Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Improved model simulation of soil carbon cycling by representing the microbially derived organic carbon pool


During the decomposition process of soil organic carbon (SOC), microbial products such as microbial necromass and microbial metabolites may form an important stable carbon (C) pool, called microbially derived C, which has different decomposition patterns from plant-derived C. However, current Earth System Models do not simulate this microbially derived C pool separately. Here, we incorporated the microbial necromass pool to the first-order kinetic model and the Michaelis–Menten model, respectively, and validated model behaviors against previous observation data from the decomposition experiments of 13C-labeled necromass. Our models showed better performance than existing models and the Michaelis–Menten model was better than the first-order kinetic model. Microbial necromass C was estimated to be 10–27% of total SOC in the study soils by our models and therefore should not be ignored. This study provides a novel modification to process-based models for better simulation of soil organic C under the context of global changes.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: The structure of the two newly proposed models with the microbial necromass pools.
Fig. 2: Comparison of modeled (lines) and observed (dots) recovery of 13C in soil organic C pool and recovery of 13C in respired CO2 using data from four decomposition experiments of 13C-labeled microbial necromass.
Fig. 3: Modeled results of the recovery of 13C in microbial biomass carbon (MBC), dissolved organic carbon (DOC), the fast pool of microbial necromass carbon (CNF) and the mineral-associated pool of microbial necromass carbon (CN-MAOM) using data from four decomposition experiments of 13C-labeled microbial necromass.
Fig. 4: The leave-one-out cross-validation test results of MIND and FOND models.
Fig. 5: The regression analysis between modeled and observed recovery of 13C in respired CO2 for the four decomposition experiments of 13C-labeled microbial necromass.
Fig. 6: Temporal variations of necromass 13C recovery in soil after 1000 years of incubation (without new C inputs) for the four studies simulated by MIND and FOND models.

Data availability

The data used can be found in Supplementary Information.

Code availability

Code used to model runs is available at


  1. 1.

    Hiederer R, Köchy M. Global soil organic carbon estimates and the harmonized world soil database. EUR. 2011;79:25225.

    Google Scholar 

  2. 2.

    Scharlemann JPW, Tanner EVJ, Hiederer R, Kapos V. Global soil carbon: understanding and managing the largest terrestrial carbon pool. Carbon Manag. 2014;5:81–91.

    CAS  Article  Google Scholar 

  3. 3.

    Wieder WR, Bonan GB, Allison SD. Global soil carbon projections are improved by modelling microbial processes. Nat Clim Chang. 2013;3:909–12.

    CAS  Article  Google Scholar 

  4. 4.

    Schimel JP, Weintraub MN. The implications of exoenzyme activity on microbial carbon and nitrogen limitation in soil: a theoretical model. Soil Biol Biochem. 2003;35:549–63.

    CAS  Article  Google Scholar 

  5. 5.

    Huang Y, Guenet B, Ciais P, Janssens IA, Soong JL, Wang Y, et al. ORCHIMIC (v1.0), a microbe-mediated model for soil organic matter decomposition. Geosci Model Dev. 2018;11:2111–38.

    CAS  Article  Google Scholar 

  6. 6.

    Georgiou K, Abramoff RZ, Harte J, Riley WJ, Torn MS. Microbial community-level regulation explains soil carbon responses to long-term litter manipulations. Nat Commun. 2017;8:1223.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  7. 7.

    Kelleher BP, Simpson AJ. Humic substances in soils: are they really chemically distinct? Environ Sci Technol. 2006;40:4605–11.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  8. 8.

    Wang C, Wang X, Pei G, Xia Z, Peng B, Sun L, et al. Stabilization of microbial residues in soil organic matter after two years of decomposition. Soil Biol Biochem. 2020;141:107687.

    CAS  Article  Google Scholar 

  9. 9.

    Cotrufo MF, Wallenstein M, Boot C, Denef K, Paul E. The microbial efficiency-matrix stabilization (MEMS) framework integrates plant litter decomposition with soil organic matter stabilization: do labile plant inputs form stable soil organic matter? Glob Change Biol. 2013;19:988–95.

    Article  Google Scholar 

  10. 10.

    Zhu X, Jackson RD, DeLucia EH, Tiedje JM, Liang C. The soil microbial carbon pump: from conceptual insights to empirical assessments. Glob Change Biol. 2020;26:6032–9.

    Article  Google Scholar 

  11. 11.

    Miltner A, Bombach P, Schmidt-Brücken B, Kästner M. SOM genesis: microbial biomass as a significant source. Biogeochemistry. 2012;111:41–55.

    CAS  Article  Google Scholar 

  12. 12.

    Torn MS, Trumbore SE, Chadwick OA, Vitousek PM, Hendricks DM. Mineral control of soil organic carbon storage and turnover. Nature. 1997;389:170–3.

    CAS  Article  Google Scholar 

  13. 13.

