Data collection

We extracted results for soil fluxes of CH 4 and N 2 O, root biomass and soil water contents from atmospheric CO 2 enrichment studies, conducted in the field, in growth chambers or in glass houses. We used Google Scholar (Google Inc.) for an exhaustive search of journal articles published before January 2011, using as search terms either “elevated CO 2 ” or “CO 2 enrichment”, and either “N 2 O” and “soil”, or “CH 4 ”. Further papers were added from a comparable search using Web of Science. For a study to be included in our data set, the atmospheric CO 2 concentration for the ambient and elevated treatments had to be in the range 350–450 p.p.m.v. and 450–800 p.p.m.v., respectively. Means and sample sizes had to be reported for both ambient and elevated CO 2 treatments.

For each study, we noted experimental duration, plant species, N fertilization rates and the type of experimental facility. Estimates of standard deviation were tabulated when available, but were not required for inclusion in the analysis. We included studies involving experiments in pots (that is, any container with dimensions <1 m) or in the field, and studies on natural or planted vegetation. We only considered studies in which soil under both CO 2 treatments had the same treatment history. One study was discarded for this reason. Studies on soil water content and root biomass were only included if data on N 2 O or CH 4 fluxes were available from the same site. When root biomass and soil water content were reported for multiple soil depths, we calculated the overall treatment effects across the entire soil profile. We included separate observations of increased CO 2 effects from a single ecosystem under different experimental treatments (that is, in multifactorial studies). Because wetlands are mostly anaerobic and therefore produce CH 4 , whereas upland soils are mostly aerobic and oxidize CH 4 , these two groups of ecosystems were considered in separate data sets. We also distinguished studies conducted in rice paddies, which like wetlands produce CH 4 . Because the low number of studies on N 2 O fluxes from rice paddies (1) and wetlands (3) did not warrant the construction of separate data sets, these studies were not included in our analysis.

We divided the studies into two categories of N availability based on N fertilization rates, that is, more or less than 30 kg N ha−1 yr−1. This cut-off point was chosen because it is comparable to maximum atmospheric N depositions in the US and most of the EU23. We also distinguished between studies on natural or planted vegetation. Agricultural ecosystems were defined as grassland and cropland that received between 30 and 300 kg N ha−1 yr−1. The upper cut-off point was based on reported average fertilization rates for croplands in the world’s most intensively fertilized region (that is, East Asia, at 150 kg N ha−1 yr−1)16, and the assumption that average fertilizer N use per hectare will be twofold higher in 205030.

Response metrics

We evaluated our data sets by using meta-analysis. As a metric for the response of GHG emissions to increased CO 2 , we used the natural log of the response ratio24. This metric starts with an estimate of the relative change in GHG emissions between ambient and increased CO 2 treatments, and log-transforms it to improve its statistical behaviour. where GHG is the flux of either CH 4 or N 2 O under increased (i) or ambient (a) conditions. We also used lnR as a metric for CO 2 responses of root biomass and soil water contents. Fluxes of CH 4 from upland soils could not be analysed using this metric, because our data set included both sites with negative (that is, CH 4 uptake) and positive (CH 4 emissions) fluxes. For this reason, we also used the difference in annual emissions, expressed on an areal basis (U) as a metric: with GHG i and GHG a as before. All but one study on wetland soils found net CH 4 emissions under both ambient and increased CO 2 conditions (Supplementary Data 2). This one study, which reported that increased CO 2 turned wetland soils from a net sink of CH 4 into a net source, was therefore excluded when calculating lnR, but included when calculating U.

Several studies only measured N 2 O and CH 4 fluxes during the growing season. In these cases, we assumed that the effect of increased CO 2 on annual fluxes occurred entirely during this period. When the length of the growing season was not explicitly indicated, we assumed a growing season of 150 days. When studies measured gas fluxes for multiple years, fluxes were averaged over time.

Weighting functions

We performed analyses using non-parametric weighting functions and generated confidence intervals (CIs) on weighted effects sizes using bootstrapping. Because effect size estimates and subsequent inferences in meta-analysis may depend on how individual studies are weighted12, we used three different weighting functions. First, weighted by replication: W R = (n a × n i )/(n a + n i ), where n a and n i are the number of replicates under ambient and increased CO 2 , respectively25. For pot studies, n equalled the number of replicate experimental facilities (that is, growth chambers, glass houses, and so on), rather than the number of pots per CO 2 treatment. Second, unweighted. Each observation was assigned an equal weight: W U = 1. Third, weighted by the inverse of the pooled variance, the weighting function conventionally used in meta-analyses26: W V = 1/(var a /GHG a 2 + var i /GHG i 2), with GHG a and GHG i as before, and var a and var i as their respective variance.

