.80 

0 
0.24 

C_{4} × Legume 
2 
0.01 
+ 
1 
0.05 
 
1 
0.11 

0 
0.42 

Forb × Legume 
0 
0.44 

1 
0.12 

0 
0.76 

0 
0.47 

no. of species 
na 
na 
na 
3 
0.0008 
+ 
na 
na 
na 
7 
<.0001 
+ 
model R² 
0.60 
0.63 
0.47 
0.54 

n 
152 
152 
152 
152 
*The % of total sumsofsquares (SS) for root biomass that can be uniquely attributed to each predictor variable.
#The sign (i.e., direction) of the effect for each model term is based on the sign of the model coefficient for that term.
†Number of species was modeled as a linear effect.
Table A2. Effects of plant functional composition and species richness on the deep root proportion. Similar results were obtained for models that excluded monoculture plots with two exceptions: the C_{3} × Legume interaction was not significant and C_{3} grass presence was not significant when species richness was not a covariate. The effect of species richness remained significant (P < 0.001) and positive when legume abundance was included in the model instead of legume presence.

without no. of sp. as covariate 
with no. of sp. as covariate 

Factor 
% SS* 
P 
Sign# 
% SS* 
P 
Sign# 
C_{3} 
3 
0.006 
 
7 
<.0001 
 
C_{4} 
0 
0.78 

0 
0.30 

Forb 
0 
0.84 

1 
0.08 
 
Legume 
28 
<.0001 
+ 
12 
<.0001 
+ 
C_{3} × C_{4} 
3 
0.01 
+ 
2 
0.04 
+ 
C_{3} × Forb 
0 
0.58 

0 
0.62 

C_{3} × Legume 
4 
0.004 
+ 
2 
0.03 
+ 
C_{4} × Forb 
0 
0.74 

0 
0.73 

C_{4} × Legume 
0 
1.00 

0 
0.50 

Forb × Legume 
0 
0.89 

0 
0.51 

no. of species† 
na 
na 

4 
0.0009 
+ 
model R² 
0.42 
0.47 

n 
152 
152 
*The percent of total sumsofsquares (SS) for deep root proportion that can be uniquely attributed to each predictor variable, using Type III sumsofsquares as described in the Methods.
#The sign (i.e., direction) of the effect for each model term is based on the sign of the model coefficient for that term.
†Number of species was modeled as a linear effect. Results were similar when number of species was modeled as a logarithmic effect and as a discrete parameter.
Table A3. Proportion of root biomass more than 30 cm below the soil surface (% deep roots) for thirteen species, or groups of similar species, used in estimating expected root depth distributions and functional diversity of root depth distributions.
Species 
Functional group 
Mean 
Median 
n 
SD 
Achillea millefolium 
forb 
9 
na 
1 
na 
Amorpha canescens / Petalostemum spp.* 
legume 
29 
na 
2 
25 
Andropogon gerardi 
C_{4} grass 
10 
na 
1 
na 
Koeleria cristata 
C_{3} grass 
1 
na 
2 
0.1 
Lespedeza capitata 
legume 
30 
27 
3 
9 
Liatris aspera 
forb 
20 
15 
3 
22 
Lupinus perennis 
legume 
31 
na 
1 
na 
Monarda fistulosa / Solidago rigida† 
forb 
21 
na 
2 
13 
Panicum virgatum 
C_{4} grass 
19 
na 
2 
12 
Petalostemum purpureum 
legume 
25 
24 
3 
5 
Poa pratensis 
C_{3} grass 
1 
na 
1 
na 
Schizachyrium scoparium 
C_{4} grass 
7 
4 
3 
7 
Sorghastrum nutans 
C_{4} grass 
16 
17 
3 
4 
*Some plots that were intended to be seeded with Petalostemum spp. were incidentally seeded with Amorpha canescens instead (www.cedarcreek.umn.edu).
†Solidago rigida did not germinate well the first year, so in the second year, Monarda fistulosa was seeded in those plots (Fargione et al. 2007).
Table A4. Effects of plant functional composition and species richness on the difference between the observed and expected fraction of total root biomass below 30 cm. Similar results were obtained when monoculture plots were excluded from the analyses. The effect of species richness remained significant (P < 0.001) and positive when legume abundance was included in the model instead of legume presence.

