Appendix C. One table showing the experimental design and six tables providing the results of statistical analyses.
TABLE C1. Experimental design. Original (sown) species richnesss and functional-group composition of resident communities in the Jena Experiment.
| Species richnesss | 1 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
| grasses | 1 |
2 |
1 |
1 |
4 |
2 |
2 |
2 |
1 |
1 |
1 |
||||||||||||||
| small herbs | 1 |
2 |
1 |
1 |
4 |
2 |
2 |
1 |
1 |
2 |
1 |
||||||||||||||
| tall herbs | 1 |
2 |
1 |
1 |
4 |
2 |
2 |
1 |
2 |
1 |
1 |
||||||||||||||
| legumes | 1 |
2 |
1 |
1 |
4 |
2 |
2 |
1 |
2 |
1 |
1 |
||||||||||||||
| Replicates | 4 |
4 |
4 |
4 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
4 |
| Species richnesss | 8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
16 |
16 |
16 |
16 |
16 |
16 |
16 |
16 |
16 |
16 |
16 |
60 |
| grasses | 8 |
4 |
4 |
2 |
3 |
3 |
2 |
16 |
8 |
8 |
5 |
5 |
6 |
4 |
16 |
||||||||||
| small herbs | 8 |
4 |
4 |
3 |
3 |
2 |
2 |
8 |
8 |
6 |
5 |
6 |
4 |
12 |
|||||||||||
| tall herbs | 8 |
4 |
4 |
3 |
2 |
3 |
2 |
16 |
8 |
8 |
6 |
5 |
5 |
4 |
20 |
||||||||||
| legumes | 8 |
4 |
4 |
3 |
2 |
3 |
2 |
8 |
8 |
6 |
5 |
5 |
4 |
12 |
|||||||||||
| Replicates | 1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
4 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
4 |
4 |
TABLE C2. Analysis of variance (ANOVA) of the number of species and the biomass (gm-2) of internal invaders per functional group per harvest quadrat. Data exclude the 60-species level, because it always contains all four functional groups. The inclusion of resident biomass as a covariable did not change the significance of the results and was omitted from the model. "Species richnesss" stands for the log2-transformed sown species richnesss of the resident community. The deviation of the species richnesss effect from log-linearity was not significant and was omitted. The results were relatively robust to the order of the terms species richnesss and presence of particular functional groups, so only the results from the model with species richnesss tested first are shown. The presence of the four functional groups was tested in the order of their explanatory power in the model. Two- and three-way interactions of functional group effects were small and therefore were omitted from the model. The weeding and seed-addition treatments (c-, c+, and w+) were used to form two contrasts. Only the first of them ("Seed addition"), representing seed addition (c+ and w+) vs. no seed-addition treatments (c-), was included in the model (the contrast between w+ and c+ was not significant). The "Home-away contrast", which represents the main contrast within the total "Invader × resident FG" interactions was tested against its deviation ("Other invader-resident FG interactions"). Other error terms are printed in italics. FG = functional group.
