Anticipating changes in variability of grassland production due to increases in interannual precipitation variability

Transcription

1 Anticipating changes in variability of grassland production due to increases in interannual precipitation variability JOANNA S. HSU 1, AND PETER B. ADLER Department of Wildland Resources and the Ecology Center, Utah State University, Logan, Utah USA Citation: Hsu, J. S., and P. B. Adler Anticipating changes in variability of grassland production due to increases in interannual precipitation variability. Ecosphere 5(5):58. Abstract. Expected increases in interannual precipitation variability due to climate change will lead to increases in the variability of primary production, with potentially important consequences for natural resource management. Previous work has suggested that various biotic and abiotic processes might amplify or buffer variation in production in response to variation in precipitation. In particular, production to rain variability ratios (PRVR), the coefficient of variation of production divided by the coefficient of variation of precipitation, indicate that production is often relatively more variable than precipitation. We used 37 long-term data sets from grasslands across the globe to test how future increases in precipitation variability might alter the variability of aboveground net primary production (ANPP). We demonstrate that PRVR is not a useful metric: it is predicted by a site s precipitation-production relationship and a PRVR greater than 1 need not imply that increases in the variability of ANPP will be disproportionately greater than increases in precipitation variability. Instead, it is the form of the precipitation-anpp relationship that determines how increases in precipitation variability will impact ANPP variability. We fit linear, lag effect, and nonlinear precipitation-anpp relationships to each data set. At most sites, the precipitation-anpp relationship is weakly nonlinear, though the lag effect model, incorporating previous year ANPP, performed best at several sites. To test whether the three models project differences in the response of ANPP to future increases in precipitation variability, we directly perturbed the observed precipitation time series and quantified the results of this perturbation on ANPP variability. Under simple linear or lag effect models, relative increases in ANPP variability were always equal to the relative increases in precipitation variability. When we modeled ANPP as a nonlinear, saturating function of precipitation, projected increases in ANPP variability were disproportionately high, with production dropping more in dry years than it increases in wet years. In six cases, increases in ANPP variability were twice as large as increases in precipitation variability. Based on Akaike model weights, a 5% increase in precipitation variability would cause a 6.3% increase in ANPP variability on average. Key words: aboveground net primary production; lag effects; legacies; precipitation variability; primary production. Received 2 July 2013; revised 21 November 2013; accepted 25 November 2013; final version received 21 March 2014; published 22 May Corresponding Editor: J. Nippert. Copyright: Ó 2014 Hsu and Adler. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 1 Present address: Department of Environmental Science, Policy and Management, University of California, Berkeley, California USA. jhsu118@gmail.com INTRODUCTION For decades, ecologists and land managers have sought to understand the factors regulating the interannual variability of grassland primary production (e.g., Smoliak 1956, Sneva and Hyder 1962, Herbel et al. 1972, Noy-Meir and Walker 1984, Le Houerou et al. 1988, Smart et al. 2007). v 1 May 2014 v Volume 5(5) v Article 58

2 Fig. 1. Examples of the three types of precipitation-anpp models used in this study. Data shown are from grasslands near Bloemfontein, South Africa (O Connor et al. 2001). At this site, the linear, nonlinear, and lag models explain 53%, 66%, and 68% of the observed interannual variability in ANPP, respectively. A nonlinear model best fits the precipitation-anpp relationship at this site (AICc weight ¼ 73%). These efforts have stemmed from an interest in the long-term stability and sustainability of primary production, a key resource and ecosystem function. For example, livestock stocking rates depend on how far and how often range conditions depart from mean conditions (Diaz- Solis et al. 2009). Interannual variability in primary production also impacts small consumer populations that depend on this resource base, increasing their risk of extinction from demographic stochasticity (Menges 2000, Boyce et al. 2006). Aboveground net primary production (ANPP) is controlled by precipitation and soil moisture dynamics in water-limited ecosystems (Noy-Meir 1973). General circulation models (GCMs) generally predict that interannual precipitation variability is increasing due to climate forcing (Räisänen 2002, Boer 2009). In one study of 19 GCMs, predictions on the high end were over 10%, but on average, the predicted increase in the standard deviation of annual precipitation for a doubling of CO 2 concentrations relative to 2002 levels was 4.2% (Räisänen 2002). An important question for ecologists is how much these increases in precipitation variability will increase the variability of ANPP (Weltzin et al. 2003, Heisler and Weltzin 2006, Knapp et al. 2008). Many previous analyses using long-term data have modeled ANPP as a linear function of precipitation (e.g., Lauenroth and Sala 1992, Knapp et al. 2006). Given a simple, linear relationship between precipitation and ANPP, the absolute increase in ANPP variability due to an increase in precipitation variability will depend on the slope of the precipitation-anpp relationship. However, the relative increase in ANPP variability will always match the relative increase in precipitation variability: a 1% increase in precipitation variability will lead to a 1% increase in the portion of ANPP variability that is explained by precipitation variability. If the precipitation-anpp relationship is not simple and linear, however, then the proportional increase in ANPP variability could be larger or smaller than the increase in precipitation variability. Two observations from the empirical literature suggest that disproportionately large increases in ANPP variability might be common. First, long-term observations frequently show that primary production is more variable than precipitation in a relative sense. The production to rain variability ratio (PRVR), the coefficient of variation (CV) of production divided by the CV of precipitation, often takes values greater than one (Le Houerou et al. 1988). Though PRVR values less than 1 have been observed (Guevara et al. 1997, Paruelo and Lauenroth 1998, Prince et v 2 May 2014 v Volume 5(5) v Article 58

