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An Absorbing Markov Chain approach to understanding the microbial role in soil carbon stabilization

Abstract

The number of studies focused on the transformation and sequestration of soil organic carbon (C) has dramatically increased in recent years due to growing interest in understanding the global C cycle. While it is readily accepted that terrestrial C dynamics are heavily influenced by the catabolic and anabolic activities of microorganisms, the incorporation of microbial biomass components into stable soil C pools (via microbial living cells and necromass) has received less attention. Nevertheless, microbial-derived C inputs to soils are now increasingly recognized as playing a far greater role in stabilization of soil organic matter than previously believed. Our understanding, however, is limited by the difficulties associated with studying microbial turnover in soils. Here, we describe the use of an Absorbing Markov Chain (AMC) to model the dynamics of soil C transformations among three microbial states: living microbial biomass, microbial necromass, and C removed from living and dead microbial sources. We find that AMC provides a powerful quantitative approach that allows prediction of how C will be distributed among these three states, and how long it will take for the entire amount of initial C to pass through the biomass and necromass pools and be moved into atmosphere. Further, assuming constant C inputs to the model, we can predict how C is eventually distributed, along with how much C sequestrated in soil is microbial-derived. Our work represents a first step in attempting to quantify the flow of C through microbial pathways, and has the potential to increase our understanding of the microbial role in soil C dynamics.

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References

  • Allison SD, Wallenstein MD, Bradford MA (2010) Soil-carbon response to warming dependent on microbial physiology. Nat Geosci 3:336–340

    Article  Google Scholar 

  • Anderson T-H, Joergensen RG (1997) Relationship between SIR and FE estimates of microbial biomass C in deciduous forest soils at different pH. Soil Biol Biochem 29:1033–1042

    Article  Google Scholar 

  • Baldock JA, Skjemstad JO (2000) Role of the soil matrix and minerals in protecting natural organic materials against biological attack. Org Geochem 31:697–710

    Article  Google Scholar 

  • Balser TC (2005) Humification. In: Hillel D (ed) Encyclopedia of soils in the environment. Elsevier, Oxford, UK, pp 195–207

    Google Scholar 

  • Ching W-K, Ng M (2005) Markov Chains: models, algorithms and applications. Springer, Berlin

    Google Scholar 

  • Dalal RC (1998) Soil microbial biomass: what do the numbers really mean? Aust J Exp Agric 38:649–665

    Article  Google Scholar 

  • del Monte-Luna P, Brook BW, Zetina-Rejon MJ, Cruz-Escalona VH (2004) The carrying capacity of ecosystems. Glob Ecol Biogeogr 13:485–495

    Article  Google Scholar 

  • Falloon PD, Smith P (2000) Modelling refractory soil organic matter. Biol Fertil Soils 30:388–398

    Article  Google Scholar 

  • Feng Y (2009a) K-Model-A continuous model of soil organic carbon dynamics: model parameterization and testing. Soil Sci 174:494–507

    Article  Google Scholar 

  • Feng Y (2009b) K-Model-A continuous model of soil organic carbon dynamics: theory. Soil Sci 174:482–493

    Article  Google Scholar 

  • Grandy AS, Neff JC (2008) Molecular C dynamics downstream: the biochemical decomposition sequence and its impact on soil organic matter structure and function. Sci Total Environ 404:297–307

    Article  Google Scholar 

  • Kiem R, Kogel-Knabner I (2003) Contribution of lignin and polysaccharides to the refractory carbon pool in C-depleted arable soils. Soil Biol Biochem 35:101–118

    Article  Google Scholar 

  • Kindler R, Miltner A, Richnow H-H, Kastner M (2006) Fate of gram-negative bacterial biomass in soil—mineralization and contribution to SOM. Soil Biol Biochem 38:2860–2870

    Article  Google Scholar 

  • Kindler R, Miltner A, Thullner M, Richnow H-H, Kastner M (2009) Fate of bacterial biomass derived fatty acids in soil and their contribution to soil organic matter. Org Geochem 40:29–37

    Article  Google Scholar 

  • Kramer MG, Sollins P, Sletten RS, Swart PK (2003) N isotope fractionation and measures of organic matter alteration during decomposition. Ecology 84:2021–2025

    Google Scholar 

  • Liang C, Balser TC (2008) Preferential sequestration of microbial carbon in subsoils of a glacial-landscape toposequence, Dane County, WI, USA. Geoderma 148:113–119

    Article  Google Scholar 

  • Liang C, Fujinuma R, Balser TC (2008) Comparing PLFA and amino sugars for microbial analysis in an Upper Michigan old growth forest. Soil Biol Biochem 40:2063–2065

    Article  Google Scholar 

  • Miltner A, Kindler R, Knicker H, Richnow H-H, Kästner M (2009) Fate of microbial biomass-derived amino acids in soil and their contribution to soil organic matter. Org Geochem 40:978–985

    Article  Google Scholar 

  • Potthoff M, Dyckmans J, Flessa H, Beese F, Joergensen R (2008) Decomposition of maize residues after manipulation of colonization and its contribution to the soil microbial biomass. Biol Fertil Soils 44:891–895

    Article  Google Scholar 

  • Simpson AJ, Simpson MJ, Smith E, Kelleher BP (2007) Microbially derived inputs to soil organic matter: are current estimates too low? Environ Sci Technol 41:8070–8076

    Article  Google Scholar 

  • Sollins P, Homann P, Caldwell BA (1996) Stabilization and destabilization of soil organic matter: mechanisms and controls. Geoderma 74:65–105

    Article  Google Scholar 

  • Sparling GP (1992) Ratio of microbial biomass carbon to soil organic carbon as a sensitive indicator of changes in soil organic matter. Aust J Soil Res 30:195–207

