the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Apr 2024
Mechanisms of soil organic carbon and nitrogen stabilization in mineral associated organic matter – Insights from modelling in phase space
Abstract. Understanding the mechanisms of plant-derived carbon (C) and nitrogen (N) transformation and stabilization in soil is fundamental for predicting soil capacity to mitigate climate change and support other soil functions. The decomposition of plant residues and particulate organic matter (POM) contributes to the formation of mineral associated (on average more stable) organic matter (MAOM) in soil. MAOM is formed from the binding of dissolved organic matter (ex vivo pathway) or microbial necromass and bioproducts (in vivo pathway) to minerals and metal colloids. Which of these two soil organic matter (SOM) stabilization pathways is more important and under which conditions remains an open question. To address this question, we propose a novel diagnostic model to describe C and N dynamics in MAOM as a function of the dynamics of residues and POM decomposition. Focusing on relations among soil compartments (i.e., modelling in phase space) rather than time trajectories allows isolating the fundamental processes underlying stabilization. Using this diagnostic model in combination with a database of ~ 40 studies in which residue C and N were tracked into POM and MAOM, we found that MAOM is predominantly fuelled by necromass produced by microbes decomposing residues and POM—the so-called ‘in vivo’ pathway of stabilization. The relevance of the in vivo pathway is higher in clayey soils, but lower in C rich soils and with N poor added residues. Overall, our novel modelling in phase space proved to be a sound diagnostic tool for the mechanistic investigation of soil C dynamics and supported the current understanding of the critical role of both microbial transformation and mineral capacity for the stabilization of C in mineral soils.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1092', Anonymous Referee #1, 15 May 2024
This study proposes a phase-space model fitted to about 40 studies which estimates that ~75% of MAOM C and nearly all of MAOM N are stabilized by the in vivo pathway, in contrast to measurements which tend to be lower than this. The authors posit a few reasons for the discrepancy, including ex vivo stabilization pathways missing from the model, and the most interesting which is that necromass may be stabilized faster but turns over at a faster rate, resulting in less persistent MAOM from necromass.
I think in order to explore the hypotheses brought up by this study it is useful to run the model considering time. I assume that you would get the same curves that can be seen in the main results (Figs 2 and 4) when running the model forward as differential equations and plotting the model output as the relationship between pools, so I’m not sure what the phase space simplification really adds. I think that retaining the ability to consider absolute values of MAOM and POM and track losses (C and N min) are relevant for addition scenarios in the field where total C retained in the system is as or more relevant than the form of C.
There were similarly some places in the text (L357-359) and Fig. 4 where I was really curious how accumulation of N vs C in MAOM was evolving over time.
I suppose my ask to the authors is to justify to readers the utility of phase space modeling compared to running the time-dependent form of the model, or to use time-dependent modeling to more completely address some of the hypotheses advanced, especially about N vs C accumulation in MAOM.
Other comments and suggestions:
L59-60: I think this sentence needs a main clause verb.
L120: Probably good to acknowledge that some C will be lost as DOC leaching, even if it is small and you don’t consider it here.
Fig 1: A fraction of necromass is sorbed and the rest goes back into particulate C… what is that fraction based on? At L322, Section 0 is referenced as where you explain how m is constrained but I could not find this section.
Eq.10 is the same as Eq. 9 but with a different boundary condition. I would suggest referencing Eq. 9 instead of printing the equation again.
N mineralization assumes a one-way flow where N is mineralized but not taken up again. This is similar to a lot of soil models but not necessarily realistic, so perhaps worth acknowledging that in text somewhere.
Table S1: If POM+residues are considered as one category in the model (Fig 1) then why are they separated out here? Please clarify how each category is allocated when used in the model. L266 seems to imply that those studies without POM+residues reported were not used, does this change the reported sample size used in analyses?
L357-359: I found it curious that a higher C:N ratio causes lower C accumulation in MAOM but higher N accumulation. Does the C:N of MAOM really decrease in this scenario or is this an artifact of only viewing Cm as relative to Cp which is also changing over time? In Figure 4, it is also interesting that N seems to accumulate faster than C in MAOM, but again we are not looking at time here so travel along either curve could occur at different speeds. Can you discuss this or provide some information about the time component?