3 al. 1998, Diouf and Lambin 2001, Veron et al. 2002, Wessels et al. 2007, Yang et al. 2008), PRVR greater than 1 is more common (Le Houerou et al. 1988, Lauenroth and Sala 1992, Xiao et al. 1996, Guevara et al. 1997, Veron et al. 2002, Wiegand et al. 2004, Hu et al. 2007, Yang et al. 2008) and PRVR values as high as 2.5 or 3 have been documented (Le Houerou et al. 1988, Guevara et al. 1997). High PRVR values appear to suggest that unknown processes somehow amplify variation in production relative to variation in precipitation. For example, Lauenroth and Sala (1992) proposed that high PRVR is related to the fact that years with the same annual precipitation may still differ in intraseasonal water availability. Lag effects (Wiegand et al. 2004), topography (Le Houerou et al. 1988), vegetation type and condition (Hu et al. 2007), and short data sets (Le Houerou et al. 1988) are additional explanations offered for why PRVR may be greater than 1. High PRVR values interested us because we thought they might imply that a small future increase in precipitation variability could cause a large increase in ANPP variability. Second, simple linear regressions of ANPP on precipitation are often outperformed by more complex or nonlinear models. For example, ANPP could exhibit a lagged response to precipitation, with current year production reflecting previous year production in addition to current year precipitation (e.g., Oesterheld et al. 2001, Wiegand et al. 2004, Yahdjian and Sala 2006, Arnone et al. 2008, Sherry et al. 2008, Sala et al. 2012). Previous authors (Oesterheld et al. 2001, Wiegand et al. 2004) have demonstrated that lag effects can amplify or dampen precipitation variability, depending on the sequence of precipitation years (Fig. 2 in Oesterheld et al. 2001). Positive lag effects can amplify ANPP variability if consecutive wet or dry years ratchet production up or down up. In contrast, lag effects would dampen precipitation variability if wet and dry years alternate (negative autocorrelation in precipitation), evening out the differences in production. These studies seem to imply that lag effects might amplify or buffer future increases in precipitation variability, depending on precipitation autocorrelation. However, Oesterheld et al. (2001) and Wiegand et al. (2004) did not explicitly address the consequences of a future increase in precipitation variability. While a lag effect model might generate more variability in ANPP for a given precipitation time series when compared to a simple, linear model, it is not clear whether the same logic applies to a perturbation in the variability of precipitation. The relationships between precipitation and production could also be nonlinear (Khumalo and Holechek 2005, Hsu et al. 2012), which might lead to disproportionate increases in ANPP variability. Nonlinear, concave-down relationships may characterize ecosystems where resources other than water limit production in wet years more than in dry years. If the relationship between precipitation and ANPP is concave down at a site, then an increase in precipitation variability could lead to a disproportionately large increase in ANPP variability. Large decreases in ANPP in dry years drive ANPP variability higher, and this effect outweighs the buffering of variability (relative to a linear model) that occurs in wet years. In this study, we use 37 long-term data sets of precipitation and ANPP in grasslands to address three research questions: First, is PRVR useful for predicting how future increases in precipitation variability might impact ANPP variability in water limited ecosystems? Second, how well do simple linear, lag effect, and nonlinear models explain historical interannual ANPP variability? Finally, do these three types of models project differences in the response of ANPP to future increases in precipitation variability? We addressed the first question by reinterpreting the PRVR in a linear regression framework, accounting for the fact that production is a function of precipitation. We show that much of the variation in observed PRVR is explained by the value of the y-intercept of a linear precipitation-anpp model, a statistical parameter with no direct ecological interpretation. We addressed the second question by comparing R 2 values from linear, lag effect, and nonlinear precipitation- ANPP models fit to each data set. Finally, to address the last question, we directly quantified the effect of a perturbation of precipitation variability on ANPP variability for the linear, lag effect, and nonlinear ANPP models, directly assessing whether increases in ANPP variability are disproportionate to changes in precipitation variability. v 3 May 2014 v Volume 5(5) v Article 58

4 Fig. 2. Histograms of observed (black) and high-variability (gray) annual precipitation time series from Jornada Long-Term Ecological Research site between 1990 and 2008 (A). The high-variability precipitation time series shown here was obtained by increasing the standard deviation of each observation by 5% without changing the precipitation mean. Panels B through D show histograms of ANPP predicted from the observed and high variability precipitation time series depicted in (A). When ANPP is a linear (B) or lagged (C) function of precipitation, a 5% increase in the variability of precipitation leads to a 5% increase in the variability of ANPP. However, when ANPP is a nonlinear, concave down function of precipitation (D), a 5% increase in the variability of precipitation leads to a 10% increase in ANPP variability. Our work continues the tradition of applying statistical techniques to long-term data sets to characterize relationships between climate and primary production (e.g., Hulett and Tomanek 1969, Le Houerou et al. 1988, Laurenroth and Sala 1992, Craine et al. 2012, Sala et al. 2012). Like previous studies, we use simple statistical models to explain historical variation in ANPP as a function of historical variation in precipitation. This is a purely retrospective approach. However, we then take an additional step: we perturb the historical precipitation time series, increasing interannual variation, and use the fitted models to project resulting changes in the variability of ANPP. This exercise is entirely prospective, focused on anticipating future changes in ANPP variability. We show that a statistical model that explains a high degree of historical variation in v 4 May 2014 v Volume 5(5) v Article 58

