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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

1

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 explore the response of each plant group to precipitation variability through

time, we ran repeated measures ANOVA to test the effect of treatment, time and time by

treatment interaction followed 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 fit linear 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

2

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.

3

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 freedomMultiple 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)


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


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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 freedomMultiple 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)


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


5

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


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 ***

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---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 41.43 on 58 degrees of freedomNumber of iterations to convergence: 1 Achieved convergence tolerance: 7.075e-0Model selection output

df AIClmot 3 617.1857NLMt 3 613.8740*NLM2t 3 621.1267

df BIClmot 3 623.4687NLMt 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


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



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

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Residual standard error: 43.1 on 58 degrees of freedom


8


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



Model selection output

df AIClmo 3 628.9522NLM 3 625.8750*NLM2 3 630.4134

df BIClmo 3 635.2353NLM 3 632.1581*NLM2 3 636.6964

We chose the second order polynomial model to explain dominant grass ANPP response to growing season precipitation.

Shrub


Call:lm(formula = prgl ~ ppt, data = ANPPc)


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


9


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




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



Model selection output

df AIClmo 3 423.3170NLM 3 423.9250NLM2 3 423.1124*

df BIClmo 3 429.6000NLM 3 430.2081NLM2 3 429.3954*

Even though the models are not clearly different, we chose the quadratic model to explain shrub ANPP response to 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.

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Rare species

Linear model: Simple linear regressionCall: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


Non-linear model: Second order polynomialFormula: 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 freedomNumber of iterations to convergence: 1 Achieved convergence tolerance: 4.965e-06

Non-linear model 2: quadraticFormula: 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 freedomNumber of iterations to convergence: 1 Achieved convergence tolerance: 3.449e-06

Model selection output df AIClmo 3 471.5287*NLM 3 473.0435NLM2 3 473.1548

df BIC

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lmo 3 477.8117*NLM 3 479.3265NLM2 3 479.4379

We chose the linear model to explain rare species ANPP response to growing season precipitation.

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Temporal-response statistical analyses

In order to explore the effect of increased precipitation variation through 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:

Total ANPP = b0 + b1 Treatment + b2 Year + b3 Treatment * Year

Repeated measures analysis:

Error: plot Df Sum Sq Mean Sqtreat 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 using tukey 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 0.431Residuals 47 100804 2145


Df Sum Sq Mean Sq F value Pr(>F)treat 2 6595 3298 1.484 0.237Residuals 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

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Tukey testLTukey(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


Df Sum Sq Mean Sq F value Pr(>F) treat 2 13056 6528 8.229 0.000863 ***Residuals 47 37285 793


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


Df Sum Sq Mean Sq F value Pr(>F) treat 2 19167 9584 10.86 0.000132 ***Residuals 47 41467 882


TUKEY TEST TO COMPARE MEANS

Confidence level: 0.9958333 Dependent variable: total Variation Coefficient: 20.6985 %

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Independent variable: treat Factors Means ambient 175.12020087 a 50%inc 148.516425901 ab 80%inc 122.684663242 b


Df Sum Sq Mean Sq F value Pr(>F) treat 2 78625 39312 22.04 1.77e-07 ***Residuals 47 83820 1783


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 grass ANPP = b0 + b1 Treatment + b2 Year + b3 Treatment * Year


Error: plot Df Sum Sq Mean Sqtreat 1 28558 28558Error: 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

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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 30975 15487 7.751 0.00123 **Residuals 47 93914 1998

Tukey testLTukey(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




TUKEY TEST TO COMPARE MEANS Confidence level: 0.9958333 Dependent variable: Pgrass Variation Coefficient: 66.37151 % Independent variable: treat Factors Means

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ambient 82.7963136 a 50%inc 48.780732 ab 80%inc 20.276256 b


Df Sum Sq Mean Sq F value Pr(>F) treat 2 52498 26249 36.99 2.24e-10 ***Residuals 47 33349 710 Tukey testLTukey(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 bYear 6: Dominant grass ANPP across variability treatments for the year 2014



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:

Shrub ANPP = b0 + b1 Treatment + b2 Year + b3 Treatment * Year


Error: plot

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Df Sum Sq Mean Sqtreat 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


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 0.179Residuals 47 574.3 12.22


Df Sum Sq Mean Sq F value Pr(>F)treat 2 82.2 41.11 0.683 0.51Residuals 47 2830.6 60.23


Df Sum Sq Mean Sq F value Pr(>F)treat 2 139 69.59 0.967 0.388Residuals 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 0.157Residuals 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 testIndependent variable: treat Factors Means 80%inc 41.201340442 a 50%inc 38.086645701 a ambient 20.23932687 b


Df Sum Sq Mean Sq F value Pr(>F)treat 2 1048 524.2 2.172 0.105Residuals 47 11341 241.3

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Tukey testLTukey(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:

Rare ANPP = b0 + b1 Treatment + b2 Year + b3 Treatment * Year



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


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 0.638Residuals 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 0.587Residuals 47 20231 430.4


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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 testLTukey(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 0.382Residuals 47 50080 1066

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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 ANOVA with annual precipitation as covariate


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

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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 Sqtreat 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 ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Repeated measures ANOVA for the last three years of the experiment


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 ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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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 responseError: plot Df Sum Sq Mean Sqtreat 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 ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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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).

Model syntax:

# Regression term accounting for the direct effect of precipitation coefficient of variation on dominant grass ANPP

'Pgrass ~ a*PPT_var

# Regression term accounting for the direct effect of precipitation variance and indirect effect of dominant grass ANPP on shrub ANPP

shrub ~ b*Pgrass

# Regression term accounting for the direct effect of precipitation mean and indirect effect of dominant grass ANPP on rare ANPP

rare ~ c*Pgrass

# Indirect effects

# Precipitation variability through dominant grass ANPP on shrub species ANPP

ab := a*b

# Precipitation variability through dominant grass ANPP on rare species ANPP

ac := a*c

Model output

lavaan (0.5-16) converged normally after 32 iterations

Number of observations 50

Estimator ML Minimum Function Test Statistic 2.474 Degrees of freedom 2 P-value (Chi-square) 0.290

Model test baseline model:

Minimum Function Test Statistic 58.418 Degrees of freedom 6 P-value 0.000

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User model versus baseline model:

Comparative Fit Index (CFI) 0.991 Tucker-Lewis Index (TLI) 0.973

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -816.940 Loglikelihood unrestricted model (H1) -815.703

Number of free parameters 7 Akaike (AIC) 1647.881 Bayesian (BIC) 1661.265 Sample-size adjusted Bayesian (BIC) 1639.293

Root Mean Square Error of Approximation:

RMSEA 0.069 90 Percent Confidence Interval 0.000 0.298 P-value RMSEA <= 0.05 0.334

Standardized Root Mean Square Residual:

SRMR 0.050

Parameter estimates:

Information Expected Standard Errors Standard

Estimate Std.err Z-value P(>|z|)Regressions: Pgrass ~ PPT_var (a) -1.024 0.172 -5.938 0.000 shrub ~ Pgrass (b) -0.107 0.037 -2.914 0.004 rare ~ Pgrass (c) -0.144 0.032 -4.514 0.000

Covariances: shrub ~~ rare -21.252 10.859 -1.957 0.050

Variances: Pgrass 737.887 147.577 shrub 84.557 16.911 rare 64.382 12.876

Defined parameters: ab 0.109 0.042 2.616 0.009 ac 0.148 0.041 3.593 0.000

R-Square:

Pgrass 0.414

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shrub 0.145 rare 0.289

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Northwestern University, Evanston. R package version 1(9).

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