Supplementary information for
Diversity of protists and bacteria determines predation performance and stability
Muhammad Saleem1+, Ingo Fetzer1#, Hauke Harms1 and Antonis Chatzinotas
The supplementary file includes detailed reports of the statistical tests used in all figures (main and supplementary figures) of this paper.
Detailed Statistical Report of Figure 1
(Fig 1a) General Regression Analysis:
1. Bacterial Species Richness versus Poterioochromonas sp. production (cells/ml)
Regression Equation
Richness = 2.46722 + 3.00889e-006 Poterioochromonas sp. production(cells/ml)
Coefficients
Term Coef SE Coef T P
Constant 2.46722 0.132451 18.6275 0.000
Pot. production (cells/ml) 0.00000 0.000002 1.4732 0.144
Summary of Model
S = 1.03934 R-Sq = 2.33% R-Sq(adj) = 1.26%
PRESS = 106.610 R-Sq(pred) = -5.93%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 2.344 2.3444 2.34445 2.17033 0.144147
Och production(cells/ml) 1 2.344 2.3444 2.34445 2.17033 0.144147
Error 91 98.301 98.3007 1.08023
Lack-of-Fit 46 55.217 55.2174 1.20038 1.25378 0.224721
Pure Error 45 43.083 43.0833 0.95741
Total 92 100.645
Fits and Diagnostics for Unusual Observations
Obs Richness Fit SE Fit Residual St Resid
1 1 3.33378 0.522459 -2.33378 -2.59748 R X
79 4 2.94563 0.270178 1.05437 1.05058 X
83 4 3.33378 0.522459 0.66622 0.74150 X
91 5 2.58758 0.107877 2.41242 2.33372 R
92 5 2.53041 0.113041 2.46959 2.39030 R
93 5 2.53642 0.111877 2.46358 2.38418 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
2. Bacterial Species Richness versus Acanthamoeba sp. production (cells/ml)
Regression Equation
Richness = 1.79773 + 1.89071e-005 Acanthamoeba sp. production cell No/ml
Coefficients
Term Coef SE Coef T P
Constant 1.79773 0.241567 7.44194 0.000
Ac cell No/ml 0.00002 0.000005 3.57621 0.001
Summary of Model
S = 0.984737 R-Sq = 12.32% R-Sq(adj) = 11.36%
PRESS = 92.1872 R-Sq(pred) = 8.40%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 12.402 12.4019 12.4019 12.7893 0.000561
Ac cell No/ml 1 12.402 12.4019 12.4019 12.7893 0.000561
Error 91 88.243 88.2433 0.9697
Lack-of-Fit 44 39.060 39.0600 0.8877 0.8483 0.707944
Pure Error 47 49.183 49.1833 1.0465
Total 92 100.645
Fits and Diagnostics for Unusual Observations
Obs Richness Fit SE Fit Residual St Resid
31 2 3.40483 0.252073 -1.40483 -1.47578 X
36 2 3.53718 0.286301 -1.53718 -1.63149 X
49 3 3.49937 0.276449 -0.49937 -0.52836 X
52 3 3.61281 0.306151 -0.61281 -0.65476 X
53 3 3.40483 0.252073 -0.40483 -0.42528 X
85 4 3.49937 0.276449 0.50063 0.52969 X
91 5 2.61073 0.102458 2.38927 2.43954 R
92 5 2.62964 0.103027 2.37036 2.42038 R
93 5 2.53511 0.102903 2.46489 2.51688 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
3. Bacterial Species Richness versus Tetrahymena sp. production (cells/ml)
Regression Equation
Richness = 1.65257 + 7.96378e-006 Tetrahymena sp. production (cells/ml)
Coefficients
Term Coef SE Coef T P
Constant 1.65257 0.235272 7.02408 0.000
Tet cell No/ml 0.00001 0.000002 4.35052 0.000
Summary of Model
S = 0.956851 R-Sq = 17.22% R-Sq(adj) = 16.31%