Following from the understanding that in vivo is more important for N than C, I wonder if this can tell us something about the rate of the in vivo pathway vs ex vivo.
Figure 3b: I know there are many data sources, but can the data source color bar be discretized?
L466: I was a little surprised to see such a strong prediction of clay trends in B and C but no trend in univariate space (Fig 5). Do you feel confident in the LME prediction?
Citation: https://doi.org/10.5194/egusphere-2024-1092-RC1 - AC2: 'Reply on RC1', Stefano Manzoni, 04 Jun 2024
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AC1: 'Dataset now available', Stefano Manzoni, 17 May 2024
With this short comment, we would like to provide the link to the dataset associated with this preprint. The dataset on residue-derived carbon and nitrogen in the residue, dissolved, particulate, and mineral associated organic matter is now accessible in the Bolin Centre Database: https://bolin.su.se/data/manzoni-2024-residue-stabilization-1. If given the opportunity to revise our manuscript, we will include this link.
We also take this opportunity to thank Anonymous Referee #1 for their comments, which we will address as soon as possible.
Citation: https://doi.org/10.5194/egusphere-2024-1092-AC1 -
RC2: 'Review of “Mechanisms of soil organic carbon and nitrogen stabilization in mineral associated organic matter – Insights from modelling in phase space” by Manzoni and Cotrufo.', Anonymous Referee #2, 21 May 2024
General Comments
Manzoni and Cotrufo propose a two-compartment model (POM + residues and MAOM), which can be used to diagnose through with pathway (in vivo vs. ex vivo) C and N are stabilized. The simplicity of the model reduces the number of parameters and allows the authors to solve their equations analytically in the so-called space phase, i.e. they focus on relations between compartments instead of analyzing temporal trajectories to detect underlaying mechanisms. The model suggests that stabilization via the in vivo pathway is more relevant in clay-rich soils and less relevant in C-rich soils, whereby the calculated fractions seem to be higher than reported by earlier studies.
Overall, the paper is well (and lively!) written and the chosen approach is an interesting method to explain potentially appearing inconsistencies in data sets. E.g. the model is able to capture MAOM stabilization during early decomposition and destabilization of MAOM in late decomposition by the same mechanism. From that perspective and because it adds a new insight into the process of C and N stabilization, the paper is a highly relevant for the BG community. Also, discrepancies with earlier studies are mentioned and discussed appropriately. However, I’m concerned about the assumptions and approximations, which are made during the deviation of the solution, and that are a bit loosely justified (see below), and would ask the authors to elaborate these parts a bit further.
Specific Comments (in addition to RC1)
As mentioned before, I’d ask the authors to explain used assumptions and approximations in more detail. Especially the assumption of (quasi-)equilibrium needs more explanation and discussion. Why (under which circumstances) can quasi-equilibrium be assumed? Are the data filtered by that? How does this relate to the later discussion about “early” and “late” decomposition? How do this assumption and the other assumptions and approximations, which are used to derive the final analytically-solvable model, i.e. the first-order decay with a constant decomposition rate or the “similar” C:N ratios, affect model results and and limit their transferability, e.g. under a changing climate?
Figure 2: I think, it would help the reader, if you could add a reference figure (base values used) to understand the overall model behavior and the direction of the changes. I would also like to see the varied values, i.e. the values that are used to derive the solid and dashed lines in each sub-figure, in the figure description.
Technical Corrections (in addition to RC1)
What is “Section 0”? (L322, L416)
L34 Please check the unit.
Table 2: I personally would like to have the Parameter/Symbol entries all centered (or maybe all right-bounded), but not changing within lines, which seems to happen for all entries that do not have subscripts. Or is there I reason for that?