without no. of sp. as covariate 
with no. of sp. (linear) 
with no. of sp. (discrete) 

Factor 
% SS* 
P 
Sign# 
% SS* 
P 
Sign# 
% SS* 
P 
Sign# 
C_{3} 
0 
0.81 

2 
0.03 
 
4 
0.005 
 
C_{4} 
6 
0.001 
+ 
2 
0.07 
+ 
0 
0.52 

Forb 
0 
0.80 

3 
0.02 
 
4 
0.004 
 
Legume 
7 
0.0008 
+ 
1 
0.21 

0 
0.86 

C_{3} × C_{4} 
0 
0.99 

0 
0.64 

0 
0.67 

C_{3} × Forb 
1 
0.26 

0 
0.93 

0 
0.77 

C_{3} × Legume 
2 
0.07 
+ 
1 
0.27 

1 
0.14 

C_{4} × Forb 
2 
0.09 
+ 
1 
0.27 

1 
0.13 

C_{4} × Legume 
9 
<.0001 
+ 
6 
0.001 
+ 
7 
0.0003 
+ 
Forb × Legume 
0 
0.99 

0 
0.41 

0 
0.63 

no. of species 
na 
na 
na 
7 
0.0003 
+ 
10 
0.001 
na 
model R² 
0.29 
0.36 
0.39 

n 
137 
137 
137 
*The percent of total sumsofsquares (SS) of the dependent variable that can be uniquely attributed to each predictor variable, using Type III sumsofsquares as described in the Methods.
#The sign (i.e., direction) of the effect for each model term is based on the sign of the model coefficient for that term.
Fig. A1. Effects of species richness on root biomass. Panel A shows the median root biomass for each depth increment and species richness level. Panel B shows the relative effect of species richness on root biomass in each depth increment (i.e., the median root biomass of each richness level divided by that of monocultures). Note the median root biomass in the 30–60 and 60–100 cm depth increments of 16speciesplots is ~7 times that of monocultures.
Fig. A2. Correlations of the deeproot proportion and the difference between observed and expected root depth distributions with the proportion of aboveground biomass attributable to legumes and C_{4} grasses in plots planted with 16 species (n = 35). All correlations have P < 0.01. In these diverse plots, the relative abundances of legumes and C_{4} grasses were inversely correlated (R² = 0.49, P < 0.001). The relative abundance of the legume Lupinus perennis was also negatively correlated with the difference between observed and expected root depth distributions (n = 33, R² = 0.47, P < 0.001). To further evaluate these relationships, we included legume and C_{4} grass relative abundance along with species richness in a model of the differences between observed and expected root depth distributions (monocultures and twospecies plots were excluded because these plots often have a value of zero for the relative abundance of different functional groups). The relative abundance of C_{4} grasses was positively correlated with the difference between observed and expected root depth distributions (P = 0.01), especially when legume abundance was high (P < 0.01 for the interaction between C_{4} grass and legume relative abundance). The effect of C_{4} grass abundance did not depend on species richness (P = 0.25 for the interaction between C_{4} grass abundance and species richness) but the negative effect of legume relative abundance was only apparent at high species richness (P<0.05 for the interaction between legume abundance and species richness).
Literature cited
Fargione, J., D. Tilman, R. Dybzinski, J. HilleRisLambers, C. Clark, W. S. Harpole, J. M. H. Knops, P. B. Reich, and M. Loreau. 2007. From selection to complementarity: shifts in the causes of biodiversityproductivity relationships in a longterm biodiversity experiment. Proceedings of the Royal Society BBiological Sciences 274:871–876.