PRESS = 86.7413 R-Sq(pred) = 13.81%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 17.329 17.3289 17.3289 18.9271 0.000035
Tet cell No/ml 1 17.329 17.3289 17.3289 18.9271 0.000035
Error 91 83.316 83.3162 0.9156
Lack-of-Fit 71 63.650 63.6496 0.8965 0.9117 0.627778
Pure Error 20 19.667 19.6667 0.9833
Total 92 100.645
Fits and Diagnostics for Unusual Observations
Obs Richness Fit SE Fit Residual St Resid
12 1 2.90288 0.123818 -1.90288 -2.00555 R
87 4 3.81075 0.299652 0.18925 0.20826 X
91 5 2.70378 0.103179 2.29622 2.41384 R
92 5 3.06215 0.148642 1.93785 2.05012 R
93 5 3.66740 0.268783 1.33260 1.45112 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
4. Bacterial Species Richness versus predator production (cells/ml) in multiple predation experiment
Regression Equation
Richness = 3.00231 - 1.69916e-006 Multiple predation production(cells/ml)
Coefficients
Term Coef SE Coef T P
Constant 3.00231 0.237974 12.6161 0.000
Multiple -0.00000 0.000001 -1.9827 0.050
Summary of Model
S = 1.02966 R-Sq = 4.14% R-Sq(adj) = 3.09%
PRESS = 101.253 R-Sq(pred) = -0.60%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 4.168 4.1675 4.16754 3.93093 0.050422
Multiple 1 4.168 4.1675 4.16754 3.93093 0.050422
Error 91 96.478 96.4776 1.06019
Lack-of-Fit 81 81.478 81.4776 1.00590 0.67060 0.842216
Pure Error 10 15.000 15.0000 1.50000
Total 92 100.645
Fits and Diagnostics for Unusual Observations
Obs Richness Fit SE Fit Residual St Resid
14 1 1.94713 0.336894 -0.94713 -0.97343 X
15 1 1.83499 0.390952 -0.83499 -0.87658 X
91 5 2.80181 0.154413 2.19819 2.15929 R
92 5 2.74744 0.135930 2.25256 2.20700 R
93 5 2.80861 0.156907 2.19139 2.15343 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
(Fig 1b) General Regression Analysis:
1. Bacterial Species Richness versus coefficient of variation (CV) of Poterioochromonas sp. production (cells/ml)
Regression Equation
Richness = 5.89781 - 3.4189 OCH CV
Coefficients
Term Coef SE Coef T P
Constant 5.89781 0.96543 6.10899 0.009
OCH CV -3.41890 1.04593 -3.26876 0.047
Summary of Model
S = 0.854832 R-Sq = 78.08% R-Sq(adj) = 70.77%
PRESS = 5.70593 R-Sq(pred) = 42.94%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 7.8078 7.80779 7.80779 10.6848 0.0468207
OCH CV 1 7.8078 7.80779 7.80779 10.6848 0.0468207
Error 3 2.1922 2.19221 0.73074
Total 4 10.0000
Fits and Diagnostics for Unusual Observations
No unusual observations
2. Bacterial Species Richness versus coefficient of variation (CV) of Acanthamoeba sp. production (cells/ml)
Regression Equation
Richness = 5.76896 - 7.65313 CV of Acanthamoeba sp. production
Coefficients
Term Coef SE Coef T P
Constant 5.76896 1.14011 5.06001 0.015
AC CV -7.65313 2.89792 -2.64090 0.078
Summary of Model
S = 1.00128 R-Sq = 69.92% R-Sq(adj) = 59.90%
PRESS = 35.6304 R-Sq(pred) = -256.30%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 6.9923 6.99229 6.99229 6.97436 0.0775960
AC CV 1 6.9923 6.99229 6.99229 6.97436 0.0775960
Error 3 3.0077 3.00771 1.00257
Total 4 10.0000
Fits and Diagnostics for Unusual Observations
No unusual observations
3. Bacterial Species Richness versus coefficient of variation (CV) of Tetrahymena sp. production (cells/ml)