Citation: https://doi.org/10.5194/egusphere-2024-1092-RC2 - AC3: 'Reply on RC2', Stefano Manzoni, 04 Jun 2024
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RC3: 'Comment on egusphere-2024-1092', Anonymous Referee #3, 26 May 2024
The submitted manuscript aims at improving our understanding of the formation of mineral associated organic matter (MAOM), particularly the relative contributions of plant versus microbial derived carbon to MAOM formation. Therefore, they apply the innovative approach of fitting respective parameters of a simple soil microbial model in phase space. The datasets used are from decomposition experiments, where added labelled residues are traced from the particulate organic matter (POM) to the MAOM fraction. Instead of looking at temporal changes, the relative proportional changes of POM and MAOM along the decomposition continuum are mathematically formulated and solved, considering both C- and N- dynamics. The results showed that the in-vivo pathway (microbial derived) was more important than the ex-vivo pathway (plant-derived) MAOM-C and particularly MAOM-N formation. It was further possible to identify some controls on the relative importance of the two pathways. The authors conclude that the in vivo-pathway is particularly important in clay rich and carbon poor soils and that this path is accordingly stronger controlled by available mineral surfaces.
The authors did a great job in writing and explaining each modelling step in the manuscript and I enjoyed reading it. I also believe that this could be an interesting new diagnostic, potentially applicable to the interpretation also of other incubation studies looking at the fate of labelled substrates in soils. Nevertheless, I still have some open questions as outlined below.
Since not being a mathematician, I am wondering how sensitive the model output is towards violating some of the assumptions made when solving the equation. One is the assumption that microbial biomass is in quasi-steady state. This might apply for individual states of the model, but not when integrating across the decomposition continuum? Since there is no input to the model, microbial biomass is first building up after residue addition (growth > mortality) and then declining (growth < mortality) during the subsequent starvation phase. Both phases are required to reconcile the studied decomposition patterns. Also, equation 8 suggests that the decomposition of the POM and the MAOM pool are proportional along the decomposition process (right?). Is that the case in the real world, or would it not change e.g. with increasing depletion of easily degradable compounds with increasing decomposition in the POM fraction, which is not necessarily paralleled in the MAOM fraction when this is indeed built up from microbial residues?Another assumption of the modelling approach is that ex-vivo and in-vivo formed MAOM have the same decomposition. Since they will differ in chemical composition and CN ratio, this might not necessarily be the case as also discussed by the authors in lines 545ff and could also have biased the results.
If I understand it correctly, parameter fitting was not done based on total carbon and nitrogen in the two pools (POM and MAOM) of the studied soils, but just the fate of labelled residues added and their transfer to the MAOM fraction was considered, right? Correlations to bulk soil carbon concentrations of the original samples were done afterwards to see how the fitted parameters were affected by background SOC?
Nitrogen will probably play an important role for model parameterization, as the in vivo pathway leads to higher MAOM-N contents than the ex vivo path. Some of the datasets seem to have contained information on both, nitrogen and carbon, others not (table S1). How were the different data-streams then used for model fitting? I was surprised that Figure 3 shows a proportional decline of C and N in POM with decomposition, since my understanding was so far, based on litter decomposition experiments (which should be equivalent to POM decomposition), that C is lost in excess to N, leading to a relative enrichment of N versus C particularly during the early stages of litter decomposition (e.g. https://doi.org/10.1016/j.ejsobi.2018.02.003, https://doi.org/10.1007/s10021-004-0026-x). The concept of the present study and outcome of the model-data integration is now, that if litter or POM is decomposed next to minerals instead of in litter bags, nitrogen is transferred to the mineral phase as microbial necromass and not accumulating in the POM fraction. It would be nice, if the authors could elaborate on these different observations a bit more.
I was further wondering, how the transformation from organic to inorganic N and the potential stabilization of ammonium on minerals was considered in the cited experiments? If N accumulation on minerals by sorption as inorganic N is not considered, could that bias the results in soils rich in clay minerals? Could this have contributed to the observation, that the in vivo pathway is more important in clay rich soils?
It also surprised me, that the in vivo pathway should be more sensitive to saturation than the ex-vivo pathway (e.g. line 561). Microbes can also live and die directly attached to mineral surfaces. Probably more microbes can potentially live on mineral surfaces if these provide more substrate at higher OM-loading, so I am wondering what the mechanism behind the expected higher sensitivity of the in vivo pathway to saturation should be.
The results presented in Figures 5 and 6 regarding the relation between microbial CUE and CN ratios seem contradictory: while it is positive in Figure 5, it is negative in Figure 6. What is the difference? This should be clarified, since in the discussion the focus is on the observed negative relation (line 565 ff).