Source |
Number of species |
Biomass |
||||||
df |
SS |
F |
P |
df |
SS |
F |
P |
|
Spatial variation |
9 |
51.1 |
3.01 |
0.005 |
9 |
619241 |
2.70 |
0.010 |
Species richnesss |
1 |
151.3 |
80.23 |
<0.001 |
1 |
815930 |
32.03 |
<0.001 |
Legume presence |
1 |
83.7 |
44.38 |
<0.001 |
1 |
302853 |
11.89 |
0.001 |
Tall herb presence |
1 |
18.7 |
9.89 |
0.003 |
1 |
85362 |
3.35 |
0.072 |
Grass presence |
1 |
0.1 |
0.05 |
0.827 |
1 |
31173 |
1.22 |
0.273 |
Small herb presence |
1 |
0.2 |
0.09 |
0.771 |
1 |
8594 |
0.34 |
0.563 |
Plot |
63 |
118.8 |
1.57 |
0.010 |
63 |
1604762 |
0.75 |
0.907 |
Invader FG |
3 |
154.1 |
42.67 |
<0.001 |
3 |
1602127 |
15.77 |
<0.001 |
Home-away contrast |
1 |
145.8 |
37.94 |
<0.001 |
1 |
2071215 |
6.50 |
0.027 |
Other invader-resident FG interactions |
11 |
42.3 |
3.19 |
<0.001 |
11 |
3506087 |
9.41 |
<0.001 |
Species richnesss × Home-away contrast |
1 |
4.5 |
1.77 |
0.205 |
1 |
15375 |
0.14 |
0.710 |
Species richnesss × Other invader-resident FG interactions |
14 |
35.2 |
2.09 |
0.014 |
14 |
1493090 |
3.15 |
<0.001 |
Plot × Invader FG |
201 |
242.0 |
2.88 |
<0.001 |
202 |
6841052 |
3.03 |
<0.001 |
Seed addition |
1 |
75.4 |
180.62 |
<0.001 |
1 |
93776 |
8.40 |
0.004 |
Species richnesss × Seed addition |
1 |
19.8 |
47.44 |
<0.001 |
1 |
15019 |
1.35 |
0.246 |
Legume presence × Seed addition |
1 |
19.6 |
46.91 |
<0.001 |
1 |
3215 |
0.29 |
0.591 |
Tall herb presence × Seed addition |
1 |
1.1 |
2.66 |
0.104 |
1 |
1568 |
0.14 |
0.708 |
Grass presence × Seed addition |
1 |
0.1 |
0.20 |
0.652 |
1 |
15890 |
1.42 |
0.233 |
Small herb presence × Seed addition |
1 |
0.0 |
0.09 |
0.770 |
1 |
62645 |
5.61 |
0.018 |
Invader FG × Seed addition |
3 |
13.9 |
11.07 |
<0.001 |
3 |
181883 |
5.43 |
<0.001 |
Home-away contrast × Seed addition |
1 |
13.6 |
20.41 |
<0.001 |
1 |
119186 |
6.65 |
0.026 |
Other invader-resident FG interactions × Seed addition |
11 |
7.3 |
1.59 |
0.097 |
11 |
197138 |
1.61 |
0.093 |
Plot × Invader FG × Subplot |
596 |
248.8 |
0.57 |
1.000 |
595 |
6639929 |
0.75 |
1.000 |
Year |
1 |
580.2 |
791.58 |
<0.001 |
1 |
2289985 |
154.69 |
<0.001 |
Plot × Invader FG × Subplot × Year |
901 |
660.4 |
2.49 |
<0.001 |
|
|
|
|
Residual |
944 |
278.3 |
|
|
921 |
13634455 |
0.65 |
1.000 |
TABLE C3. Analysis of variance (ANOVA) of the number of species of external invaders per harvest quadrat. Data exclude the 60-species level. The inclusion of resident biomass as a covariable did not change the significance of the results and was omitted from the model. "Species richnesss" stands for the log2-transformed sown species-richnesss of the resident community. The deviation of the species richnesss effect from log-linearity was not significant and was omitted. The results were relatively robust to the order of the terms species richnesss and presence of particular functional groups, so only the results from the model with species richnesss tested first are shown. The presence of the four functional groups was tested in the order of their explanatory power in the model. Two- and three-way interactions of functional group effects were small and were therefore omitted from the model. All error terms are printed in italics.
