Supporting Information: Enhanced precipitation variability decreases grass- and increases shrub-productivity
Overview:
SI- Statistical analyses description and summary output
Mean five-year response statistical analyses
ANPP response to growing season precipitation
Temporal-response statistical analyses
Temporal-response analysis with annual precipitation as covariate
Split temporal-response analyses
Lag-effect analysis
Structural equation model description and output
References
SI- Statistical analyses description and summary output
Statistical analyses
We analyzed the effect of inter-annual precipitation coefficient of variation on mean productivity for the six years of the experiment. We did regression analyses of mean 6-year ANPP as a function of precipitation coefficient of variation during the same period. We ran four analyses, one for total ANPP and one for each plant-group ANPP.
In order to explorethe response of each plant group to precipitation variability through time,we ran repeated measures ANOVA to test the effect oftreatment, timeand time by treatment interactionfollowed by sliced ANOVA analyses on each year to test for treatment effects within each time step with multiple comparisons corrected by Bonferroni to avoid p-value inflation. Moreover, we ran additional repeated measures ANOVA including annual precipitation as a covariate in order to account for potential effects of specific rainfall patters. Finally, we ran two separate analyses for the first and last three years of the experiment. All analyses support the differential response of plant types and the amplifying effect of precipitation variability through time.
In order to explore linear and non-linear ANPP responses to precipitation amount among plant- types, we fitlinear and non-linear models of total and plant-type ANPP as a function of growing-season precipitation. We chose the best model fit through Akaike’s(1) and Bayesian(2) information criteria. For these analyses, we only considered control plots tracking the response of different plant groups under natural conditions.
Finally, we fit a structural equation model to test for indirect effects of precipitation coefficient of variation on plant-functional type ANPP (Fig.5). Direct effects of precipitation coefficient of variation on dominant grass and shrub ANPP were included while for rare species we only included indirect effects through dominant grass and shrub species because precipitation variability effects were non-significant from the beginning.
We performed all analyses and created all figures using R version 3.0.2(3). We ran packages: MASS(4), car(5), psych(6), doBy(7), lavaan(8), and semPlot.
Mean five-year response statistical analyses
Analysis of six-year mean ANPP as a function precipitation coefficient of variation for five precipitation-CV treatments.
Full Model for total ANPP
ANPP mean (6 years) = b0 + b1 PPT CV (6 years)
Total ANPP analysis
Regression analysis
Call:
lm(formula = anpp$total ~ anpp$treat)
Residuals:
Min 1Q Median 3Q Max
-44.059 -18.240 -2.885 17.283 49.356
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 183.0541 12.4896 14.657 < 2e-16 ***
anpp$treat -0.7923 0.1450 -5.465 1.63e-06 ***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 22.83 on 48 degrees of freedom
Multiple R-squared: 0.3835,Adjusted R-squared: 0.3707
F-statistic: 29.86 on 1 and 48 DF, p-value: 1.628e-06
Grass ANPP regression analysis
Call:
lm(formula = anpp$Pgrass ~ anpp$treat)
Residuals:
Min 1Q Median 3Q Max
-57.953 -21.945 -2.516 14.942 60.424
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 155.803 15.165 10.274 1.04e-13 ***
anpp$treat -1.024 0.176 -5.818 4.75e-07 ***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 27.72 on 48 degrees of freedom
Multiple R-squared: 0.4136,Adjusted R-squared: 0.4013
F-statistic: 33.85 on 1 and 48 DF, p-value: 4.75e-07
Shrub ANPP regression analysis
Call:
lm(formula = anpp$prgl ~ anpp$treat)
Residuals:
Min 1Q Median 3Q Max
-15.936 -7.852 0.538 4.620 33.378
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.00970 5.25901 1.523 0.1343
anpp$treat 0.14321 0.06105 2.346 0.0232 *
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.614 on 48 degrees of freedom
Multiple R-squared: 0.1028,Adjusted R-squared: 0.08416
F-statistic: 5.503 on 1 and 48 DF, p-value: 0.02317
Rare species regression analysis
Call:
lm(formula = anpp$annual ~ anpp$treat)
Residuals:
Min 1Q Median 3Q Max
-18.5770 -6.3052 -0.8689 4.4111 24.6887
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 19.24108 5.19861 3.701 0.000553 ***
anpp$treat 0.08867 0.06035 1.469 0.148255
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.504 on 48 degrees of freedom
Multiple R-squared: 0.04304,Adjusted R-squared: 0.02311
F-statistic: 2.159 on 1 and 48 DF, p-value: 0.1483
ANPP response to growing season precipitation for each plant-functional type
We fit three different models: (lmo) a linear model, (NLM) a second order polynomial model and (NLM2) a quadratic model. These non-linear models allowed for concave-up as well as concave-down responses that are biologically possible. Other models such as those explained by power functions were excluded because a negative power model does not make biological sense. Then we selected the best fit based on AIC and BIC scores.