5 ANPP need not project future increases in ANPP variability that are disproportionate with respect to future precipitation variability. Conversely, models which explain only a modest portion of historical ANPP variability can project disproportionately large changes in future ANPP variability. METHODS Data sets We used 37 time series of annual precipitation and ANPP from grassland sites, a subset of the data used in a previous study that also examined temporal precipitation-anpp relationships (Hsu et al. 2012). That study examined whether average ANPP is sensitive to changes in precipitation, while this study focuses on how variability in grassland ANPP may respond to changes in precipitation variability. For sites where growing season precipitation was available and accounted for more variation in ANPP than total annual precipitation, we used growing season precipitation in all analyses. Note that this choice did not affect our conclusions. All time series contained at least 11 consecutive years of data. Most of the data sets are from long-term ecological research sites in the United States, Eurasia, and South Africa. Due to the difficulty of estimating ANPP under grazed conditions, we only used ANPP observations from ungrazed pastures. Remotely sensed data and data from fertilized plots were excluded. Table 1 shows the data sets used in this study. All analyses were conducted in R version Predicting PRVR PRVR, the coefficient of variation of production (CV ANPP ) divided by the CV of precipitation (CV PPT ), directly compares the interannual variability in precipitation and production: PRVR ¼ CV ANPP ¼ r ANPPPPT CV PPT r PPT ANPP : ð1þ In Eq. 1, ANPP and r ANPP are the mean and standard deviation of production, and PPT and r PPT are the mean and standard deviation of precipitation. Eq. 1 does not account for the fact that production is a function of precipitation at most water-limited sites, which has an influence on the variability of production. Here, we rewrite PRVR in terms of a linear regression of ANPP on precipitation. In least squares regression, the intercept k of a least squares regression line can be calculated: k ¼ Ȳ m X where X and Y are the predictor and response variables, respectively. The slope of the fitted regression line, m, is related to the correlation coefficient r and the standard deviations of the two variables (r x, r y ): m ¼ r r y r x. Rearranging these equations and substituting in precipitation and production for our x and y, we obtain the following expressions for the mean and standard deviation of ANPP: ANPP ¼ k þ m PPT and r ANPP ¼ mr PPT r If we substitute these expressions in for the mean and standard deviation of ANPP into Eq. 1, we obtain the following equation for PRVR: mppt PRVR ¼ ðk þ mpptþr : ð2þ Eq. 2 shows that PRVR depends on the correlation r and on each site s unique precipitation-production relationship. PRVR is inversely proportional to both r and mean ANPP. When r ¼ 1, all of the variability in ANPP can be attributed to variability in precipitation. Even in this case, when r ANPP is perfectly proportional to r PPT, PRVR is only 1 when the y-intercept is 0. Eq. 2 highlights the importance of the y-intercept in determining PRVR; PRVR is greater than 1 whenever k, mppt 1 r 1 : We fit a linear model to each time series to predict ANPP from precipitation in year y: ANPP y ¼ k þ m 3 precipitation y. We then used Eq. 2 to derive PRVR for each site. We regressed PRVR on k, m, r, ANPP and PPT to weigh how important each variable was in determining PRVR. Temporal precipitation-anpp models We used least squares regression to fit two additional models to each data set: a lag effect model (ANPP y ¼ d þ f 3 precipitation þ g 3 ANPP y 1 ) and a nonlinear model (ANPP y ¼ a b/ precipitation y ). In the lag model, the lag parameter g controls how much ANPP is influenced by previous-year ANPP. The nonlinear model is a concave down, saturating function when a and b are positive. This nonlinear function is parsimonious, linear in its parameters (so that unique least squares parameter estimates are guaranteed v 5 May 2014 v Volume 5(5) v Article 58

6 Table 1. Summary of data sets used in this analysis. Data sets were obtained from published papers, data archives from long-term study sites, and the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center, accessible at Data set Reference No. years Location Study site Grassland type 1 Andales et al Cheyenne, Wyoming, United States 1 ORNL 25 Badkyz, Mary, Turkmenistan 1 Bai et al Ewenke Qi, Inner Mongolia, China 1 Bai et al Damao Qi, Inner Mongolia, China High Plains Grasslands Research Station Badkhzy Nature Reserve Station Ewenke Grassland Management Station Damao Grassland Management Station San Joaquin 1 Bentley and Talbot Oneals, California, United States Experimental Range 4 Cedar Creek LTER 11 Bethel, Minnesota, Cedar Creek United States Ecosystem Science Reserve 1 ORNL 21 Dzhanybek, West Dzhanybek Kazakhstan, Research Station Kazakhstan 1 Guo et al Zhenglan Qi, Inner Mongolia, China 1 Hulett and Tomanek Hays, Kansas, United States 3 Jornada LTER 19 Las Cruces, New Mexico, United States 1 Kellogg Biological Station LTER 18 Hickory Corners, Michigan, United States MAP (mm) PRVR mixed prairie desert steppe meadow steppe desert steppe annual grassland old field semi-arid steppe Inner Mongolia study site temperate steppe near Fort Hays mixed prairie Experiment Station Jornada LTER desert grassland Kellogg Biological Station LTER 3 Konza Prairie LTER 27 Manhattan, Kansas, United States Konza Prairie Biological Station 1 ORNL 30 Kursk, Kursk Kursk long-term Oblast, Russia ecological study site 1 Ma et al Xilinhot, Inner Mongolia,China 1 ORNL 11 Texcoco, Mexico, Mexico 1 Murphy Hopland, California, United States 1 O Connor et al Bloemfontein, Free State, South Africa 2 Patton et al Streeter, North Dakota, United States 1 Rogler and Haas Mandan, North Dakota, United States 7 Shortgrass Steppe LTER 23 Nunn, Colorado, United States 1 Smoliak Manyberries, Alberta, Canada 1 Towne and Owensby Manhattan, Kansas, United States 1 ORNL 26 Bela-Bela, Limpopo, South Africa Inner Mongolia Grassland Ecosystem Research Station Colegio de Postgraduodos site Hopland Field Station Sydenham farm, Univ. of Orange Free State Central Grasslands Research Extension Center Northern Great Plains Grassland Station old field tallgrass prairie meadow steppe typical steppe saline grassland annual grassland semi-arid grassland mixed prairie mixed prairie Shortgrass Steppe LTER shortgrass steppe Agriculture Canada mixed prairie Research Substation Kansas Flint Hills tallgrass prairie Towoomba Research Station Note: Abbreviations are: MAP, mean annual precipitation; PRVR, production to rain variability ratios. mesic grassland v 6 May 2014 v Volume 5(5) v Article 58