|
df |
SS |
F |
P |
Spatial variation |
9 |
10.3663 |
0.88 |
0.549 |
Species richnesss |
1 |
28.9082 |
22.03 |
<0.001 |
Legume presence |
1 |
10.9671 |
8.36 |
0.005 |
Small herb presence |
1 |
6.0697 |
4.63 |
0.035 |
Tall herb presence |
1 |
0.0013 |
0.00 |
0.975 |
Grass presence |
1 |
0.2808 |
0.21 |
0.645 |
Plot |
67 |
87.9229 |
4.12 |
<0.001 |
Seed addition |
1 |
0.823 |
2.58 |
0.112 |
Species richnesss × Seed addition |
1 |
0.6031 |
1.89 |
0.173 |
Legume presence × Seed addition |
1 |
0.0001 |
0.00 |
0.986 |
Small herb presence × Seed addition |
1 |
1.2136 |
3.81 |
0.055 |
Tall herb presence × Seed addition |
1 |
0.7482 |
2.35 |
0.130 |
Grass presence × Seed addition |
1 |
0.044 |
0.14 |
0.711 |
Plot × Subplot |
76 |
24.2346 |
1.18 |
0.190 |
Year |
1 |
2.686 |
9.97 |
0.002 |
Species richnesss × Year |
1 |
1.0648 |
3.95 |
0.049 |
Legume presence × Year |
1 |
2.732 |
10.14 |
0.002 |
Small herb presence × Year |
1 |
2.3659 |
8.78 |
0.004 |
Tall herb presence × Year |
1 |
0.0043 |
0.02 |
0.900 |
Grass presence × Year |
1 |
0.3525 |
1.31 |
0.255 |
Seed addition × Year |
1 |
0.1736 |
0.64 |
0.423 |
Plot × Subplot Year |
155 |
41.7673 |
0.91 |
0.713 |
Residual |
160 |
47.1871 |
|
|
TABLE C4. Analysis of variance (ANOVA) of the biomass (gm-2) of external invaders per harvest quadrat. Data exclude the 60-species level. The inclusion of resident biomass as a covariable did not change the significance of the results and was omitted from the model. "Species richnesss" stands for the log2-transformed sown species richnesss of the resident community. The deviation of the species-richnesss effect from log-linearity was not significant and was omitted. The results were relatively robust to the order of the terms species richnesss and presence of particular functional groups, so only the results from the model with species richnesss tested first are shown. The presence of the four functional groups was tested in the order of their explanatory power in the model. Two- and three-way interactions of functional group effects were small and were therefore omitted from the model. All error terms are printed in italics.
|
df |
SS |
F |
P |
Spatial variation |
9 |
42165 |
1.66 |
0.115 |
Species richnesss |
1 |
38314 |
13.61 |
<0.001 |
Grass presence |
1 |
4248 |
1.51 |
0.224 |
Small herb presence |
1 |
3561 |
1.26 |
0.265 |
Legume presence |
1 |
4541 |
1.61 |
0.209 |
Tall herb presence |
1 |
0 |
0.00 |
1.000 |
Plot |
67 |
188639 |
1.58 |
0.027 |
Seed addition |
1 |
1522 |
0.85 |
0.359 |
Species richnesss × Seed addition |
1 |
1535 |
0.86 |
0.357 |
Grass presence × Seed addition |
1 |
31 |
0.02 |
0.896 |
Small herb presence × Seed addition |
1 |
570 |
0.32 |
0.574 |
Legume presence × Seed addition |
1 |
763 |
0.43 |
0.515 |
Tall herb presence × Seed addition |
1 |
4455 |
2.49 |
0.118 |
Plot × Subplot |
76 |
135726 |
2.61 |
<0.001 |
Year |
1 |
5827 |
8.53 |
0.004 |
Species richnesss × Year |
1 |
3751 |
5.49 |
0.020 |
Grass presence × Year |
1 |
230 |
0.34 |
0.563 |
Small herb presence × Year |
1 |
634 |
0.93 |
0.337 |
Legume presence × Year |
1 |
39 |
0.06 |
0.811 |
Tall herb presence × Year |
1 |
2636 |
3.86 |
0.051 |
Seed addition × Year |
1 |
778 |
1.14 |
0.288 |
Plot × Subplot Year |
155 |
105942 |
0.31 |
1 |
Residual |
160 |
353360 |
|
|
TABLE C5. Analysis of variance (ANOVA) of the total number of species per harvest quadrat and of community biomass (gm-2). Target species were residents in weeded controls (w-), but residents, external and internal invaders in non-weeded subplots (c- and c+). "Species richnesss" is the sown species richnesss of the resident community. The weeding and seed-addition treatments (w-, c- and c+) were used to form two contrasts. The first of them ("Invasion") represents weeded controls (w-) vs. invasion treatments (c- and c+), the second ("Seed addition") represents non-weeded treatments without seed addition (c-) vs. with seed addition (c+). Error terms are printed in italics.