It was not clear to me, why the authors always use the term “residues + POM” throughout the manuscript – what is the difference? Does the term “residue” stand for the labelled material added and traced into MAOM? Why is the same distinction then not also necessary for MAOM when it is composed of both, residue- and POM-derived OM?
In line 19 of the abstract, the authors state that MAOM is fuelled by microbes decomposing POM – since there were two microbial pools in the model – can a distinction be made how much MAOM is from each microbial pool? Similar to direct input by microbes in the MOM, also plant/ex vivo-derived MAOM is subsequently recycled in microbial biomass – is this not also a kind of in vivo OM transformation, since it will also affect MAOM CN ratios?
Line 539: remove “tend” or adapt accordinglyCitation: https://doi.org/10.5194/egusphere-2024-1092-RC3 - AC4: 'Reply on RC3', Stefano Manzoni, 04 Jun 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1092', Anonymous Referee #1, 15 May 2024
This study proposes a phase-space model fitted to about 40 studies which estimates that ~75% of MAOM C and nearly all of MAOM N are stabilized by the in vivo pathway, in contrast to measurements which tend to be lower than this. The authors posit a few reasons for the discrepancy, including ex vivo stabilization pathways missing from the model, and the most interesting which is that necromass may be stabilized faster but turns over at a faster rate, resulting in less persistent MAOM from necromass.
I think in order to explore the hypotheses brought up by this study it is useful to run the model considering time. I assume that you would get the same curves that can be seen in the main results (Figs 2 and 4) when running the model forward as differential equations and plotting the model output as the relationship between pools, so I’m not sure what the phase space simplification really adds. I think that retaining the ability to consider absolute values of MAOM and POM and track losses (C and N min) are relevant for addition scenarios in the field where total C retained in the system is as or more relevant than the form of C.
There were similarly some places in the text (L357-359) and Fig. 4 where I was really curious how accumulation of N vs C in MAOM was evolving over time.
I suppose my ask to the authors is to justify to readers the utility of phase space modeling compared to running the time-dependent form of the model, or to use time-dependent modeling to more completely address some of the hypotheses advanced, especially about N vs C accumulation in MAOM.
Other comments and suggestions:
L59-60: I think this sentence needs a main clause verb.
L120: Probably good to acknowledge that some C will be lost as DOC leaching, even if it is small and you don’t consider it here.
Fig 1: A fraction of necromass is sorbed and the rest goes back into particulate C… what is that fraction based on? At L322, Section 0 is referenced as where you explain how m is constrained but I could not find this section.
Eq.10 is the same as Eq. 9 but with a different boundary condition. I would suggest referencing Eq. 9 instead of printing the equation again.
N mineralization assumes a one-way flow where N is mineralized but not taken up again. This is similar to a lot of soil models but not necessarily realistic, so perhaps worth acknowledging that in text somewhere.
Table S1: If POM+residues are considered as one category in the model (Fig 1) then why are they separated out here? Please clarify how each category is allocated when used in the model. L266 seems to imply that those studies without POM+residues reported were not used, does this change the reported sample size used in analyses?
L357-359: I found it curious that a higher C:N ratio causes lower C accumulation in MAOM but higher N accumulation. Does the C:N of MAOM really decrease in this scenario or is this an artifact of only viewing Cm as relative to Cp which is also changing over time? In Figure 4, it is also interesting that N seems to accumulate faster than C in MAOM, but again we are not looking at time here so travel along either curve could occur at different speeds. Can you discuss this or provide some information about the time component?
Following from the understanding that in vivo is more important for N than C, I wonder if this can tell us something about the rate of the in vivo pathway vs ex vivo.
Figure 3b: I know there are many data sources, but can the data source color bar be discretized?
L466: I was a little surprised to see such a strong prediction of clay trends in B and C but no trend in univariate space (Fig 5). Do you feel confident in the LME prediction?
Citation: https://doi.org/10.5194/egusphere-2024-1092-RC1 - AC2: 'Reply on RC1', Stefano Manzoni, 04 Jun 2024
-
AC1: 'Dataset now available', Stefano Manzoni, 17 May 2024
With this short comment, we would like to provide the link to the dataset associated with this preprint. The dataset on residue-derived carbon and nitrogen in the residue, dissolved, particulate, and mineral associated organic matter is now accessible in the Bolin Centre Database: https://bolin.su.se/data/manzoni-2024-residue-stabilization-1. If given the opportunity to revise our manuscript, we will include this link.