7 to exist), and fit the data better than other saturating models we tested. We fit all models excluding the first year of data so that each model would be based on the same number of observations as the lag effect model. Fig. 1 shows the linear, lag, and nonlinear models fit to a data set. Next, we used F-tests to determine whether any of these precipitation-based models (linear, lag effect, nonlinear) predicted interannual variation in ANPP better than a simple mean. For 14 data sets, none of the three models fit the data significantly better ( p. 0.05) than a model with only a mean term, which emphasizes that precipitation is only one of many factors driving variability in ANPP. These 14 data sets were excluded from subsequent analyses. The remaining 23 data sets from 15 different study sites averaged 22 years in length. For each of these data sets, we used coefficients of variation (R 2 )to quantify the amount ANPP variability explained by each precipitation model. We compared linear, nonlinear, and lag model fits using Akaike s Information Criterion (AICc), a model evaluation tool which balances goodness-of-fit and parsimony. We also calculated Akaike s weights, which represent the relative likelihood of each model given the suite of fitted models. Perturbation of precipitation variability We used the fitted model parameters and the observed precipitation time series to generate predictions of ANPP for each data set based on the linear, lag, and nonlinear models. Variability in these predicted ANPP time series reflects variability in precipitation and not any other sources of variability. Thus, our analysis focuses only on the portion of ANPP variability deterministically related to precipitation. This approach assumes that the unexplained variation in ANPP (the model residuals) is not sensitive to precipitation variability, an assumption we return to in the Discussion. To project changes in ANPP variability due to increases in precipitation variability, we perturbed the interannual variation of the observed precipitation time series, increasing the standard deviation of each precipitation time series by 5% without changing precipitation mean (Fig. 2A). This approach preserves the observed sequence and distribution of precipitation. We then used these perturbed precipitation time series to generate a second set of predicted ANPP values for each of the models (Fig. 2B D). Again, all the interannual variability in these predicted ANPP time series can be attributed to interannual variability in precipitation. We compared absolute and relative variability between the two sets of predicted ANPP time series (e.g., linear ANPP predictions based on observed precipitation were compared with linear ANPP predictions based on perturbed precipitation). We calculated absolute changes in ANPP variability as the difference in ANPP standard deviation. We divided these differences in standard deviation by the standard deviation of the unperturbed ANPP time series to yield relative changes in ANPP variability. Finally, we compared relative changes in ANPP variability with the perturbation of precipitation variability (5%) to determine whether changes in ANPP variability were proportional to changes in precipitation variability. To obtain the final result for each data set, we calculated a weighted average of the relative changes in ANPP standard deviation using Akaike weights from the model fitting. In cases where multiple data sets of the same vegetation type were available from the same study, we averaged across data sets to obtain mean changes in ANPP variability for that site. We repeated the analysis with perturbations of 1%, 2%, and 10% to capture the range of increased precipitation variability predicted by GCMs (Räisänen 2002). RESULTS Predicting PRVR Eq. 2 predicts PRVR at all sites (Fig. 3). The y- intercept of the linear, temporal precipitation- ANPP relationship accounts for 39.2% of the variation in PRVR across sites (Fig. 3A). Mean ANPP accounts for another 32.0% of the variation in PRVR. Slope, correlation, and mean precipitation each explained 2% or less of the variation in PRVR. Temporal precipitation-anpp relationships Linear and nonlinear precipitation models each explained an average of 39% of the interannual variability in ANPP (Table 2). A lag model did slightly better, explaining 44% of the variability in ANPP on average. Both lag and v 7 May 2014 v Volume 5(5) v Article 58

8 Fig. 3. PRVR is strongly controlled by mean ANPP and the y-intercept fitted to a linear regression model of precipitation and production. The y-intercept explains 39.2% of the variation in PRVR across sites (A) and mean production (B) explains 30% of the variation. The other variables that determine PRVR the slope of the regression relationship (C), mean precipitation (D), and the correlation coefficient between precipitation and production (not shown) do not explain substantial variation in PRVR. The data shown are from 37 long-term data sets of precipitation and primary production from around the globe. nonlinear ANPP models predicted ANPP in the wettest and driest years fairly well, averaging (by median) within 15 g/m 2 of observed ANPP. In contrast, simple linear models consistently overestimated ANPP in both the wettest (by 66 g/m 2 on average) and driest years (by 20 g/m 2 on average) at all except the driest sites. Although a lag model explained the most variability in ANPP in 16 data sets, this model was penalized when AICc was used to compare models. Of the 23 data sets, AICc indicated the most support for linear, lag, and nonlinear models in 8, 3 and 12 cases, respectively. The average Akaike weights for the linear, lag, and nonlinear models were 0.36, 0.22, and 0.42, respectively. Across data sets, there were no patterns between mean annual precipitation or temperature and Akaike weights or R 2 for any of the models. In the lag model, estimates for the lag parameter g ranged from 0.39 to 0.46 across data sets, but were statistically significant ( p, 0.05) at only the following four sites: Shortgrass Steppe LTER; Bloemfontein, South Africa; Kursk, Russia; and Alberta, Canada. All of these data sets except for Bloemfontein best fit a lag model over a linear or nonlinear model. Estimates for the lag parameter g within these data sets ranged from 0.42 to 0.46, while estimates for the precipitation parameter f were smaller, ranging from 0.17 to All four sites average between 300 and 600 mm of rainfall each year. On v 8 May 2014 v Volume 5(5) v Article 58