Regression Equation
Richness = 7.58338 - 11.1653 CV of Tetrahymenasp. production
Coefficients
Term Coef SE Coef T P
Constant 7.5834 1.55474 4.87760 0.016
Tet CV -11.1653 3.65796 -3.05232 0.055
Summary of Model
S = 0.901060 R-Sq = 75.64% R-Sq(adj) = 67.52%
PRESS = 7.62180 R-Sq(pred) = 23.78%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 7.5643 7.56427 7.56427 9.31665 0.0553268
Tet CV 1 7.5643 7.56427 7.56427 9.31665 0.0553268
Error 3 2.4357 2.43573 0.81191
Total 4 10.0000
Fits and Diagnostics for Unusual Observations
No unusual observations
3. Bacterial Species Richness versus coefficient of variation (CV) of predator production (cells/ml) in multiple predation experiment
Regression Equation
Richness = 5.11627 - 4.74076 CV of predator production (cells/ml) in multiple predation experiment
Coefficients
Term Coef SE Coef T P
Constant 5.11627 1.91567 2.67075 0.076
Mul CV -4.74076 4.01640 -1.18035 0.323
Summary of Model
S = 1.50872 R-Sq = 31.71% R-Sq(adj) = 8.95%
PRESS = 25.8930 R-Sq(pred) = -158.93%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 3.1713 3.17131 3.17131 1.39323 0.322926
Mul CV 1 3.1713 3.17131 3.17131 1.39323 0.322926
Error 3 6.8287 6.82869 2.27623
Total 4 10.0000
Fits and Diagnostics for Unusual Observations
No unusual observations
Detailed Statistical Report of Figure 2
General Regression Analysis:
Bacterial Species Richness versus predator evenness in multiple predation experiments
Regression Equation
Richness = 1.21608 + 2.32033 predator evenness
Coefficients
Term Coef SE Coef T P
Constant 1.21608 0.376463 3.23027 0.002
Evenness 2.32033 0.616466 3.76393 0.000
Summary of Model
S = 0.978265 R-Sq = 13.47% R-Sq(adj) = 12.52%
PRESS = 90.7094 R-Sq(pred) = 9.87%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 13.558 13.5580 13.5580 14.1672 0.0002960
Evenness 1 13.558 13.5580 13.5580 14.1672 0.0002960
Error 91 87.087 87.0872 0.9570
Total 92 100.645
Fits and Diagnostics for Unusual Observations
Obs Richness Fit SE Fit Residual St Resid
5 1 1.56880 0.287330 -0.56880 -0.60826 X
49 3 1.61367 0.276209 1.38633 1.47724 X
91 5 2.77215 0.113485 2.22785 2.29283 R
92 5 2.55921 0.101601 2.44079 2.50859 R
93 5 2.75501 0.111519 2.24499 2.30993 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
Detailed Statistical Report of Figure 3
General Regression Analysis:
One-way ANOVA: Predators production in different richness level
M- Multiple(predator production in mixture)
S- Single (Predator production in monoculture)
Source DF SS MS F P
Richness 1 7.78168E+11 7.78168E+11 135.84 0.000
Error 122 6.98883E+11 5728551302
Total 123 1.47705E+12
S = 75687 R-Sq = 52.68% R-Sq(adj) = 52.30%
Individual 95% CIs For Mean Based on Pooled StDev
Level N Mean StDev --+------+------+------+------
M 31 248161 118277 (---*----)
S 93 65214 55089 (--*-)
--+------+------+------+------
60000 120000 180000 240000
Pooled StDev = 75687
Grouping Information Using T-test
Richness N Mean Grouping
M 31 248161 A
S 93 65214 B
Means that do not share a letter are significantly different.