Source |
Number of species |
Biomass |
||||||
df |
SS |
F |
P |
df |
SS |
F |
P |
|
Spatial variation |
9 |
1100.7 |
9.05 |
<0.001 |
9 |
4440201 |
1.16 |
0.333 |
Species richnesss (log2) |
1 |
3655.3 |
270.36 |
<0.001 |
1 |
12139477 |
28.63 |
<0.001 |
Species richnesss (deviation from log-linear) |
4 |
1206.8 |
22.32 |
<0.001 |
4 |
1651207 |
0.97 |
0.428 |
Plot |
67 |
905.8 |
3.28 |
<0.001 |
67 |
28408418 |
5.88 |
<0.001 |
Invasion |
1 |
2915.7 |
706.83 |
<0.001 |
1 |
5018898 |
69.59 |
<0.001 |
Seed addition |
1 |
203.5 |
49.34 |
<0.001 |
1 |
251564 |
3.49 |
0.064 |
Species richnesss (log2) × Invasion |
1 |
289.2 |
70.10 |
<0.001 |
1 |
1080842 |
14.99 |
<0.001 |
Species richnesss (deviation from log-linear) × Invasion |
4 |
0.8 |
0.05 |
0.995 |
4 |
445103 |
1.54 |
0.193 |
Species richnesss (log2) × Seed addition |
1 |
40.2 |
9.75 |
0.002 |
1 |
65241 |
0.90 |
0.343 |
Species richnesss (deviation from log-linear) × Seed addition |
4 |
20.2 |
1.22 |
0.303 |
4 |
256648 |
0.89 |
0.472 |
Plot × Subplot |
150 |
618.8 |
0.99 |
0.522 |
150 |
10818315 |
0.75 |
0.970 |
Year |
1 |
663.5 |
159.32 |
<0.001 |
1 |
8354184 |
87.12 |
<0.001 |
Species richnesss (log2) × Year |
1 |
246.6 |
59.20 |
<0.001 |
1 |
38361 |
0.40 |
0.528 |
Species richnesss (deviation from log-linear) × Year |
4 |
36.3 |
2.18 |
0.072 |
4 |
1745162 |
4.55 |
0.001 |
Invasion × Year |
1 |
357.2 |
85.75 |
<0.001 |
1 |
1586364 |
16.54 |
<0.001 |
Seed addition × Year |
1 |
114.4 |
27.46 |
<0.001 |
1 |
61793 |
0.64 |
0.423 |
Species richnesss (log2) × Invasion × Year |
1 |
87.4 |
20.98 |
<0.001 |
1 |
59669 |
0.62 |
0.431 |
Species richnesss (deviation from log-linear) × Invasion × Year |
4 |
7.2 |
0.43 |
0.787 |
4 |
203245 |
0.53 |
0.714 |
Species richnesss (log2) × Seed addition × Year |
1 |
12.6 |
3.02 |
0.084 |
1 |
87566 |
0.91 |
0.340 |
Species richnesss (deviation from log-linear) × Seed addition × Year |
4 |
5.2 |
0.31 |
0.868 |
4 |
291002 |
0.76 |
0.553 |
Plot × Subplot × Year |
224 |
932.9 |
2.13 |
<0.001 |
224 |
21480355 |
1.41 |
0.005 |
Residual |
242 |
472.5 |
|
|
242 |
16501297 |
|
|
TABLE C6. Analysis of variance (ANOVA) of community biomass, including the effect of observed (=realized) species richnesss. Target species were residents in weeded controls (w-), but residents, external and internal invaders in non-weeded subplots (c- and c+). The influence of "realized species richnesss (log2-transformed)" on community biomass was tested against the interaction "Plot × Subplot × Year". The weeding and seed-addition treatments (w-, c-, and c+) were used to form two contrasts. The first of them ("Invasion") represents weeded controls (w-) vs. non-weeded treatments (c- and c+), the second ("Seed addition") represents non-weeded treatments without seed addition (c-) vs. with seed addition (c+). Error terms are printed in italics.