We also take this opportunity to thank Anonymous Referee #1 for their comments, which we will address as soon as possible.
Citation: https://doi.org/10.5194/egusphere-2024-1092-AC1 -
RC2: 'Review of “Mechanisms of soil organic carbon and nitrogen stabilization in mineral associated organic matter – Insights from modelling in phase space” by Manzoni and Cotrufo.', Anonymous Referee #2, 21 May 2024
General Comments
Manzoni and Cotrufo propose a two-compartment model (POM + residues and MAOM), which can be used to diagnose through with pathway (in vivo vs. ex vivo) C and N are stabilized. The simplicity of the model reduces the number of parameters and allows the authors to solve their equations analytically in the so-called space phase, i.e. they focus on relations between compartments instead of analyzing temporal trajectories to detect underlaying mechanisms. The model suggests that stabilization via the in vivo pathway is more relevant in clay-rich soils and less relevant in C-rich soils, whereby the calculated fractions seem to be higher than reported by earlier studies.
Overall, the paper is well (and lively!) written and the chosen approach is an interesting method to explain potentially appearing inconsistencies in data sets. E.g. the model is able to capture MAOM stabilization during early decomposition and destabilization of MAOM in late decomposition by the same mechanism. From that perspective and because it adds a new insight into the process of C and N stabilization, the paper is a highly relevant for the BG community. Also, discrepancies with earlier studies are mentioned and discussed appropriately. However, I’m concerned about the assumptions and approximations, which are made during the deviation of the solution, and that are a bit loosely justified (see below), and would ask the authors to elaborate these parts a bit further.
Specific Comments (in addition to RC1)
As mentioned before, I’d ask the authors to explain used assumptions and approximations in more detail. Especially the assumption of (quasi-)equilibrium needs more explanation and discussion. Why (under which circumstances) can quasi-equilibrium be assumed? Are the data filtered by that? How does this relate to the later discussion about “early” and “late” decomposition? How do this assumption and the other assumptions and approximations, which are used to derive the final analytically-solvable model, i.e. the first-order decay with a constant decomposition rate or the “similar” C:N ratios, affect model results and and limit their transferability, e.g. under a changing climate?
Figure 2: I think, it would help the reader, if you could add a reference figure (base values used) to understand the overall model behavior and the direction of the changes. I would also like to see the varied values, i.e. the values that are used to derive the solid and dashed lines in each sub-figure, in the figure description.
Technical Corrections (in addition to RC1)
What is “Section 0”? (L322, L416)
L34 Please check the unit.
Table 2: I personally would like to have the Parameter/Symbol entries all centered (or maybe all right-bounded), but not changing within lines, which seems to happen for all entries that do not have subscripts. Or is there I reason for that?
Citation: https://doi.org/10.5194/egusphere-2024-1092-RC2 - AC3: 'Reply on RC2', Stefano Manzoni, 04 Jun 2024
-
RC3: 'Comment on egusphere-2024-1092', Anonymous Referee #3, 26 May 2024
The submitted manuscript aims at improving our understanding of the formation of mineral associated organic matter (MAOM), particularly the relative contributions of plant versus microbial derived carbon to MAOM formation. Therefore, they apply the innovative approach of fitting respective parameters of a simple soil microbial model in phase space. The datasets used are from decomposition experiments, where added labelled residues are traced from the particulate organic matter (POM) to the MAOM fraction. Instead of looking at temporal changes, the relative proportional changes of POM and MAOM along the decomposition continuum are mathematically formulated and solved, considering both C- and N- dynamics. The results showed that the in-vivo pathway (microbial derived) was more important than the ex-vivo pathway (plant-derived) MAOM-C and particularly MAOM-N formation. It was further possible to identify some controls on the relative importance of the two pathways. The authors conclude that the in vivo-pathway is particularly important in clay rich and carbon poor soils and that this path is accordingly stronger controlled by available mineral surfaces.
The authors did a great job in writing and explaining each modelling step in the manuscript and I enjoyed reading it. I also believe that this could be an interesting new diagnostic, potentially applicable to the interpretation also of other incubation studies looking at the fate of labelled substrates in soils. Nevertheless, I still have some open questions as outlined below.
