Simulated N and P limitation to the NPP of a non N fixer across the climate gradient, evaluated for the full model using the program newprodall and including BNF and a deep soil layer, is shown in Fig. 4. The productivity of the simulated non N fixer is limited by both N and P between ~ 8 and ~ 19 cm/month and above ~ 25 cm/month of precipitation, and limited by N (alone) between ~ 19 and ~ 25 cm/month of simulated precipitation. (P limitation to simulated NPP occurs over less of the gradient than is reported in Vitousek et al. 2021) because of the changes described above in modeling the P cycle). The maximum extent of N limitation (maximum difference between NPP of the non N fixer with versus without added N) occurs at 20 cm/month of simulated precipitation. Since it is long-term response to simulated fertilization that is reported here (fertilization with 10 units of N or P per month − enough to ensure that neither N nor P limited NPP − began after 45,000 months, and results are averaged from 50,000 to 60,000 months), it is possible that where both N and P limit the growth of the non N fixer that added P stimulates the growth of the N fixer which then adds N to the system, enhancing growth of the non N fixer.
We then used the related program newprodnofixcr to evaluate nutrient limitation both with and without N fixation, with no losses of dissolved organic nutrients and no temporal variation in simulated precipitation or disturbance (Fig. 5). In this situation (without BNF or any uncontrollable losses of nutrient elements, but with N losses as nitrate or ammonia), neither N nor P limited production of the non N fixer above 9 cm/month of simulated precipitation because weathering of P-containing minerals and atmospheric deposition of N accumulated sufficient nutrients to offset limitation. Below 10 cm/month of simulated precipitation, N supply limited NPP of the non N fixer because insufficient N accumulated from atmospheric N deposition to offset limitation, in a long-term transient phenomenon. We demonstrated this process of accumulation by running the model (here tcnewprodnofixcr) without BNF or uncontrollable N losses for 120,000 months rather than the standard 60,000 months, with simulated N fertilization after 105,000 months, and results averaged from 110,000 to 120,000 months (Fig. S1). Under these conditions, enough N accumulated to offset N limitation at 8 (not shown) and 9 cm/month of simulated precipitation (Fig. S1), as well as at 12 cm/month (as had been true after 60,000 months—Fig. 5).
We then evaluated each of the potential pathways of biologically uncontrollable N losses that we identified (DON leaching, temporal variability in precipitation, ecosystem-level disturbance) by adding these processes into the programs newprodnofixcr and/or tcnewprodnofixcr individually, with and without BNF, and determining where and how each process could drive N losses that organisms could not control. We evaluated losses of DON first (Fig. 6a, b). Without temporal variation in precipitation, there is no leaching loss of water or nutrients at or below the point where potential evapotranspiration (PET) equals precipitation (PPT) (here 15 cm/month of simulated PPT); leaching losses of water (and so DON losses) increase progressively where PPT exceeds PET in wetter sites. Accordingly, in the absence of BNF, NPP of the non-fixer becomes progressively (and profoundly) more N-limited in wetter portions of the gradient, as is demonstrated by the response to simulated N fertilization there (Fig. 6a). With BNF active (Fig. 6b), NPP of the N fixer increases in wetter portions of the gradient, and the N that the fixer adds to the system maintains higher NPP than occurs in the absence of BNF (Fig. 6a). BNF also adds N that prevents N limitation in drier sites (except for the driest sites, where BNF is suppressed within the program as described in Vitousek et al. (2021) and the excerpt from that paper on-line to match the low abundance of symbiotic N fixers observed in these dry sites (Fig. 6a,b). The ongoing uncontrollable losses of DON drive ongoing N limitation to the NPP of the non N fixer (and so ongoing BNF by the N fixer) in wetter sites; we wonder if one of the reasons for the widespread abundance of symbiotic N fixing trees in wet tropical forests (Hedin et al. 2009) is the high rainfall in many of those systems, with its attendant DON losses. With BNF active (Fig. 6b), the sum of NPP by a non N fixer plus 1.5 times the NPP of an N fixer [1.5 to account for the N-rich stoichiometry of the N fixer—McKey (1994)—and so to put NPP of non N fixers and N fixers on a comparable basis] is very slightly greater than the NPP of an N-fertilized non N fixer, showing that the existence of N limitation here requires barriers to BNF as well as losses of DON.