9 Table 2. Linear, nonlinear (Nl), and lag models fit to precipitation-anpp data sets. Only data sets for which precipitation was a significant predictor of ANPP are shown. The last six columns show the increase in ANPP standard deviation given a 5% increase in precipitation standard deviation during all years, only years with rainfall below mean precipitation, and only years above mean precipitation. The weighted model averages projections from the three models based on their Akaike weights. Increase in r ANPP (%) R 2 Akaike weight Nonlinear model Weighted model average Study site Lin model Nl model Lag model Lin model NI Model Lag model All Dry Wet All Dry Wet Agriculture Canada Research Substation Badkhzy Nature Reserve Station Central Grasslands Research Extension Center Dzhanybek Research Station High Plains Grasslands Research Station Jornada LTER (BASN) Jornada LTER (IBPE) Jornada LTER (SUMM) Kansas Flint Hills Konza Prairie Biological Station Kursk long-term ecological study site near Fort Hays Experiment Station Northern Great Plains grassland Station San Joaquin Experimental Range Shortgrass Steppe LTER (ESA1) Shortgrass Steppe LTER (Forage) Shortgrass Steppe LTER (Midslope) Shortgrass Steppe LTER (OC) Shortgrass Steppe LTER (Ridge) Shortgrass Steppe LTER (Sec25) Shortgrass Steppe LTER (Swale) Sydenham farm, Univ. of Orange Free State Towoomba Research Station Note: Abbreviations are: Nl ¼ nolinear model; Lin ¼ linear model; All ¼ all years; Dry ¼ dry years; Wet ¼ wet years. v 9 May 2014 v Volume 5(5) v Article 58

10 Fig. 4. Relative changes in ANPP standard deviation (%) given a 5% increase in the standard deviation of annual precipitation for 23 data sets from 15 different grassland sites. A 5% increase in the variability of precipitation always results in a 5% increase in the variability of ANPP when the relationship between precipitation and ANPP is linear or lagged, but results in a disproportionately large increase in ANPP variability when the precipitation-anpp relationship is nonlinear. The weighted ANPP model accounts for AICc weights for linear, lag, and nonlinear models fitted to each data set. The inset of the weighted model shows that the change in ANPP variability is disproportionately high for dry years and disproportionately low for wet years due to the contribution of the nonlinear model. average, adding a lag parameter to a linear precipitation-anpp model explained only an additional 5.3% of the variability in ANPP at a site, but explained an additional 17.4% of the variability at the four sites with significant lag effects. Perturbations of precipitation variability Table 2 shows the results from the precipitation perturbations for each data set. A 5% increase in precipitation standard deviation led to an absolute increase of 1.6, 1.6, and 2.9 g/m 2 in the standard deviation of ANPP across the linear, lag, and nonlinear models, respectively. As expected, a 5% increase in precipitation standard deviation always led to a 5% increase in ANPP standard deviation when ANPP was modeled as a linear function of precipitation. The relative increase in ANPP standard deviation for the lag model was also always very close to 5% (ranging from 4.98% to 5.01%), meaning that the lag model did not cause a disproportionate increase in ANPP for any of the data sets (Fig. 2C). The relative increase in ANPP standard deviation for the nonlinear model across data sets ranged from 5.6% to 20%, averaging 9.0%. A nonlinear, concave down precipitation-anpp model produces an ANPP distribution that is left-skewed compared to the distribution of precipitation (Fig. 2D). As a result, ANPP variances predicted by this model, as well as changes in ANPP variance due to perturbations, are not symmetric about the mean of ANPP. On average, a 5% increase in precipitation standard deviation caused a 9.0% increase in ANPP standard deviation, which was comprised of a 2.6% increase in variability in years where precipitation was above the mean and an 11.8% increase in years when precipitation was below mean. Note that the nonlinear model generates negative ANPP predictions for one very dry year in each of three data sets, which leads to artificially high standard deviations, especially in the perturbed time series. However, removing these three data sets from the analysis does not change our conclusions. Averaging across multiple data sets from the same study site using Akaike weights, relative increases in ANPP standard deviation ranged v 10 May 2014 v Volume 5(5) v Article 58