Total
Linear model: Simple linear regression
Call:
lm(formula = total ~ ppt, data = ANPPc)
Residuals:
Min 1Q Median 3Q Max
-94.467 -28.706 0.048 16.441 109.076
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 59.23676 12.87733 4.600 2.34e-05 ***
ppt 0.68420 0.09242 7.403 6.16e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 40.09 on 58 degrees of freedom
Multiple R-squared: 0.4858,Adjusted R-squared: 0.477
F-statistic: 54.81 on 1 and 58 DF, p-value: 6.158e-10
Non-linear model: Second order polynomial
Formula: total ~ a * ppt + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 1.7335307 0.1352371 12.818 < 2e-16 ***
b -0.0038307 0.0007563 -5.065 4.44e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 39 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 2.795e-06
Non-linear model 2: quadratic
Formula: total ~ a + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 1.006e+02 8.535e+00 11.790 < 2e-16 ***
b 2.364e-03 3.426e-04 6.902 4.28e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 41.43 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 7.075e-0
Model selection output
df AIC
lmot 3 617.1857
NLMt 3 613.8740*
NLM2t 3 621.1267
df BIC
lmot 3 623.4687
NLMt 3 620.1570*
NLM2t 3 627.4097
We chose the second order polynomial model to explain total ANPP response to growing season precipitation.
Dominant grasses
Linear model: Simple linear regression
Call:
lm(formula = Pgrass ~ ppt, data = ANPPc)
Residuals:
Min 1Q Median 3Q Max
-92.016 -39.044 0.518 22.144 107.087
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 71.0311 14.2040 5.001 5.6e-06 ***
ppt 0.3302 0.1019 3.239 0.00198 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 44.22 on 58 degrees of freedom
Multiple R-squared: 0.1532,Adjusted R-squared: 0.1386
F-statistic: 10.49 on 1 and 58 DF, p-value: 0.001985
Non-linear model: Second order polynomial
Formula: Pgrass ~ a * ppt + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 1.5776366 0.1494614 10.55 4.03e-15 ***
b -0.0045305 0.0008359 -5.42 1.20e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 43.1 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 2.467e-06
Non-linear model 2: quadratic
Formula: Pgrass ~ a + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 9.179e+01 9.222e+00 9.954 3.69e-14 ***
b 1.101e-03 3.701e-04 2.974 0.00427 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 44.77 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 6.544e-06
Model selection output
df AIC
lmo 3 628.9522
NLM 3 625.8750*
NLM2 3 630.4134
df BIC
lmo 3 635.2353
NLM 3 632.1581*
NLM2 3 636.6964
We chose the second order polynomial model to explain dominant grass ANPP responseto growing season precipitation.
Shrub
Linear model: Simple linear regression
Call:
lm(formula = prgl ~ ppt, data = ANPPc)
Residuals:
Min 1Q Median 3Q Max
-13.982 -5.894 -3.103 5.629 20.713
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.20639 2.55972 1.643 0.105731
ppt 0.07478 0.01837 4.071 0.000144 ***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.97 on 58 degrees of freedom
Multiple R-squared: 0.2222,Adjusted R-squared: 0.2088
F-statistic: 16.57 on 1 and 58 DF, p-value: 0.0001437
Non-linear model: Second order polynomial
Formula: prgl ~ a * ppt + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 0.1411013 0.0277746 5.080 4.2e-06 ***
b -0.0002245 0.0001553 -1.445 0.154
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 8.01 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 7.86e-06
Non-linear model 2: quadratic
Formula: prgl ~ a + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 8.509e+00 1.639e+00 5.192 2.8e-06 ***
b 2.698e-04 6.578e-05 4.102 0.00013 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.956 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 5.216e-06
Model selection output
df AIC
lmo 3 423.3170
NLM 3 423.9250
NLM2 3 423.1124*
df BIC
lmo 3 429.6000
NLM 3 430.2081
NLM2 3 429.3954*
Even though the models are not clearly different, we chose the quadratic model to explain shrub ANPP responseto growing season precipitation because it has the lowest scores. Since the effect of precipitation variability on shrubs is relatively weak, it is expected to find a weak non-linearity too.