    Article  Google Scholar 

  • von Lützow M, Kögel-Knabner I, Ekschmitt K, Matzner E, Guggenberger G, Marschner B, Flessa H (2006) Stabilization of organic matter in temperate soils: mechanisms and their relevance under different soil conditions—a review. Eur J Soil Sci 57:426–445

    Article  Google Scholar 

  • Wardle DA (1992) A comparative assessment of factors which influence microbial biomass carbon and nitrogen levels in soil. Biol Rev 67:321–358

    Google Scholar 

  • Yao H, Shi W (2010) Soil organic matter stabilization in turfgrass ecosystems: importance of microbial processing. Soil Biol Biochem 42:642–648

    Article  Google Scholar 

  • Zech W, Senesi N, Guggenberger G, Kaiser K, Lehmann J, Miano TM, Miltner A, Schroth G (1997) Factors controlling humification and mineralization of soil organic matter in the tropics. Geoderma 79:117–161

    Article  Google Scholar 

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Acknowledgments

This work was financially supported by the DOE Great Lakes Bioenergy Research Center (DOE BER Office of Science DE-FC02-07ER64494), USDA-CSREES and NSF-DMS 0906497. We would like to thank Dr. R. Jackson for his help with the proposed idea, Drs. C. Xu and J. Zhu for the discussions on the earlier stage of this study. We would also like to thank the editor and two anonymous reviewers. The manuscript is much improved because of their inputs.

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Correspondence to Chao Liang.

Appendix

Appendix

Prove why T = [ m / ( m + n )] ( Lx + Ly   2)  + [ n / ( m + n )](Dx + Dy   2) holds:

Step 1: we first show that the expected number of transitions from state L to state D is the (1; 2)-th element of the fundamental matrix N minus one, i.e. Ly − 1.

Let C(s) = 1 if the C starts from L and enters D in the s-th step, C(s) = 0 otherwise. In order to calculate the expectation of C(s), we need to know the probability of the event that C starts from L and enters D in the S-th step, denoted by p (S) LD . In other words, the expectation is

$$ M[C(S)] = \sum\limits_{S = 1}^{\infty } {p_{LD}^{(S)} } $$

By the Markov Chain rule, we know p (S) LD equals to the (2, 3)-th element of PS. Furthermore, we know it also equals to the (1, 2)-th element of QS by the canonical form of Pt. Hence, we have

$$ M[C(S)] = \sum\limits_{S = 1}^{\infty } {p_{LD}^{(S)} } = \sum\limits_{S = 1}^{\infty } {Q_{12}^{(S)} } = Ly - 1 $$

The last equality follows from Eq. 6

$$ {\mathbf{N}} = \left( {{\text{I}} - {\text{Q}}} \right)^{ - 1} = {\text{I}} + {\text{Q}} + {\text{Q}}^{ 2} + {\text{Q}}^{ 3} + \ldots $$

Step 2: We next calculate the expected number of transitions that the C transit from the state L or D to the air state. We consider two cases: (i) C starts from L; (ii) C starts from D.

For the case (i), the expected number of transitions from L to L (D) is Lx − 1 and Ly − 1, respectively, based on the results in step 1. For the case (ii), the expected number of transitions from D to L (D) is Dx − 1 and Dy − 1, respectively, based on the results in step 1. Then, the expected number of total transitions equal to

P(C starts from L) × (Lx + Ly − 2) + P(C starts from D) × (Dx + Dy − 2) = 

$$ \left[ {m/\left( {m + n} \right)} \right]\left( {Lx + Ly - 2} \right) + \left[ {n/\left( {m + n} \right)} \right]\left( {Dx + Dy - 2} \right) $$

This completes the whole proof.

Prove why L(stable) = f · Lx and D(stable) = f · Ly holds:

We first have the following relations:

$$ \begin{aligned} & {\text{Z}}^{(0)} = \left[ {{\text{L}}^{(0)} ;{\text{D}}^{(0)} } \right] \\ & {\text{Z}}^{( 1)} = {\text{Z}}^{(0)} {\text{P}} + \left[ {{\text{f}};0} \right] \\ & {\text{Z}}^{( 2)} = {\text{Z}}^{( 1)} {\text{P}} + \left[ {{\text{f}};0} \right] \\ & \ldots \\ \end{aligned} $$

where (L(0); D(0)) are the initial distribution of (L; D), respectively. Based on the above relation, we can prove that

$$ \left[ {{\text{L}}^{{({\text{k}})}} ;{\text{D}}^{{({\text{k}})}} } \right] = \left[ {{\text{L}}^{(0)} ;{\text{D}}^{( 0)} } \right]{\text{Q}^{k}} + \left[ {f;0} \right]\left( {I + \sum\limits_{i = 1}^{k - 1} {Q^{i} } } \right) $$

through mathematical inductions. Since our model is the AMC, Qk → ∞ as k → ∞. Then we have

$$ \left[ {{\text{L}}^{{({\text{k}})}} ;{\text{ D}}^{{({\text{k}})}} } \right] \to \left[ {f;0} \right]\left( {I + \sum\limits_{i = 1}^{k - 1} {Q^{i} } } \right) \to \left[ {f;0} \right]N $$

by the equation that N = (I − Q)−1 = I + Q + Q 2 + 

Hence we have L(stable) = f · Lx and D(stable) = f · Ly as k approaches infinity.

This completes the whole proof.

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Liang, C., Cheng, G., Wixon, D.L. et al. An Absorbing Markov Chain approach to understanding the microbial role in soil carbon stabilization. Biogeochemistry 106, 303–309 (2011). https://doi.org/10.1007/s10533-010-9525-3

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  • DOI: https://doi.org/10.1007/s10533-010-9525-3

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