11 from 5.0% to 10.5%, averaging 6.2% across 15 different study sites (Fig. 4). The extent to which nonlinearity amplifies precipitation variability depends on the size of the perturbation. Perturbations of 1%, 2%, 5%, and 10% led to mean relative increases in ANPP variability of 1.2%, 2.4%, 6.1%, and 12.6%, respectively. DISCUSSION At water-limited sites, increased interannual precipitation variability will translate into increases in ANPP variability. Our results show that the magnitude of the increase in ANPP variability does not depend on the PRVR but rather on the functional relationships between precipitation and ANPP. PRVR describes the relative variability of production and precipitation, but does not measure the ability of vegetation to amplify variability in precipitation. PRVR greater or less than 1 does not necessarily reflect lag effects, vegetation or site characteristics, or lack of appropriate data. Instead, we show that PRVR is largely controlled by mean ANPP and the y- intercept of the regression line that predicts production from precipitation, two correlated measures. If we compare two sites that produce the same amount of biomass per unit precipitation (same slope) and have the same r, the site with a lower mean ANPP will have a lower y- intercept, a higher CV PROD and higher PRVR. Thus, in many cases, high PRVR may simply indicate that a site has a low mean ANPP. Note that y-intercepts are also important in estimating rain use efficiency (Veron et al. 2005). From a statistical perspective, whether interannual variability in precipitation can be amplified by vegetation is dictated by the functional relationship between precipitation and production. Both model selection and coefficients of variation indicate that in grasslands where ANPP is correlated with precipitation, the typical precipitation-anpp relationship is weakly nonlinear. Though both linear and nonlinear models explain nearly 40% of the variability in ANPP, linear models consistently overestimate ANPP in mesic grasslands in very wet or dry years. Given nonlinear, concave-down precipitation- ANPP relationships, increases in interannual precipitation variability will translate into disproportionate increases in ANPP variability. Even though nonlinearities in ANPP were not very strong, they resulted in considerable amplification of precipitation variability due to the asymmetric change in ANPP variability in wet and dry years. Increases in precipitation variability lead to especially large decreases in ANPP in dry years, where the slope of the precipitation- ANPP relationship is steep. However, in wet years, increases in precipitation variability lead to small increases in ANPP due to the leveling-off of the precipitation-anpp slope. In other words, an increase in interannual precipitation variability will typically lead to increases in primary production in wet years that are smaller than decreases in production in dry years. On average, when ANPP was modeled as a nonlinear function of precipitation, relative increases in predicted ANPP variability were 1.5 times larger than increases in precipitation variability. At a few sites, simple linear and nonlinear models were inadequate for characterizing the precipitation-anpp relationship. At these sites, accounting for previous year lag effects with an additional model parameter was critical; the average extra variability explained by a lag model over a linear or nonlinear model was 17%. Nevertheless, only 4 out of 27 data sets exhibited significant lag effects, suggesting that very strong interannual lag effects are not common at grassland sites. However, our statistical power to detect lagged ANPP responses is limited by the length of our data sets. We were only able to detect significant lag effects at the longest of the seven ANPP data sets from Shortgrass Steppe LTER site. The average length of the four data sets with significant lag effects was 31 years, nearly ten years longer than the average length of the data sets included in this study. Lag effects may also operate on time scales that these data sets do not capture; many studies report intra-annual lag effects in production (e.g., Nicholson and Farrar 1994, Wiegand et al. 2004, Nippert et al. 2006, Sherry et al. 2008, Ma et al. 2010). Lag effects did not cause disproportionate changes in predicted ANPP variability because our lag model maintained the linear relationship between precipitation and ANPP. The amplification of precipitation variability referred to by v 11 May 2014 v Volume 5(5) v Article 58

12 Oesterheld et al. (2001) and Wiegand et al. (2004) occurs when comparing variance explained by two different regression models for a given precipitation sequence, not when evaluating the effect of increased precipitation variability. Our perturbation of precipitation variability preserved the sequence of precipitation, so it did not lead to a disproportionate change in ANPP variability via lag effects. If climate change were to alter precipitation autocorrelation, then we could see disproportionate responses in ANPP variability due to lag effects, but to our knowledge climate models have not projected important changes in interannual autocorrelation. After accounting for linear, lag, and nonlinear model weights, a 5% increase in precipitation variability led to a 6.2% increase in grassland ANPP variability, on average. At some sites, increases were much larger: 10.5% in mixed prairie in North Dakota and 7.5% in desert grasslands in New Mexico. Furthermore, under the nonlinear models, ANPP will be decreasing more in dry years than it is increasing in wet years, increasing the frequency of low production years more than the frequency of high production years despite a symmetric increase in the frequency of wet and dry years. These increases in ANPP variability will make primary production more difficult to forecast and could exacerbate existing challenges for natural resource management, especially when combined with alterations in ANPP caused by changes in the annual mean of precipitation (Hsu et al. 2012) as well as the intra-annual variability and timing of precipitation (Swemmer et al. 2007, Heisler- White et al. 2009, Craine et al. 2012). Our analysis focused only on the portion of ANPP variability related to precipitation and assumed that remaining variation in ANPP is not sensitive to interannual precipitation variability. However, other drivers of ANPP may be indirectly influenced by precipitation and precipitation variability. For example, nitrogen availability, especially in arid and semi-arid regions, is strongly controlled by water availability (Noy-Meir 1973, Schlesinger 1997, Austin et al. 2004, Yahdjian et al. 2006). Increases in precipitation variability could lead to changes in the duration and timing of nitrogen mineralization and plant uptake, which would impact ANPP variability. Altered precipitation will also influence air temperature through the effects of evapotranspiration on sensible and latent heat. Within the data sets used in this study, which represent grasslands where precipitation influences ANPP, an average of 39% of the variability in ANPP is directly explained by precipitation, but the percentage of ANPP that is indirectly affected by precipitation could actually be higher. Process-based simulation models offer an alternative approach for understanding and predicting ANPP dynamics that accounts for a much wider range of factors and interactions, such as interactions between water and nitrogen availability (e.g., McGuire et al. 2001). However, our finding that nonlinearity determines how variability in a climate driver translates into future variability in ANPP also applies to process-based models: if any function contained within the process-based simulation is nonlinear, then changes in ANPP variability could be amplified or buffered relative to changes in climate variability. Similarly, while we only analyzed data from ungrazed sites, our results show that for grazing to buffer or amplify future variability in ANPP, it must influence the nonlinearity of the precipitation-anpp relationship. Thus, our results extend well beyond precipitation-anpp relationships and should help ecologists anticipate future changes in the variability of a wide variety of ecological response variables. ACKNOWLEDGMENTS Our first and foremost thanks goes to the researchers that collected data year after year at these long-term study sites. Next, we thank John Stark and Ron Ryel for critical discussions and the members of Katie Suding s lab for helpful feedback on an earlier draft of this manuscript. J. S. Hsu was supported by a Quinney Foundation Fellowship and an NSF Graduate Research Fellowship. P. B. Adler was supported by NSF DEB and the Utah Agricultural Experiment Station, Utah State University, which approves this work as journal paper number LITERATURE CITED Andales, A., J. Derner, L. Ahuja, and R. Hart Strategic and tactical prediction of forage production in northern mixed-grass prairie. Rangeland Ecology and Management 59: Arnone, J. A., P. S. J. Verburg, D. W. Johnson, J. D. v 12 May 2014 v Volume 5(5) v Article 58