Rare species
Linear model: Simple linear regression
Call:
lm(formula = rare ~ ppt, data = ANPPc)
Residuals:
Min 1Q Median 3Q Max
-25.661 -5.106 -1.745 3.280 44.575
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -16.00070 3.82539 -4.183 9.87e-05 ***
ppt 0.27919 0.02745 10.169 1.66e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 11.91 on 58 degrees of freedom
Multiple R-squared: 0.6407,Adjusted R-squared: 0.6345
F-statistic: 103.4 on 1 and 58 DF, p-value: 1.661e-14
Non-linear model: Second order polynomial
Formula: rare ~ a * ppt + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 0.0147921 0.0418228 0.354 0.724858
b 0.0009242 0.0002339 3.951 0.000213 ***
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12.06 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 4.965e-06
Non-linear model 2: quadratic
Formula: rare ~ a + b * (ppt^2)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 3.273e-01 2.487e+00 0.132 0.896
b 9.937e-04 9.982e-05 9.955 3.67e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12.07 on 58 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 3.449e-06
Model selection output
df AIC
lmo 3 471.5287*
NLM 3 473.0435
NLM2 3 473.1548
df BIC
lmo 3 477.8117*
NLM 3 479.3265
NLM2 3 479.4379
We chose the linear model to explain rare species ANPP response to growing season precipitation.
Temporal-response statistical analyses
In order to explore the effect of increased precipitation variationthrough time avoiding confounding effects of precipitation amount we combined 50% and 80% treatments starting from drought and irrigation. For example, we combined +50% and -50% treatments for each year and compared those to the control and to a similar combination of the 80% treatment.
Full Model for total ANPP:
TotalANPP = b0 + b1 Treatment+ b2Year + b3Treatment* Year
Repeated measures analysis:
Error: plot
Df Sum Sq Mean Sq
treat 1 9396 9396
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 93226 46613 18.43 2.88e-08 ***
year 1 28149 28149 11.13 0.000958 ***
treat:year 2 30646 15323 6.06 0.002638 **
Residuals 293 740893 2529
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Sliced analyses for each year
We performed sliced anova analyses for each year usingtukey comparisons when treatment differences were significant. For multiple comparisons we corrected our p-value to maintain a family confidence level of 95%. We applied the bonferroni correction as 1-alpha / number of comparisons.
Year 1: Total ANPP as a function of precipitation variation treatment for the year 2009
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 3677 1838 0.857 0.431
Residuals 47 100804 2145
Year 2: Total ANPP as a function of precipitation variation treatment for the year 2010
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 6595 3298 1.484 0.237
Residuals 47 104460 2223
Year 3: Total ANPP as a function of precipitation variation treatment for the year 2011
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 21571 10785 4.748 0.0132 *
Residuals 47 106766 2272
Tukey test
LTukey(ann1t3,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: total
Variation Coefficient: 49.67763 %
Independent variable: treat
Factors Means
ambient 129.772622132 a
50%inc 100.959119822 a
80%inc 74.00794509 a
Year 4: Total ANPP as a function of precipitation variation treatment for the year 2012
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 13056 6528 8.229 0.000863 ***
Residuals 47 37285 793
Tukey test
LTukey(ann1t4,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: total
Variation Coefficient: 38.12666 %
Independent variable: treat
Factors Means
ambient 97.901366876 a
50%inc 79.949071004 ab
80%inc 55.783887804 b
Year 5: Total ANPP as a function of precipitation variation treatment for the year 2013
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 19167 9584 10.86 0.000132 ***
Residuals 47 41467 882
Tukey test
LTukey(ann1t5,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: total
Variation Coefficient: 20.6985 %
Independent variable: treat
Factors Means
ambient 175.12020087 a
50%inc 148.516425901 ab
80%inc 122.684663242 b
Year 6: Total ANPP as a function of precipitation variation treatment for the year 2014
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 78625 39312 22.04 1.77e-07 ***
Residuals 47 83820 1783
Tukey test
LTukey(ann1t6,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: total
Variation Coefficient: 29.57183 %
Independent variable: treat
Factors Means
ambient 219.498048 a
50%inc 134.930124 b
80%inc 112.33678 b
The same procedure was followed for each plant functional type.