When variance estimates were missing for a study, we calculated the average coefficient of variation (CV) within each data set, and then approximated the missing variance by multiplying the reported mean by the average CV and squaring the result.

When multiple effects were extracted from the same experimental site, we adjusted the weights defined above by the total number of observations from that site. This approach ensured that all experimental comparisons in multifactor studies could be included in the data set without dominating the overall effect size. For three experimental sites, multiple studies were done on the same GHG fluxes at different points in time. We adjusted the weights of observations from these studies by the total number of observations per site. Thus, the final weights used in the analyses were w f ,i = W f ,i /n c , where n c was the number of observations from the same site as the ith observation, and f was the index that referred to one of the three weighting functions defined above.

Mean effects sizes ( , ) for different categories of studies were estimated as: We used METAWIN 2.127 to generate these mean effect sizes and 95% bootstrapped CIs (4,999 iterations). Treatment effects were considered significant if the 95% CI did not overlap with 0. The results for the analyses on lnR were back-transformed and reported as percentage change under increased CO 2 (that is, 100 × (R − 1)) to ease interpretation.

We tested whether lnR for GHG emissions was correlated with lnR for root biomass using the statistical package SPSS 19. Similarly, we tested whether lnR for GHG emissions was correlated with experiment duration or the level of CO 2 enrichment. The effect of increased CO 2 on soil emissions of N 2 O, but not CH 4 , showed a weak positive correlation with experiment duration (Supplementary Figs 2 and 3). lnR was not significantly correlated with the degree of CO 2 enrichment for either N 2 O or CH 4 emissions (Supplementary Figs 4 and 5). This result is probably due to the large variation in treatment effects between studies, masking effects of the degree in CO 2 enrichment. Alternatively, the results may reflect that plant growth is a saturating function of CO 2 concentrations. Since experiments increased atmospheric CO 2 to a similar extent for all data sets (Supplementary Table 13), we did not normalize effect sizes for the level of CO 2 enrichment.

Results using the different weighting functions were qualitatively similar. However, the variance-based weighting function, W v , yielded weights that varied over 1,000 times in magnitude (Supplementary Data 1 and 2). By assigning extreme importance to individual observations, average effect sizes were largely determined by a small number of studies. Because variance estimates are notoriously unreliable (especially given the small samples common in many of these studies), we favoured the use of the alternative weighting functions (which assigned less extreme weights). In this Letter, we provide results of the analyses on effect sizes that were weighted by replication; results for all weighting functions can be found in Supplementary Tables 2–8, 11 and 12.

Scaling of results

We scaled up the results from the experiments by multiplying them by the total land area covered by the particular type of habitat that was being summarized. In other words, we took the mean effects and confidence intervals for U calculated above and scaled them: where F is expressed in Pg CO 2 equiv. yr−1, and H is the amount of habitat in uplands, wetlands, or rice paddies (103.1, 5.7, and 1.3 million km2, respectively28,29). Because N fertilization increases N 2 O emissions16,17 and enhances plant growth, we distinguished between upland agricultural ecosystems (that is, 19.0 million km2 of fertilized grasslands and croplands16, minus 1.3 million km2 of rice paddies28) and ecosystems receiving little or no fertilizer (103.1 – 19.0 + 1.3 = 85.4 million km2).

We estimated the contribution of winter N 2 O emissions to total N 2 O emissions from a recently published data set16. For agricultural soils and soils under natural vegetation, studies conducted over the growing season and lasting 100–200 days were compared to studies conducted over the entire year (that is, lasting >300 days). Because tropical and subtropical systems do not experience marked growing seasons, we excluded studies from those regions. For agricultural soils, we only considered studies on grassland and cropland receiving 30–300 kg N ha−1 yr−1 (that is, the same restrictions that applied to our data sets 1 and 2 for the global extrapolation shown in Fig. 2). The difference in mean N 2 O emissions between the two categories of study duration was assumed to be representative of N 2 O emissions outside the growing season.