13 Larsen, R. L. Jasoni, A. J. Lucchesi, C. M. Batts, C. von Nagy, W. G. Coulombe, D. E. Schorran, P. E. Buck, B. H. Braswell, J. S. Coleman, R. A. Sherry, L. L. Wallace, Y. Q. Luo, and D. S. Schimel Prolonged suppression of ecosystem carbon dioxide uptake after an anomalously warm year. Nature 455: Austin, A. T., L. Yahdjian, J. M. Stark, J. Belnap, A. Porporato, U. Norton, D. A. Ravetta, and S. M. Schaeffer Water pulses and biogeochemical cycles in arid and semiarid ecosystems. Oecologia 141: Bai, Y., L. Li, J. Huang, and Z. Chen The influence of plant diversity and functional composition on ecosystem stability of four Stipa communities in the Inner Mongolia Plateau. Acta Botanica Sinica 43: Bentley, J., and M. Talbot Efficient use of annual plants on cattle ranges in the California foothills. United States Department of Agriculture Circular. Boer, G. J Changes in interannual variability and decadal potential predictability under global warming. Journal of Climate 22: Boyce, M. S., C. K. Haridas, C. T. Lee, C. L. Boggs, E. M. Bruna, T. Coulson, D. Doak, J. M. Drake, J. M. Gaillard, C. C. Horvitz, S. Kalisz, B. E. Kendall, T. Knight, M. Mastrandrea, E. S. Menges, W. F. Morris, C. A. Pfister, and S. D. Tuljapurkar Demography in an increasingly variable world. Trends in Ecology and Evolution 21: Craine, J., J. Nippert, A. Elmore, A. Skibbe, S. Hutchinson, and N. Brunsell Timing of climate variability and grassland productivity. Proceedings of the National Academy of Sciences 109: Díaz-Solís, H., W. E. Grant, M. M. Kothmann, W. R. Teague, and J. A. Díaz-García Adaptive management of stocking rates to reduce effects of drought on cow-calf production systems in semiarid rangelands. Agricultural Systems 100: Diouf, A., and E. Lambin Monitoring land-cover changes in semi-arid regions: remote sensing data and field observations in the Ferlo, Senegal. Journal of Arid Environments 48: Guevara, J., J. Cavagnaro, O. Estevez, H. Le Houerou, and C. Stasi Productivity, management and development problems in the arid rangelands of the central Mendoza plains (Argentina). Journal of Arid Environments 35: Guo, R., X. K. Wang, Z. Y. Ouyang, and Y. N. Li Spatial and temporal relationships between precipitation and ANPP of four types of grasslands in northern China. Journal of Environmental Sciences- China 18: Heisler, J., and J. Weltzin Variability matters: towards a perspective on the influence of precipitation on terrestrial ecosystems. New Phytologist 172: Heisler-White, J., J. Blair, E. Kelly, K. Harmoney, and A. Knapp Contingent productivity responses to more extreme rainfall regimes across a grassland biome. Global Change Biology 15: Herbel, C. H., F. N. Ares, and R. A. Wright Drought effects on a semidesert grassland range. Ecology 53:1084. Hsu, J. S., J. Powell, and P. B. Adler Sensitivity of mean annual primary production to precipitation. Global Change Biology 18: Hu, Z., J. Fan, H. Zhong, and G. Yu Spatiotemporal dynamics of aboveground primary productivity along a precipitation gradient in Chinese temperate grassland. Science in China Series D- Earth Sciences 50: Hulett, G., and G. Tomanek Forage production on a clay upland range site in western Kansas. Journal of Range Management 22: Khumalo, G., and J. Holechek Relationships between Chihuahuan Desert Perennial Grass Production and Precipitation. Rangeland Ecology and Management 58: Knapp, A. K., C. Beier, D. D. Briske, A. T. Classen, Y. Luo, M. Reichstein, M. D. Smith, S. D. Smith, J. E. Bell, P. A. Fay, J. L. Heisler, S. W. Leavitt, R. Sherry, B. Smith, and E. Weng Consequences of more extreme precipitation regimes for terrestrial ecosystems. BioScience 58: Knapp, A. K., C. E. Burns, R. W. S. Fynn, K. P. Kirkman, C. D. Morris, and M. D. Smith Convergence and contingency in production-precipitation relationships in North American and South African C4 grasslands. Oecologia 149: Lauenroth, W. K., and O. E. Sala Long-term forage production of North American shortgrass steppe. Ecological Applications 2: Le Houerou, H. N., R. L. Bingham, and W. Skerbek Relationship between the variability of primary production and the variability of annual precipitation in world arid lands. Journal of Arid Environments 15:1 18. Ma, W., Z. Liu, Z. Wang, W. Wang, C. Liang, Y. Tang, J. He, and J. Fang Climate change alters interannual variation of grassland aboveground productivity: evidence from a 22-year measurement series in the Inner Mongolian grassland. Journal of Plant Research 123: McGuire, A. D., S. Sitch, J. S. Clein, R. Dargaville, G. Esser, J. Foley, M. Heimann, F. Joos, J. Kaplan, D. W. Kicklighter, R. A. Meier, J. M. Melillo, B. Moore, I. C. Prentice, N. Ramankutty, T. Reichenau, A. Schloss, H. Tian, L. J. Williams, and U. Wittenberg Carbon balance of the terrestrial biosphere in the Twentieth Century: Analyses of CO2, climate and land use effects with four v 13 May 2014 v Volume 5(5) v Article 58