Dominant grasses
Full Model for dominant grass ANPP:
Dominant grassANPP = b0 + b1 Treatment+ b2Year + b3Treatment* Year
Repeated measures analysis:
Error: plot
Df Sum Sq Mean Sq
treat 1 28558 28558
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 157816 78908 43.30 < 2e-16 ***
year 1 57034 57034 31.30 5.08e-08 ***
treat:year 2 62764 31382 17.22 8.49e-08 ***
Residuals 293 533955 1822
Sliced analyses for each year
We performed sliced anova analyses for each year using tukey comparisons when treatment differences were significant.
Year 1: Dominant grass ANPP across variability treatments for the year 2009
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 4148 2074 0.977 0.384
Residuals 47 99793 2123
Year 2: Dominant grass ANPP across variability treatments for the year 2010
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 5421 2711 1.578 0.217
Residuals 47 80733 1718
Year 3: Dominant grass ANPP across variability treatments for the year 2011
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 30975 15487 7.751 0.00123 **
Residuals 47 93914 1998
Tukey test
LTukey(ann1PG3,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: Pgrass
Variation Coefficient: 67.91797 %
Independent variable: treat
Factors Means
ambient 104.552448 a
50%inc 73.609536 ab
80%inc 38.654616 b
Year 4: Dominant grass ANPP across variability treatments for the year 2012
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 26763 13382 15.56 6.52e-06 ***
Residuals 47 40416 860
Tukey test
LTukey(ann1PG4,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: Pgrass
Variation Coefficient: 66.37151 %
Independent variable: treat
Factors Means
ambient 82.7963136 a
50%inc 48.780732 ab
80%inc 20.276256 b
Year 5: Dominant grass ANPP across variability treatments for the year 2013
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 52498 26249 36.99 2.24e-10 ***
Residuals 47 33349 710
Tukey test
LTukey(ann1PG5,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: Pgrass
Variation Coefficient: 57.08302 %
Independent variable: treat
Factors Means
ambient 108.924816 a
50%inc 41.153112 b
80%inc 21.045024 b
Year 6: Dominant grass ANPP across variability treatments for the year 2014
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 127411 63706 39.95 7.29e-11 ***
Residuals 47 74944 1595
Tukey test
LTukey(ann1PG6,which="treat",conf.level=1-0.05/12)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9958333
Dependent variable: Pgrass
Variation Coefficient: 56.83005 %
Independent variable: treat
Factors Means
ambient 167.92776 a
50%inc 60.156096 b
80%inc 31.543512 b
Shrubs
Full Model for shrub ANPP:
ShrubANPP = b0 + b1 Treatment+ b2Year + b3Treatment* Year
Repeated measures analysis:
Error: plot
Df Sum Sq Mean Sq
treat 1 2.193 2.193
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 3453 1726 9.334 0.000118 ***
year 1 22349 22349 120.837 < 2e-16 ***
treat:year 2 1275 637 3.446 0.033179 *
Residuals 293 54190 185
Sliced analyses for each year
Year 1: shrub ANPP across variability treatments for the year 2009
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 43.7 21.84 1.787 0.179
Residuals 47 574.3 12.22
Year 2: shrub ANPP across variability treatments for the year 2010
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 82.2 41.11 0.683 0.51
Residuals 47 2830.6 60.23
Year 3: shrub ANPP across variability treatments for the year 2011
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 139 69.59 0.967 0.388
Residuals 47 3382 71.96
Year 4: shrub ANPP across variability treatments for the year 2012
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 958 479.1 1.925 0.157
Residuals 47 11701 248.9
Year 5: shrub ANPP across variability treatments for the year 2013
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 3109 1554.7 3.988 0.0251 *
Residuals 47 18322 389.8
Tukey test
Independent variable: treat
Factors Means
80%inc 41.201340442 a
50%inc 38.086645701 a
ambient 20.23932687 b
Year 6: shrub ANPP across variability treatments for the year 2014
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 1048 524.2 2.172 0.105
Residuals 47 11341 241.3
Tukey test
LTukey(ann1sh5,which="treat",conf.level=1-0.05/3)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9833333
Dependent variable: prgl
Variation Coefficient: 55.20859 %
Independent variable: treat
Factors Means
80%inc 41.201340442 a
50%inc 38.086645701 ab
ambient 20.23932687 b
Rare species
Full Model for rare ANPP:
RareANPP = b0 + b1 Treatment+ b2Year + b3Treatment* Year
Repeated measures analysis:
Error: plot