Next we evaluated the consequences of temporal variability in precipitation. Vitousek et al. (2021) suggested that variability in precipitation could drive an imbalance between the supply of N to N-limited organisms and demand for that N. Losses of nitrate (normally a form of N for which losses can be controlled by N-limited organisms) could occur by either nitrate leaching or denitrification when the supply of N was in excess of demand, and those losses could mean that there would not be enough biologically available N for maximum growth at other times, such that N could be limiting, if there are also constraints to biological N fixation. This asynchrony between N supply and demand, leading to N losses, had been reported in semi-arid and arid ecosystems by Dijkstra et al. 2012, Nielson and Ball (2015), and others. We modified the program newprodnofixcr to include the level of temporal variation in precipitation modeled (and observed) across the climate gradient (Fig. 3), and evaluated N limitation to NPP caused by precipitation variability with and without BNF, and with only putatively controllable losses of ammonium or nitrate active (Fig. 7a, b). Precipitation variability at the levels observed on the climate gradient caused N limitation to the non N fixer at all levels of precipitation below ~ 22 cm/month of simulated precipitation (not just in semi-arid or arid ecosystems) (Fig. 7a), as demonstrated by the response to simulated N fertilization there; when we made BNF active, it increased the NPP of the non N fixer, but not to the level that simulated N fertilization did (Fig. 7b). Indeed, the NPP of the non N fixer plus 1.5 times that of the N fixer was less than that of the non N fixer with simulated N fertilization (Fig. 7a, b) in the precipitation range from ~ 12 to ~ 22 cm/month.
We evaluated the potential importance of precipitation variability in driving N limitation further by examining different intensities of precipitation variability at 20 cm/month of precipitation, the point at which N limitation to NPP was maximized (Fig. 4). To carry out this analysis, we ran the program tcnewprodnofixcr at 5 different intensities of temporal variability in precipitation, with the middle intensity corresponding to the observed temporal variation at 20 cm/month of simulated PPT on the climate gradient, two lower levels of temporal variability, including no temporal variability, and two higher levels of temporal variability in precipitation. For each level of variability, we compared the biomass of a non N fixer without added nutrients to its biomass with added N to visualize the extent of N limitation. (We used biomass rather than NPP here because biomass is less variable than NPP and so the effects of temporal variation are more observable, but as described above biomass is a many month integration of NPP.) Results of this analysis are shown in Fig. 8a–e. Nitrogen limitation was absent where there was no temporal variation in precipitation (Fig. 8a), but increasing levels of temporal variation in simulated precipitation in the absence of BNF increased N limitation and decreased the biomass of a non N fixer progressively (Fig. 8b–e).
The results in Fig. 8 provide strong evidence that temporal variation in precipitation like that anticipated (and observed) to occur with ongoing anthropogenic climate change can drive biotically uncontrollable losses of N, even in relatively high-rainfall systems, and that it is already doing so at current levels of temporal variation (especially in low-rainfall sites where such variability is greater). We tested the mechanism underlying this result by plotting the demand for N by non N fixers (the amount of N that would support maximum productivity by the non N fixer, given the climate conditions in that time step), the supply of N (the amount of N available for uptake, from all sources), leaching of water, and leaching of nitrate from the system with the observed level of temporal variability in precipitation at 20 cm/month of simulated precipitation, using the program tcnewprodnofixcr (Fig. S2) beginning 12,500 months into the simulation, shortly after temporal variation in precipitation began. Most losses of nitrate occurred when there was leaching loss of water at a time when the supply of N was greater than demand for N. We then evaluated the consequences of these losses of N by turning off both losses of nitrate and ammonia volatilization in the model; the consequence of doing so (in the absence of BNF) was no N limitation to NPP of the non N fixer across the climate gradient (Fig. S3).
Finally (in terms of temporal variability in simulated precipitation), we evaluated the joint effects of temporal variation and losses of DON both with and without BNF, recognizing that temporal variation in precipitation would drive losses of DON at lower rainfall than would be the case without such variation. The results of this analysis are shown in Fig. S4a,b; not surprisingly, without BNF N limitation to the NPP of the non N fixer occurred everywhere on the climate gradient (Fig. S4a), and (given the effect of precipitation variability on the responsiveness of the N fixer to N deficiency discussed above) the sum of NPP by the non N fixer plus 1.5 times the NPP of the N fixer was substantially less than the NPP of the non N fixer with added N (in the absence of BNF) at simulated precipitation levels above ~ 12 cm/month (Fig. S4a,b).
The final pathway of nitrogen losses that we evaluated was ecosystem-level disturbance. Large scale consumptive disturbances like fire and harvest remove nitrogen from ecosystems and provide no pathway by which biota within systems can prevent those losses. These disturbances, and even disturbances that don’t remove nitrogen from ecosystems directly, like windthrow, also disrupt the cycling of N within ecosystems and so drive losses of N in forms like nitrate that normally are available to organisms, with such losses occurring at times when N is superabundant to organisms. Once N is lost at such times, the lower quantity of N within ecosystems that results could reduce N supply and so drive N limitation at times when N is not superabundant.
We evaluated the consequences of disturbance by introducing one of three forms of disturbance (loosely corresponding to harvest, fire, and windthrow, as described above) after 45,000 months of simulation, and repeating that disturbance every 500 months thereafter. This analysis was carried out with losses of dissolved organic forms of nutrients set to 0, with no temporal variation in precipitation, and with ongoing losses via nitrate leaching and ammonia volatilization and with and without BNF, using the program newprodnofixcr, Results of these analyses are shown in Fig. 9 for the situation in which BNF was absent, and in Fig. 10 for the situation with BNF active. N limited the NPP of the non N fixer for every type of disturbance (Fig. 9a–c). However, with BNF active (Fig. 10), it was able to add enough N to offset N limitation to NPP (Fig. 10a, b). The effects of fire and harvest were identical in this analysis, because both were modeled as removing equal amount of N, and P does not limit NPP under these conditions, so we show only fire and windthrow in Fig. 10.