95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Richness
Individual confidence level = 95.00%
Richness = M subtracted from:
Richness Lower Center Upper ------+------+------+------+---
S -214020 -182947 -151874 (-----*----)
------+------+------+------+---
-180000 -120000 -60000 0
Detailed Statistical Report of Figure 4
(a) General Regression Analysis: TIC versus Predator Biomass
Regression Equation
TIC = -13.5302 + 1.25217 Predator Biomass
Coefficients
Term Coef SE Coef T P
Constant -13.5302 2.47319 -5.4707 0.000
Predator Biomass 1.2522 0.09023 13.8768 0.000
Summary of Model
S = 5.84569 R-Sq = 86.91% R-Sq(adj) = 86.46%
PRESS = 1198.49 R-Sq(pred) = 84.17%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 6580.40 6580.40 6580.40 192.567 0.0000000
Predator Biomass 1 6580.40 6580.40 6580.40 192.567 0.0000000
Error 29 990.99 990.99 34.17
Total 30 7571.39
Fits and Diagnostics for Unusual Observations
Obs TIC Fit SE Fit Residual St Resid
5 70.3362 59.4715 3.19863 10.8647 2.22050 R X
23 42.2595 29.7532 1.36983 12.5063 2.20068 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
(b) General Regression Analysis: DE versus Predator Biomass
Regression Equation
DE = 1.95266 - 0.0449657 Predator Biomass
Coefficients
Term Coef SE Coef T P
Constant 1.95266 0.667883 2.92365 0.007
Predator Biomass -0.04497 0.024368 -1.84529 0.075
Summary of Model
S = 1.57862 R-Sq = 10.51% R-Sq(adj) = 7.42%
PRESS = 79.3880 R-Sq(pred) = 1.69%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 8.4857 8.4857 8.48567 3.40511 0.0752288
Predator Biomass 1 8.4857 8.4857 8.48567 3.40511 0.0752288
Error 29 72.2692 72.2692 2.49204
Total 30 80.7548
Fits and Diagnostics for Unusual Observations
Obs DE Fit SE Fit Residual St Resid
5 -1.57463 -0.668842 0.863786 -0.905791 -0.685514 X
X denotes an observation whose X value gives it large leverage.
(c) General Regression Analysis: TC versus Predator Biomass
Regression Equation
TDC = 5.05612 - 0.207208 Predator Biomass
Coefficients
Term Coef SE Coef T P
Constant 5.05612 1.90979 2.64747 0.013
Predator Biomass -0.20721 0.06968 -2.97374 0.006
Summary of Model
S = 4.51403 R-Sq = 23.37% R-Sq(adj) = 20.73%
PRESS = 744.778 R-Sq(pred) = 3.41%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 180.192 180.192 180.192 8.84315 0.0058709
Predator Biomass 1 180.192 180.192 180.192 8.84315 0.0058709
Error 29 590.916 590.916 20.376
Total 30 771.108
Fits and Diagnostics for Unusual Observations
Obs TDC Fit SE Fit Residual St Resid
5 -16.9830 -7.02409 2.46997 -9.9590 -2.63582 R X
23 -12.3140 -2.10636 1.05778 -10.2077 -2.32609 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
(d). One-way ANOVA: Effect size of NBE Components: Tripartite partitioning of NBE components
Source DF SS MS F P
Components 2 6104.8 3052.4 32.61 0.000
Error 90 8423.3 93.6
Total 92 14528.1
S = 9.674 R-Sq = 42.02% R-Sq(adj) = 40.73%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev -----+------+------+------+----
DE 31 0.837 1.641 (----*----)
TDC 31 -0.086 5.070 (----*----)
TIC 31 17.544 15.886 (----*----)
-----+------+------+------+----
0.0 7.0 14.0 21.0
Pooled StDev = 9.674
Grouping Information Using T-test
Components N Mean Grouping
TIC 31 17.544 A
DE 31 0.837 B
TDC 31 -0.086 B
Means that do not share a letter are significantly different.