Df Sum Sq Mean Sq
treat 1 5408 5408
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 1657 828 1.474 0.231
year 1 66101 66101 117.624 <2e-16 ***
treat:year 2 1651 825 1.469 0.232
Residuals 293 164656 562
Sliced analyses for each year
Year 1: rare species ANPP across treatments for the year 2009
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 44.4 22.22 0.453 0.638
Residuals 47 2305.1 49.05
Year 2: rare species ANPP across treatments for the year 2010
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 465 232.3 0.54 0.587
Residuals 47 20231 430.4
Year 3: rare species ANPP across treatments for the year 2011
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 361 180.4 0.742 0.482
Residuals 47 11422 243.0
Year 4: rare species ANPP across treatments for the year 2012
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 504 251.8 2.039 0.141
Residuals 47 5804 123.5
Year 5: rare species ANPP across treatments for the year 2013
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 3639 1819.6 5.302 0.00839 **
Residuals 47 16131 343.2
Tukey test
LTukey(anr5,which="treat",conf.level=1-0.05/3)
TUKEY TEST TO COMPARE MEANS
Confidence level: 0.9833333
Dependent variable: rare
Variation Coefficient: 30.33254 %
Independent variable: treat
Factors Means
50%inc 69.2766682 a
80%inc 60.4382988 ab
ambient 45.956058 b
Year 6: rare species ANPP across treatments for the year 2014
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 2091 1045 0.981 0.382
Residuals 47 50080 1066
Temporal-response analysis with annual precipitation as covariate
Furthermore, in order to avoid confounding effects of unusual precipitation patterns during the experimental period, we added annual precipitation as a covariate into our analysis obtaining the same result.
Repeated measures ANOVAwith annual precipitation as covariate
Error: plot
Df Sum Sq Mean Sq
treat 1 9396 9396
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
ppt 1 196723 196723 108.10 < 2e-16 ***
treat 2 93226 46613 25.61 5.63e-11 ***
year 1 40950 40950 22.50 3.29e-06 ***
treat:year 2 30646 15323 8.42 0.000278 ***
Residuals 292 531368 1820
---
Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Split temporal-response analyses
In order to explore responses over time further, we split our results in two non-overlapping time periods. One period included for the first three years of the experiments and the second time period included the last three years of the experiment.
Repeated measures ANOVA for the first three years of the experiment
Error: plot
Df Sum Sq Mean Sq
treat 1 422.5 422.5
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 22833 11417 3.720 0.0266 *
year 1 373 373 0.121 0.7280
treat:year 2 3775 1887 0.615 0.5421
Residuals 143 438881 3069
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Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Repeated measures ANOVA for the last three years of the experiment
Error: plot
Df Sum Sq Mean Sq
treat 1 13579 13579
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 83291 41645 29.714 1.62e-11 ***
year 1 118794 118794 84.758 3.81e-16 ***
treat:year 2 17347 8673 6.188 0.00265 **
Residuals 143 200423 1402
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Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Lag-effect analysis
In order to separate lag effects from those caused by amplifying response, we calculated the lag effect on perennial grass productivity using an equation developed for the same site and same species (9). Where, legacy effects are a function of the difference between current and previous year precipitation. Then, we discounted such effect form perennial-grass ANPP and ran repeated measures ANOVA and compared the results of perennial-grass ANPP without legacy effect (Fig. S2) to those presented in Fig. 4b.
Repeated measures anova on de-lagged perennial grass response
Error: plot
Df Sum Sq Mean Sq
treat 1 29482 29482
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
treat 2 157632 78816 44.39 < 2e-16 ***
year 1 85397 85397 48.10 2.60e-11 ***
treat:year 2 62764 31382 17.68 5.66e-08 ***
Residuals 293 520219 1775
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Signif.codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Structural equation model description and output
We fit a model including direct effects that were significant in overall analyses (SM2) and indirect effects of precipitation variation through dominant grass ANPP on shrub and rare species ANPP. We used the sem() function in the lavaan(8) package in R(3).