    Dwivedi D, Riley WJ, Torn MS, Spycher N, Maggi F, Tang JY. Mineral properties, microbes, transport, and plant-input profiles control vertical distribution and age of soil carbon stocks. Soil Biol Biochem. 2017;107:244–59.

    CAS  Article  Google Scholar 

  14. 14.

    Mikutta R, Kleber M, Torn MS, Jahn R. Stabilization of soil organic matter: association with minerals or chemical recalcitrance? Biogeochemistry. 2006;77:25–56.

    CAS  Article  Google Scholar 

  15. 15.

    Liang C, Balser TC. Microbial production of recalcitrant organic matter in global soils: Implications for productivity and climate policy. Nat Rev Microbiol. 2011;9:75–75.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  16. 16.

    Khan KS, Mack R, Castillo X, Kaiser M, Joergensen RG. Microbial biomass, fungal and bacterial residues, and their relationships to the soil organic matter C/N/P/S ratios. Geoderma. 2016;271:115–23.

    CAS  Article  Google Scholar 

  17. 17.

    Liang C, Amelung W, Lehmann J, Kästner M. Quantitative assessment of microbial necromass contribution to soil organic matter. Glob Chang Biol. 2019;25:3578–90.

    PubMed  Article  PubMed Central  Google Scholar 

  18. 18.

    Kögel-Knabner I. The macromolecular organic composition of plant and microbial residues as inputs to soil organic matter: fourteen years on. Soil Biol Biochem. 2017;105:A3–8.

    Article  CAS  Google Scholar 

  19. 19.

    Todd-Brown KEO, Randerson JT, Post WM, Hoffman FM, Tarnocai C, Schuur EAG, et al. Causes of variation in soil carbon simulations from CMIP5 Earth System Models and comparison with observations. Biogeosciences. 2013;10:1717–36.

    Article  Google Scholar 

  20. 20.

    Parton WJ, Schimel DS, Cole CV, Ojima DS. Analysis of factors controlling soil organic matter levels in great plains grasslands. Soil Sci Soc Am J. 1987;51:1173–9.

    CAS  Article  Google Scholar 

  21. 21.

    Wang G, Post WM, Mayes MA. Development of microbial‐enzyme‐mediated decomposition model parameters through steady‐state and dynamic analyses. Ecol Appl. 2013;23:255–72.

    PubMed  Article  PubMed Central  Google Scholar 

  22. 22.

    Wang G, Mayes MA, Gu L, Schadt CW. Representation of dormant and active microbial dynamics for ecosystem modeling. PLoS ONE. 2014;9:e89252.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  23. 23.

    Wang G, Jagadamma S, Mayes MA, Schadt CW, Steinweg JM, Gu L, et al. Microbial dormancy improves development and experimental validation of ecosystem model. ISME J. 2015;9:226–37.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  24. 24.

    German D, Marcelo K, Stone M, Allison S. The Michaelis–Menten kinetics of soil extracellular enzymes in response to temperature: a cross-latitudinal study. Glob Change Biol. 2012;18:1468–79.

    Article  Google Scholar 

  25. 25.

    Allison SD, Wallenstein MD, Bradford MA. Soil-carbon response to warming dependent on microbial physiology. Nat Geosci. 2010;3:336–40.

    CAS  Article  Google Scholar 

  26. 26.

    Li J, Wang G, Allison SD, Mayes MA, Luo Y. Soil carbon sensitivity to temperature and carbon use efficiency compared across microbial-ecosystem models of varying complexity. Biogeochemistry. 2014;119:67–84.

    Article  Google Scholar 

  27. 27.

    Wieder WR, Grandy AS, Kallenbach CM, Bonan GB. Integrating microbial physiology and physio-chemical principles in soils with the MIcrobial-MIneral Carbon Stabilization (MIMICS) model. Biogeosciences. 2014;11:3899–917.

    Article  CAS  Google Scholar 

  28. 28.

    Tang J, Riley WJ. Weaker soil carbon–climate feedbacks resulting from microbial and abiotic interactions. Nat Clim Chang. 2015;5:56–60.

    CAS  Article  Google Scholar 

  29. 29.

    Sulman BN, Moore JA, Abramoff R, Averill C, Kivlin S, Georgiou K, et al. Multiple models and experiments underscore large uncertainty in soil carbon dynamics. Biogeochemistry. 2018;141:109–23.

    CAS  Article  Google Scholar 

  30. 30.

    Sulman BN, Phillips RP, Oishi AC, Shevliakova E, Pacala SW. Microbe-driven turnover offsets mineral-mediated storage of soil carbon under elevated CO2. Nat Clim Change. 2014;4:1099–102.

    CAS  Article  Google Scholar 

  31. 31.

    Lawrence C, Neff J, Schimel J. Does adding microbial mechanisms of decomposition improve soil organic matter models? A comparison of four models using data from a pulsed rewetting experiment. Soil Biol Biochem. 2009;41:1923–34.