Source |
df |
SS |
F |
P |
Spatial variation |
9 |
4085251 |
6.00 |
0.307 |
realized richness (log2) |
1 |
15619722 |
160.67 |
<0.001 |
Plot |
72 |
36869246 |
6.83 |
<0.001 |
Invasion |
1 |
75710 |
1.01 |
0.316 |
Seed addition |
1 |
27015 |
0.36 |
0.549 |
realized richness (log2) × Invasion |
1 |
557075 |
5.73 |
0.017 |
realized richness (log2) × Seed addition |
1 |
658371 |
6.77 |
0.010 |
Plot × Subplot |
160 |
11987260 |
0.77 |
0.962 |
Year |
1 |
3874550 |
39.85 |
<0.001 |
realized richnesss (log2) × Year |
1 |
1850417 |
19.03 |
<0.001 |
Invasion × Year |
1 |
1347 |
0.01 |
0.906 |
Seed addition × Year |
1 |
15993 |
0.16 |
0.685 |
realized richness (log2) × Invasion × Year |
1 |
563858 |
5.80 |
0.017 |
realized richness (log2) × Seed addition × Year |
1 |
85679 |
0.88 |
0.349 |
Plot × Subplot × Year |
239 |
23234778 |
1.55 |
<0.001 |
Residual |
233 |
14571877 |
|
|
TABLE C7. Analysis of variance (ANOVA) of the community biomass, including the effect of observed (=realized) functional-group proportions. In this analysis, external invaders were excluded because they could not be grouped into the respective functional groups, so target species in this case were residents in weeded controls (w-), but residents and internal invaders in non-weeded subplots (c- and c+). Three outliers with very high biomass were excluded. The realized functional-group proportions were included in the model in the order of their explanatory power and their influence was tested against the "Residual". The weeding and seed-addition treatments (w-, c-, and c+) were used to form two contrasts. The first of them ("Invasion") represents weeded controls (w-) vs. non-weeded treatments (c- and c+), the second ("Seed addition") represents non-weeded treatments without seed addition (c-) vs. with seed addition (c+). Error terms are printed in italics.
Source |
df |
SS |
F |
P |
Spatial variation |
9 |
2609852 |
2.10 |
0.041 |
Proportion of legumes |
1 |
4847743 |
80.23 |
<0.001 |
Proportion of small herbs |
1 |
1161391 |
19.22 |
<0.001 |
Proportion of grasses |
1 |
1483 |
0.02 |
0.876 |
Plot |
72 |
9961269 |
2.29 |
<0.001 |
Invasion |
1 |
3875505 |
64.14 |
<0.001 |
Seed addition |
1 |
142731 |
2.36 |
0.126 |
Proportion of legumes × Invasion |
1 |
924491 |
15.30 |
<0.001 |
Proportion of small herbs × Invasion |
1 |
41616 |
0.69 |
0.408 |
Proportion of grasses × Invasion |
1 |
256598 |
4.25 |
0.041 |
Proportion of legumes × Seed addition |
1 |
39499 |
0.65 |
0.420 |
Proportion of small herbs × Seed addition |
1 |
9209 |
0.15 |
0.697 |
Proportion of grasses × Seed addition |
1 |
410 |
0.01 |
0.934 |
Residual |
147 |
8882268 |
|
|