95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Components
Individual confidence level = 98.07%
Components = DE subtracted from:
Components Lower Center Upper +------+------+------+------
TDC -6.778 -0.923 4.933 (----*----)
TIC 10.852 16.707 22.563 (----*----)
+------+------+------+------
-24 -12 0 12
Components = TDC subtracted from:
Components Lower Center Upper +------+------+------+------
TIC 11.774 17.630 23.485 (----*----)
+------+------+------+------
-24 -12 0 12
Detailed Statistical Report of Figure 5
(a)Slope deviation statistical results
Results of ANOVA slope deviation of Linear model fitting to data ('Model 2') from Nullmodel ('Model 1', Linear model with slope=1 (given by 'offset (predation free control)') and Intercept=0)
- Deviation of slope of relative abundance in predation free microcosms (predation free control) versus relative abundance in the microcosms under Acanthamoeba sp. predation pressure
> Ac.aov
Analysis of Variance Table
Model 1: Ac ~ offset(no.predation) + 0
Model 2: Ac ~ no.predation
Res.Df RSS Df Sum of Sq F Pr(>F)
1 75 2.2102
2 73 2.2029 2 0.0073316 0.1215 0.8858
- Deviation of slope of relative abundance in predation free microcosms (predation free control) versus relative abundance in the microcosms under Poterioochromonas sp. predation pressure
> Pot.aov
Analysis of Variance Table
Model 1: Pot ~ offset(no.predation) + 0
Model 2: Pot ~ no.predation
Res.Df RSS Df Sum of Sq F Pr(>F)
1 75 0.72734
2 73 0.72303 2 0.0043041 0.2173 0.8052
- Deviation of slope of relative abundance in predation free microcosms (predation free control) versus relative abundance in the microcosms under Tetrahymena sp. predation pressure
> Tet.aov
Analysis of Variance Table
Model 1: Tet ~ offset(no.predation) + 0
Model 2: Tet ~ no.predation
Res.Df RSS Df Sum of Sq F Pr(>F)
1 75 4.8196
2 73 4.2414 2 0.57815 4.9753 0.009427 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
- Deviation of slope of relative abundance in predation free microcosms (predation free control) versus relative abundance in the microcosms under multiple predation pressure
> Multi.aov
Analysis of Variance Table
Model 1: multiple ~ offset(no.predation) + 0
Model 2: multiple ~ no.predation
Res.Df RSS Df Sum of Sq F Pr(>F)
1 75 7.1018
2 73 5.3893 2 1.7126 11.599 4.225e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
- Results of Outlier test
> outlierTest(Ac.mod)
No Studentized residuals with Bonferonni p < 0.05
Largest |rstudent|:
rstudent unadjusted p-value Bonferonni p
70 -2.992269 0.0037909 0.28432
> outlierTest(Pot.mod)
No Studentized residuals with Bonferonni p < 0.05
Largest |rstudent|:
rstudent unadjusted p-value Bonferonni p
42 3.169948 0.0022395 0.16796
> outlierTest(Tet.mod)
No Studentized residuals with Bonferonni p < 0.05
Largest |rstudent|:
rstudent unadjusted p-value Bonferonni p
43 2.833773 0.0059646 0.44734
> outlierTest(multiple.mod)
No Studentized residuals with Bonferonni p < 0.05
Largest |rstudent|:
rstudent unadjusted p-value Bonferonni p
62 2.507438 0.014417 NA
Diagrammatic view of residuals plotting.
(b) General Regression Analysis:
Relative Abundance in predation free microcosms (Predation free control) versus Relative Abundance in the microcosms under Acanthamoeba sp. predation pressure.
Regression Equation
Control = 0.0604374 + 0.825661 AC
Coefficients
Term Coef SE Coef T P
Constant 0.060437 0.0248507 2.4320 0.017
AC 0.825661 0.0479097 17.2337 0.000
Summary of Model
S = 0.160088 R-Sq = 80.27% R-Sq(adj) = 80.00%
PRESS = 1.96769 R-Sq(pred) = 79.25%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 7.61162 7.61162 7.61162 297.000 0.000000
AC 1 7.61162 7.61162 7.61162 297.000 0.000000
Error 73 1.87087 1.87087 0.02563
Lack-of-Fit 56 1.54106 1.54106 0.02752 1.418 0.215534
Pure Error 17 0.32981 0.32981 0.01940
Total 74 9.48249
Fits and Diagnostics for Unusual Observations
Obs Control Fit SE Fit Residual St Resid
9 0.619946 0.297573 0.0187036 0.322374 2.02761 R
13 0.978173 0.625364 0.0245608 0.352809 2.23024 R
15 0.371703 0.698835 0.0275553 -0.327133 -2.07441 R
40 0.493827 0.865107 0.0353086 -0.371280 -2.37777 R
45 0.611511 0.230677 0.0196725 0.380834 2.39706 R
70 0.493827 0.060437 0.0248507 0.433390 2.74041 R
R denotes an observation with a large standardized residual.