Since not being a mathematician, I am wondering how sensitive the model output is towards violating some of the assumptions made when solving the equation. One is the assumption that microbial biomass is in quasi-steady state. This might apply for individual states of the model, but not when integrating across the decomposition continuum? Since there is no input to the model, microbial biomass is first building up after residue addition (growth > mortality) and then declining (growth < mortality) during the subsequent starvation phase. Both phases are required to reconcile the studied decomposition patterns. Also, equation 8 suggests that the decomposition of the POM and the MAOM pool are proportional along the decomposition process (right?). Is that the case in the real world, or would it not change e.g. with increasing depletion of easily degradable compounds with increasing decomposition in the POM fraction, which is not necessarily paralleled in the MAOM fraction when this is indeed built up from microbial residues?Another assumption of the modelling approach is that ex-vivo and in-vivo formed MAOM have the same decomposition. Since they will differ in chemical composition and CN ratio, this might not necessarily be the case as also discussed by the authors in lines 545ff and could also have biased the results.
If I understand it correctly, parameter fitting was not done based on total carbon and nitrogen in the two pools (POM and MAOM) of the studied soils, but just the fate of labelled residues added and their transfer to the MAOM fraction was considered, right? Correlations to bulk soil carbon concentrations of the original samples were done afterwards to see how the fitted parameters were affected by background SOC?
Nitrogen will probably play an important role for model parameterization, as the in vivo pathway leads to higher MAOM-N contents than the ex vivo path. Some of the datasets seem to have contained information on both, nitrogen and carbon, others not (table S1). How were the different data-streams then used for model fitting? I was surprised that Figure 3 shows a proportional decline of C and N in POM with decomposition, since my understanding was so far, based on litter decomposition experiments (which should be equivalent to POM decomposition), that C is lost in excess to N, leading to a relative enrichment of N versus C particularly during the early stages of litter decomposition (e.g. https://doi.org/10.1016/j.ejsobi.2018.02.003, https://doi.org/10.1007/s10021-004-0026-x). The concept of the present study and outcome of the model-data integration is now, that if litter or POM is decomposed next to minerals instead of in litter bags, nitrogen is transferred to the mineral phase as microbial necromass and not accumulating in the POM fraction. It would be nice, if the authors could elaborate on these different observations a bit more.
I was further wondering, how the transformation from organic to inorganic N and the potential stabilization of ammonium on minerals was considered in the cited experiments? If N accumulation on minerals by sorption as inorganic N is not considered, could that bias the results in soils rich in clay minerals? Could this have contributed to the observation, that the in vivo pathway is more important in clay rich soils?
It also surprised me, that the in vivo pathway should be more sensitive to saturation than the ex-vivo pathway (e.g. line 561). Microbes can also live and die directly attached to mineral surfaces. Probably more microbes can potentially live on mineral surfaces if these provide more substrate at higher OM-loading, so I am wondering what the mechanism behind the expected higher sensitivity of the in vivo pathway to saturation should be.
The results presented in Figures 5 and 6 regarding the relation between microbial CUE and CN ratios seem contradictory: while it is positive in Figure 5, it is negative in Figure 6. What is the difference? This should be clarified, since in the discussion the focus is on the observed negative relation (line 565 ff).
It was not clear to me, why the authors always use the term “residues + POM” throughout the manuscript – what is the difference? Does the term “residue” stand for the labelled material added and traced into MAOM? Why is the same distinction then not also necessary for MAOM when it is composed of both, residue- and POM-derived OM?
In line 19 of the abstract, the authors state that MAOM is fuelled by microbes decomposing POM – since there were two microbial pools in the model – can a distinction be made how much MAOM is from each microbial pool? Similar to direct input by microbes in the MOM, also plant/ex vivo-derived MAOM is subsequently recycled in microbial biomass – is this not also a kind of in vivo OM transformation, since it will also affect MAOM CN ratios?
Line 539: remove “tend” or adapt accordinglyCitation: https://doi.org/10.5194/egusphere-2024-1092-RC3 - AC4: 'Reply on RC3', Stefano Manzoni, 04 Jun 2024
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Stefano Manzoni
Francesca Cotrufo
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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