#### 2.1. Data Analysis

[7] In our literature survey, we limited our analysis to experiments that examined the effects of elevated CO_{2}, warming, and N addition on natural or seminatural communities. We have attempted to be exhaustive, especially for studies published in the last decade. We did not take into account the studies that measured N_{2}O fluxes from agricultural soils, as these data have been extensively reviewed [*Bouwman et al.*, 2002]. The data were sorted by treatment (elevated CO_{2}, N addition, warming), process measured (field and laboratory N_{2}O emissions, net and gross nitrification, nitrifying enzyme activity (NEA), net and gross denitrification, denitrifying enzyme activity (DEA)), type of ecosystem (woody or herbaceous), type of experiment (field or mesocosm), and duration of treatment. CO_{2} treatments ranged from 550 to 750 μmol mol^{−1} in the experiments we assessed, but we considered all of these as a common treatment in our analysis primarily because of low sample size. By contrast, N addition treatments ranged from 25 to 420 kg N ha^{−1} yr^{−1}, so in addition to the meta-analysis we examined the relationship between N_{2}O emissions and the amount of N added. N was generally added as NH_{4}NO_{3} in the experiments that we analyzed, but N was also added as urea [*Mosier et al.*, 1991; *Castro et al.*, 1994; *Hungate et al.*, 1997b], atmospheric deposition [*Skiba et al.*, 1998; *Lovett and Rueth*, 1999], mixing of soils with different N availability [*Ambus and Robertson*, 1999; *Zak et al.*, 2000a], or NH_{4}SO_{4} [*Brumme and Beese*, 1992]. We considered only the warming studies in the field or using mesocosms: We did not include soil incubation studies.

[8] We restricted our analyses to experimental results for which the measurement error was available, either from reported values or figures in published articles, or from data provided as personal communications. On the basis of control and treatment means (_{c} and _{t}, respectively), standard deviations (S_{c} and S_{t}), and sample sizes (n_{c} and n_{t}), we used the response ratio r = _{t}/_{c} as a metric. Following *Curtis and Wang* [1998], the log-transformation of r is lr = ln(r), approximately normally distributed if _{c} and _{t} are normally distributed and _{c} is unlikely to be negative. The mean of lr is approximately the true response ratio, and its variance *v* is equal to

The 95% confidence interval for the logged response ratio is then

The confidence limits for the unlogged response ratio are obtained by computing their respective antilogs. From the mean and confidence limits of this unlogged response ratio, the mean and 95% confidence limits for the relative effect (%effect = (r − 1) × 100) can then be calculated. Note that the significance levels based on the 95% confidence interval calculated this way may differ slightly from those in the original papers, due to possible data transformations in these papers and elements of the experiments that were not taken into account in our analysis. The data were analyzed to check whether mean control values and percent effect of treatment might be correlated, since the range of background values was often quite large. No correlation between mean control values and % effect of treatment was found for any of the variables measured.

[9] When several measurements in time were available, we used the overall mean, weighted by the number of replicates at each measurement. In that case, for *i* repeated measures with n_{i} replicates and SE_{i} standard errors at each measurement time, pooled standard error SE was calculated as follows. The equation of analysis of variance [*Fourgeaud and Fuchs*, 1967] shows that for *j* groups, each composed of measures *i* repeated n_{i} times, the total sum of squares of means (TSS) is a the sum of within-groups sum of squares of means (ISS) and between-groups sum of squares of means (WSS),

where *X*_{ij} is the measure *i* of group *j*, and is the value of the mean over all groups.

[10] In the data we collected, the samples are small, and the unbiased variance among the means σ^{2} is

where *N* is the total number of measurements added over time.

[11] Pooled standard error is expressed as

From equations (3) and (4), we can calculate

Following equation (5), we then obtain

The pooled standard error is then

[12] Meta-analysis was performed on the data, following *Hedges et al.* [1999], to estimate the mean effect size (magnitude of response of the processes measured) across experiments, and whether this effect was significantly different from zero. In brief, we used the response ratio r as a metric of effect size [*Hedges et al.*, 1999], and each experiment was weighted by its within-experiment variance to calculate overall mean effect size and 95% confidence interval. Similarly as described above, the results are presented as mean and 95% confidence interval limits of the relative effect of treatment. *Hedges et al.* [1999] warn that when the number of studies (k) used in a meta-analysis is small (e.g., k ≤ 20), the calculated 95% confidence interval may actually be as low as 91%. In this case, caution is warranted in the interpretation of results where a limit of the 95% confidence interval is close to the zero response ratio.

#### 2.2. Processes

[13] Nitrifying enzyme activity (NEA, also called potential nitrification, measured in the laboratory) reflects the enzymatic potential of the soil nitrifying bacteria to oxidize NH_{4}^{+} into NO_{2}^{−} or NO_{3}^{−} under optimal conditions [*Lensi et al.*, 1986]. In the absence of de novo synthesis of nitrifying enzymes during the laboratory incubation, NEA measurements provide a measure of the environmental constraints on soil nitrifiers prior to the NEA assay. *Grundmann et al.* [1995] have shown that changes in NEA are correlated with modifications of the major environmental constraints on nitrification, such as temperature, ammonium availability, and soil aeration. Gross nitrification is the amount of NO_{3}^{−} produced by nitrification, while net nitrification is the difference between gross nitrification and microbial NO_{3}^{−} consumption. Net nitrification was measured here by isotopic methods [*Bengtsson and Bergwall*, 2000; *Zak et al.*, 2000a], laboratory incubation [*Lovett and Rueth*, 1999; *Finzi et al.*, 2001; *Carnol et al.*, 2002], or in situ buried-bag techniques [*Kjønaas et al.*, 1998]. Gross nitrification was measured by isotope pool dilution [*Hungate et al.*, 1997b; *Zak et al.*, 2000a].

[14] We considered denitrifying enzyme activity (DEA, or potential denitrification) to reflect the size of the pool of functionally active denitrifying enzymes in the soil. Measured in the laboratory, the assay reflects the enzymatic potential of the soil denitrifying bacteria to reduce NO_{3}^{−} to N oxides or N_{2} under optimal conditions [*Tiedje*, 1994], and in the absence of de novo synthesis of denitrifying enzymes during the laboratory incubation, the environmental constraints on soil denitrifiers prior to the DEA assay will then be indicated by their enzymatic capacity under the optimal assay conditions [*Smith and Tiedje*, 1979]. We used only studies of DEA in which soil incubation was no longer than 8 hours, due to the high probability of de novo synthesis of enzymes during longer incubations (X. Le Roux, personal communication, 2000). DEA has been shown to be correlated with annual denitrification rates in some studies [*Groffman and Tiedje*, 1989; *Watson et al.*, 1994]. Net denitrification (i.e., NO_{3}^{−} transformed to N_{2}O in field conditions) was measured with static field chambers and ethylene inhibition [*Phoenix et al.*, 2003], or by isotopic method [*Bengtsson and Bergwall*, 2000].

[15] We also examined N_{2}O fluxes measured in the field (using static chambers) or under laboratory conditions. The measured N_{2}O flux represents total emissions from both nitrification and denitrification, as these processes can occur simultaneously [*Abbasi and Adams*, 2000; *Wolf and Brumme*, 2002].