General Regression Analysis: Relative Abundance in predation free microcosms (Predation free control) versus Relative Abundance in the microcosms under predation pressure of Poterioochromonas sp.
Regression Equation
Control = 0.016673 + 0.945588 Poteriooch
Coefficients
Term Coef SE Coef T P
Constant 0.016673 0.0156832 1.0631 0.291
Poteriooch 0.945588 0.0311931 30.3140 0.000
Summary of Model
S = 0.0977731 R-Sq = 92.64% R-Sq(adj) = 92.54%
PRESS = 0.727036 R-Sq(pred) = 92.33%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 8.78464 8.78464 8.78464 918.936 0.0000000
Poteriooch 1 8.78464 8.78464 8.78464 918.936 0.0000000
Error 73 0.69785 0.69785 0.00956
Lack-of-Fit 54 0.66918 0.66918 0.01239 8.213 0.0000034
Pure Error 19 0.02867 0.02867 0.00151
Total 74 9.48249
Fits and Diagnostics for Unusual Observations
Obs Control Fit SE Fit Residual St Resid
8 0.493827 0.294787 0.0114188 0.199040 2.04976 R
23 0.431579 0.644861 0.0149741 -0.213282 -2.20744 R
42 0.323529 0.604725 0.0141397 -0.281196 -2.90656 R
68 0.568421 0.330767 0.0113020 0.237654 2.44708 R
70 0.493827 0.257077 0.0116703 0.236750 2.43886 R
R denotes an observation with a large standardized residual.
General Regression Analysis: Relative Abundance in predation free microcosms (Predation free control) versus Relative Abundance in the microcosms under Tetrahymena sp. predation pressure.
Regression Equation
Control = 0.0893096 + 0.742376 Tet
Coefficients
Term Coef SE Coef T P
Constant 0.089310 0.0384611 2.32208 0.023
Tet 0.742376 0.0771642 9.62073 0.000
Summary of Model
S = 0.239323 R-Sq = 55.91% R-Sq(adj) = 55.30%
PRESS = 4.41298 R-Sq(pred) = 53.46%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 5.30136 5.30136 5.30136 92.5585 0.0000000
Tet 1 5.30136 5.30136 5.30136 92.5585 0.0000000
Error 73 4.18113 4.18113 0.05728
Lack-of-Fit 57 3.84793 3.84793 0.06751 3.2417 0.0059330
Pure Error 16 0.33320 0.33320 0.02082
Total 74 9.48249
Fits and Diagnostics for Unusual Observations
Obs Control Fit SE Fit Residual St Resid
1 0.947205 0.407471 0.0283482 0.539734 2.27124 R
14 0.689655 0.132979 0.0354544 0.556676 2.35199 R
43 0.275862 0.788017 0.0535554 -0.512155 -2.19569 R
R denotes an observation with a large standardized residual.
General Regression Analysis: Relative Abundance in predation free microcosms (Predation free control) versus Relative Abundance in the microcosms under MultiplePredation pressure.
Regression Equation
Control = 0.124927 + 0.639633 multiple
Coefficients
Term Coef SE Coef T P
Constant 0.124927 0.0474619 2.63216 0.010
multiple 0.639633 0.0981489 6.51696 0.000
Summary of Model
S = 0.286566 R-Sq = 36.78% R-Sq(adj) = 35.91%
PRESS = 6.29777 R-Sq(pred) = 33.59%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 3.48771 3.48771 3.48771 42.4708 0.0000000
multiple 1 3.48771 3.48771 3.48771 42.4708 0.0000000
Error 73 5.99478 5.99478 0.08212
Lack-of-Fit 54 5.20368 5.20368 0.09636 2.3144 0.0233008
Pure Error 19 0.79110 0.79110 0.04164
Total 74 9.48249
Fits and Diagnostics for Unusual Observations
Obs Control Fit SE Fit Residual St Resid
10 0.913978 0.186522 0.0412165 0.727457 2.56520 R
13 0.978173 0.308193 0.0336123 0.669980 2.35421 R
R denotes an observation with a large standardized residual.
