Elevated CO_{2} indirectly stimulates N_{2}-fixation via its impact on legume biomass: a Bayesian meta-analysis

The impact of rising atmospheric CO2 on terrestrial carbon (C) accumulation depends in part on nitrogen (N) availability, an important source of which is biological N2-fixation. Higher rates of N2-fixation with rising CO2 could provide the necessary N for maintaining the future land C sink. Yet, experimental results show mixed support for this hypothesis. We extracted data from 77 studies reporting experimental results of the effect of elevated CO2 (eCO2) on N2-fixation. For all (468) records, we extracted the mean N2-fixation rate for the control and eCO2 treatments, and, when available, the corresponding standard deviation (SD). We also extracted information on other factors that might influence the response to eCO2, including non-symbiotic vs symbiotic associations, inside vs outside experiments, monocultures vs mixed communities, phosphorus added vs not, intact vs disturbed soil, and the reported biomass (mean and SD) of N2-fixing plants. For each record, we computed the log response ratio (LRR) and its corresponding SD, for both N2-fixation and plant biomass. To accommodate the complexity of the compiled data, and to estimate key quantities of interest, we conducted a hierarchical Bayesian meta-analysis of the LRR data. The LRRs and SDs for N2-fixation and plant biomass were simultaneously analyzed, allowing us to impute missing biomass LRRs, and to model N2-fixation LRR as a function of the corresponding biomass LRR (observed or imputed), important experimental factors, and within and among study random effects. We estimated the global LRR of N2-fixation across all studies and experimental factors, and for five scenarios describing a gradient from "most natural" (i.e., outside, intact soil, mixed community, no P addition) to "most artificial" (inside, disturbed soil, P added). The Bayesian model revealed that the N2-fixation response was governed by the biomass response; eCO2 generally stimulated production of N2-fixing plants, which in turn lead to higher rates of N2-fixation under eCO2. Both plant biomass and N2-fixation were most strongly stimulated by eCO2 under more artificial conditions, and neither were significantly affected by eCO2 under more natural settings. However, the N2-fixation and plant biomass responses to eCO2 were most strongly coupled under the most natural (undisturbed, outside) and most artificial (inside) settings, whereas they were only weakly coupled under disturbed, outside conditions. Additionally, non-symbiotic N2-fixation generally did not respond to eCO2, whereas there was a clear trend for symbiotic N2-fixation to respond positively to eCO2, but again, only under artificial conditions. In summary, the Bayesian meta-analysis (1) provided little support for direct effects of eCO2 on N2-fixation, and instead indicated an indirect response mediate through the direct effects of eCO2 on biomass production of N2-fixing plants, and (2) showed that neither N2-fixation nor plant biomass responded to eCO2 in natural, intact ecosystems; it was only under more artificial conditions that eCO2 led to increased plant biomass and N2-fixation. These results argue against the hypothesis that rising CO2 will stimulate N2-fixation in terrestrial ecosystems, and caution against building that expectation into models of the future land C sink.