14 process-based ecosystem models. Global Biogeochemical Cycles 15: Menges, E. S Population viability analyses in plants: challenges and opportunities. Trends in Ecology and Evolution 15: Murphy, A. H Predicted forage yield based on fall precipitation in California annual grasslands. Journal of Range Management 23: Nicholson, S., and T. Farrar The influence of soil type on the relationships between ndvi, rainfall, and soil-moisture in semiarid Botswana 1: NDVI response to rainfall. Remote Sensing of Environment 50: Nippert, J., A. Knapp, and J. Briggs Intra-annual rainfall variability and grassland productivity: can the past predict the future? Plant Ecology 184: Noy-Meir, I Desert ecosystems: environment and producers. Annual Review of Ecology and Systematics 4: Noy-Meir, I., and B. Walker Stability and resilience in rangelands. Pages in Rangelands: a resource under siege. Proceedings of the Second International Rangeland Congress. Australian Academy of Sciences, Canberra, ACT, Australia. O Connor, T., L. Haines, and H. Snyman Influence of precipitation and species composition on phytomass of a semi-arid African grassland. Journal of Ecology 89: Oesterheld, M., J. Loreti, M. Semmartin, and O. E. Sala Inter-annual variation in primary production of a semi-arid grassland related to previous-year production. Journal of Vegetation Science 12: Paruelo, J., and W. Lauenroth Interannual variability of NDVI and its relationship to climate for North American shrublands and grasslands. Journal of Biogeography 25: Patton, B. D., X. Dong, P. E. Nyren, and A. Nyren Effects of grazing intensity, precipitation, and temperature on forage production. Rangeland Ecology and Management 60: Prince, S., E. De Colstoun, and L. Kravitz Evidence from rain-use efficiencies does not indicate extensive Sahelian desertification. Global Change Biology 4: Räisänen, J CO 2 -induced changes in interannual temperature and precipitation variability in 19 CMIP2 experiments. Journal of Climate 15: Rogler, G., and H. Haas Range production as related to soil moisture and precipitation on the Northern Great Plains. Journal of the American Society of Agronomy 39: Sala, O. E., L. A. Gherardi, L. Reichmann, E. Jobbágy, and D. Peters Legacies of precipitation fluctuations on primary production: theory and data synthesis. Philosophical Transactions of the Royal Society B 367: Schlesinger, W. H Biogeochemistry: an analysis of global change. Second edition. Academic Press, River Grove, Illinois, USA. Sherry, R. A., E. S. Weng, J. A. Arnone, D. W. Johnson, D. S. Schimel, P. S. Verburg, L. L. Wallace, and Y. Q. Luo Lagged effects of experimental warming and doubled precipitation on annual and seasonal aboveground biomass production in a tallgrass prairie. Global Change Biology 14: Smart, A. J., B. H. Dunn, P. S. Johnson, L. Xu, and R. N. Gates Using weather data to explain herbage yield on three Great Plains plant communities. Rangeland Ecology and Management 60: Smoliak, S Influence of climatic conditions on forage production of shortgrass rangeland. Journal of Range Management 9: Smoliak, S Influence of climatic conditions on production of Stipa-Bouteloua prairie over a 50- year period. Journal of Range Management 39: Sneva, F. A., and D. N. Hyder Estimating herbage production on semiarid ranges in the intermountain region. Journal of Range Management 15:88. Swemmer, A., A. Knapp, and H. Snyman Intraseasonal precipitation patterns and above-ground productivity in three perennial grasslands. Journal of Ecology 95: Towne, G., and C. Owensby Long-term effects of annual burning at different dates in ungrazed Kansas tallgrass prairie. Journal of Range Management 37: Veron, S., M. Oesterheld, and J. Paruelo Production as a function of resource availability: Slopes and efficiencies are different. Journal of Vegetation Science 16: Veron, S., J. Paruelo, O. Sala, and W. Lauenroth Environmental controls of primary production in agricultural systems of the Argentine Pampas. Ecosystems 5: Weltzin, J. F., M. E. Loik, S. Schwinning, D. G. Williams, P. A. Fay, B. M. Haddad, J. Harte, T. E. Huxman, A. K. Knapp, G. H. Lin, W. T. Pockman, M. R. Shaw, E. E. Small, M. D. Smith, S. D. Smith, D. T. Tissue, and J. C. Zak Assessing the response of terrestrial ecosystems to potential changes in precipitation. BioScience 53: Wessels, K., S. Prince, J. Malherbe, J. Small, P. Frost, and D. VanZyl Can human-induced land degradation be distinguished from the effects of rainfall variability? A case study in South Africa. Journal of Arid Environments 68: Wiegand, T., H. A. Snyman, K. Kellner, and J. M. Paruelo Do grasslands have a memory: v 14 May 2014 v Volume 5(5) v Article 58