Box S1. Detailed Statistical Report of impact of prey-predator richness on predator production
Detailed Statistical Report of Figure 1 Supplementary
One-way ANOVA: Prey Production in different predation treatments
C- Prey production without predators(predation free control microcosms)
S- Prey production under single predation pressure
M- Prey production under multiple predation pressure
Source DF SS MS F P
Group 2 3361.9 1680.9 23.41 0.000
Error 90 6461.3 71.8
Total 92 9823.2
S = 8.473 R-Sq = 34.22% R-Sq(adj) = 32.76%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ----+------+------+------+-----
C 31 14.610 12.695 (----*----)
M 31 0.636 0.627 (----*----)
S 31 11.649 7.336 (----*----)
----+------+------+------+-----
0.0 6.0 12.0 18.0
Pooled StDev = 8.473
Grouping Information Using T-test
Group N Mean Grouping
C 31 14.610 A
S 31 11.649 A
M 31 0.636 B
Means that do not share a letter are significantly different.
95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Group
Individual confidence level = 98.07%
Group = C subtracted from:
Group Lower Center Upper ------+------+------+------+
M -19.102 -13.974 -8.846 (----*----)
S -8.089 -2.960 2.168 (----*----)
------+------+------+------+
-10 0 10 20
Group = M subtracted from:
Group Lower Center Upper ------+------+------+------+
S 5.885 11.014 16.142 (----*----)
------+------+------+------+
-10 0 10 20
Detailed Statistical Report of Figure 2 Supplementary
(a). General Regression Analysis: TIC versus NBE
Regression Equation
TIC = -5.36425 + 1.25217 NBE
Coefficients
Term Coef SE Coef T P
Constant -5.36425 1.95641 -2.7419 0.010
NBE 1.25217 0.09023 13.8768 0.000
Summary of Model
S = 5.84569 R-Sq = 86.91% R-Sq(adj) = 86.46%
PRESS = 1198.49 R-Sq(pred) = 84.17%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 6580.40 6580.40 6580.40 192.567 0.0000000
NBE 1 6580.40 6580.40 6580.40 192.567 0.0000000
Error 29 990.99 990.99 34.17
Total 30 7571.39
Fits and Diagnostics for Unusual Observations
Obs TIC Fit SE Fit Residual St Resid
5 70.3362 59.4715 3.19863 10.8647 2.22050 R X
23 42.2595 29.7532 1.36983 12.5063 2.20068 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.
(b). General Regression Analysis: DE versus NBE
Regression Equation
DE = 1.65942 - 0.0449657 NBE
Coefficients
Term Coef SE Coef T P
Constant 1.65942 0.528325 3.14090 0.004
NBE -0.04497 0.024368 -1.84529 0.075
Summary of Model
S = 1.57862 R-Sq = 10.51% R-Sq(adj) = 7.42%
PRESS = 79.3880 R-Sq(pred) = 1.69%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 8.4857 8.4857 8.48567 3.40511 0.0752288
NBE 1 8.4857 8.4857 8.48567 3.40511 0.0752288
Error 29 72.2692 72.2692 2.49204
Total 30 80.7548
Fits and Diagnostics for Unusual Observations
Obs DE Fit SE Fit Residual St Resid
5 -1.57463 -0.668842 0.863786 -0.905791 -0.685514 X
X denotes an observation whose X value gives it large leverage.
(c). General Regression Analysis: TDC versus NBE
Regression Equation
TDC = 3.70483 - 0.207208 NBE
Coefficients
Term Coef SE Coef T P
Constant 3.70483 1.51073 2.45234 0.020
NBE -0.20721 0.06968 -2.97374 0.006
Summary of Model
S = 4.51403 R-Sq = 23.37% R-Sq(adj) = 20.73%
PRESS = 744.778 R-Sq(pred) = 3.41%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 1 180.192 180.192 180.192 8.84315 0.0058709
NBE 1 180.192 180.192 180.192 8.84315 0.0058709
Error 29 590.916 590.916 20.376
Total 30 771.108
Fits and Diagnostics for Unusual Observations
Obs TDC Fit SE Fit Residual St Resid
5 -16.9830 -7.02409 2.46997 -9.9590 -2.63582 R X
23 -12.3140 -2.10636 1.05778 -10.2077 -2.32609 R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.