N limitation caused by disturbance occurred in part because N supply can limit NPP in non-equilibrium situations (Fig. 5) and the disturbed ecosystems as modeled are perpetually recovering from disturbance, after the first one, and in part because there are enhanced losses of N from disturbed sites. In this respect, windthrow is more interesting than harvest or fire, in that we modeled no direct removal of nutrients by windthrow, rather the biomass killed by windthrow was added to the soil organic C, N, and P pools and any N losses that occur in this simulation are of potentially biologically available forms after disturbance. To explore controls of N losses with disturbance further, we used the program tcnewprodnofixcr at a simulated precipitation of 20 cm/month, and evaluated the first disturbance imposed upon the system after 45,000 months without disturbance, and a second disturbance that occurred after 55,000 months. This second disturbance was the 11th in the sequence of the disturbances. Results of this analysis are shown for windthrow in Fig. S5a and for fire in Fig. S6a. Losses of nitrate were much greater after the first than the 11th disturbance in the sequence, and the losses of nitrate that occurred following simulated windthrow at simulated precipitation levels greater than 15 cm/month of simulated precipitation (above which leaching losses of water and nitrate occur) were sufficient to induce N limitation in the regrowing ecosystem following windthrow (Fig. S5c). We also simulated NPP and N dynamics following the first disturbance at a simulated precipitation of 10 cm/month (Figs. S5b, S6b), a level at which leaching losses of water and nitrate did not occur. Here (as in wetter sites) simulated windthrow added plant material to the soil with C:N ratios well above the threshold for net N mineralization, so losses of nitrate in wetter sites were delayed following windthrow more than were losses following fire (Figs. S5a, S6a). This effect also contributed to N limitation in sites receiving 10 cm/month of simulated precipitation (Figs. S5b, S6b), and in any site drier than the leaching threshold of 15 cm/month of simulated precipitation. In contrast, nitrate losses following fire at a simulated precipitation of 20 cm/month were less than half of total N losses (including those caused directly by fire), and the ecosystems regrowing following fire were more profoundly limited by N supply than those regrowing following windthrow (Figs. S5c, S6c).
Our analysis demonstrates that there are at least three pathways of losses of N that cannot be prevented even where the growth of plants is limited by N supply - losses of biologically unavailable forms of DON, temporal variability in precipitation that causes losses of forms of N at times when it is in excess of plant’s demand for N, and ecosystem-level disturbances. The effect of each of these alone and in combination is summarized in Fig. S7. However, in our analyses, BNF responded to N losses caused by DON leaching or ecosystem-level disturbance and prevented profound and/or prolonged N limitation; in contrast, temporal variation in precipitation constrained the responsiveness of BNF to N deficiency as well as driving biologically uncontrollable losses of N.
What constraints to BNF could allow N to limit primary productivity where uncontrollable N losses are important? We evaluated this question by removing (one by one and together) the additional constraints to symbiotic N fixers that have been identified (in addition to the absolute priority that the non N fixer in the model enjoys for light, water, and P resources as long as N is available to it—a priority that isn’t sufficient to cause N limitation that is more than marginal and/or ephemeral). These additional constraints include differential growth responses to shade, differentially higher P requirements of symbiotic N fixers, and differentially intense grazing on symbiotic N fixers because of their N- and P-rich stoichiometry (Vitousek and Field 1999). We carried out this analysis for ecosystems influenced by a combination of DON losses and losses associated with temporal variation in precipitation. Although ecosystem-level disturbance is pervasive and represents a major source of uncontrollable N losses across much of Earth (Vitousek 2003) (Fig. S7), these disturbances are idiosyncratic, in that we need to know the history of each place in order to model them appropriately. In contrast losses of DON and losses driven by temporal variation in precipitation are ubiquitous and general.
We carried out our analyses using the complete model, including BNF and deep soils, using the program newprodall. Without any additional constraints to BNF, the sum of NPP by a non N fixer plus 1.5 times the NPP of an N fixer is less than the NPP of the N-fertilized non N fixer (Fig. S8a) indicating that BNF did not respond fully to N deficiency. As was demonstrated above, temporal variability in precipitation has this effect (Fig. 7), in addition to causing uncontrollable losses of N. Including differential effects of shading on the NPP of an N fixer (Fig. S8b) or the effect of a differentially P-rich stoichiometry for the N fixer (Fig. S8c) had no additional effect on this result (not surprisingly for P, because the NPP of an N fixer was not constrained by P supply under these conditions). However, differentially intense grazing on an N- and P-rich N fixer suppressed the growth of both N fixer and non N fixer substantially, and increased the extent of N limitation (Fig. S8d). The pattern for all of these additional constraints to N fixation combined was identical to that for the effects of differentially intense grazing on the N fixer (Fig. S8d, e), demonstrating that in this model under these conditions the dominant constraint to the responsiveness of BNF to N deficiency was differential grazing.