    CAS  Article  Google Scholar 

  32. 32.

    Wang X, Wang C, Cotrufo MF, Sun L, Jiang P, Liu Z, et al. Elevated temperature increases the accumulation of microbial necromass nitrogen in soil via increasing microbial turnover. Glob Change Biol. 2020;26:5277–89.

    Article  Google Scholar 

  33. 33.

    Throckmorton HM, Bird JA, Dane L, Firestone MK, Horwath WR. The source of microbial C has little impact on soil organic matter stabilisation in forest ecosystems. Ecol Lett. 2012;15:1257–65.

    PubMed  Article  PubMed Central  Google Scholar 

  34. 34.

    Kindler R, Miltner A, Richnow H-H, Kästner M. Fate of gram-negative bacterial biomass in soil—mineralization and contribution to SOM. Soil Biol Biochem. 2006;38:2860–70.

    CAS  Article  Google Scholar 

  35. 35.

    Schweigert M, Herrmann S, Miltner A, Fester T, Kästner M. Fate of ectomycorrhizal fungal biomass in a soil bioreactor system and its contribution to soil organic matter formation. Soil Biol Biochem. 2015;88:120–7.

    CAS  Article  Google Scholar 

  36. 36.

    Derrien D, Amelung W. Computing the mean residence time of soil carbon fractions using stable isotopes: impacts of the model framework. Eur J Soil Sci. 2011;62:237–52.

    Article  Google Scholar 

  37. 37.

    Dormand JR, Prince PJ. A family of embedded Runge-Kutta formulae. J Comput Appl Math. 1980;6:19–26.

    Article  Google Scholar 

  38. 38.

    Shampine LF, Reichelt MW. The MATLAB ODE suite. Siam J Sci Comput. 1997;18:1–22.

    Article  Google Scholar 

  39. 39.

    Coleman TF, Li Y. On the convergence of reflective newton methods for large-scale nonlinear minimization subject to bounds. Math Program. 1994;67:189–224.

    Article  Google Scholar 

  40. 40.

    Coleman TF, Li Y. An interior trust region approach for nonlinear minimization subject to bounds. SIAM J Optim. 1996;6:418–45.

    Article  Google Scholar 

  41. 41.

    Moré JJ. The Levenberg–Marquardt algorithm: implementation and theory. In: Watson GA (ed). Numerical Analysis. Springer: Berlin, Heidelberg, 1978, p. 105–16.

  42. 42.

    Leave-one-out cross-validation. In: Sammut C, Webb GI, editors. Encyclopedia of machine learning. Boston, MA: Springer USA; 2010. p. 600–1.

  43. 43.

    Wang C, Qu L, Yang L, Liu D, Morrissey E, Miao R, et al. Large-scale importance of microbial carbon use efficiency and necromass to soil organic carbon. Glob Chang Biol. 2021.

  44. 44.

    Farrell M, Prendergast-Miller M, Jones DL, Hill PW, Condron LM. Soil microbial organic nitrogen uptake is regulated by carbon availability. Soil Biol Biochem. 2014;77:261–7.

    CAS  Article  Google Scholar 

  45. 45.

    Hagerty SB, Allison SD, Schimel JP. Evaluating soil microbial carbon use efficiency explicitly as a function of cellular processes: implications for measurements and models. Biogeochemistry. 2018;140:269–83.

    CAS  Article  Google Scholar 

  46. 46.

    Qiao Y, Wang J, Liang G, Du Z, Zhou J, Zhu C, et al. Global variation of soil microbial carbon-use efficiency in relation to growth temperature and substrate supply. Sci Rep. 2019;9:5621.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  47. 47.

    Krinner G, Viovy N, de Noblet-Ducoudré N, Ogée J, Polcher J, Friedlingstein P, et al. A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system. Glob Biogeochem Cycles. 2005;19:GB1015.

    Article  CAS  Google Scholar 

  48. 48.

    Wang G, Post WM, Mayes MA, Frerichs JT, Sindhu J. Parameter estimation for models of ligninolytic and cellulolytic enzyme kinetics. Soil Biol Biochem. 2012;48:28–38.

    Article  CAS  Google Scholar 

  49. 49.

    Davidson EA, Janssens IA. Temperature sensitivity of soil carbon decomposition and feedbacks to climate change. Nature. 2006;440:165–73.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  50. 50.

    Fick SE, Hijmans RJ. WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas. Int J Climatol. 2017;37:4302–15.

    Article  Google Scholar 

  51. 51.

    Guevara M, Taufer M, Vargas R. Gap-free global annual soil moisture: 15 km grids for 1991–2018. Earth Syst Sci Data. 2020;2020:1–65.

    Google Scholar 

  52. 52.

    Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, et al. The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc. 1996;77:437–72.

    Article  Google Scholar 

  53. 53.

    Batjes NH. Harmonized soil property values for broad-scale modelling (WISE30sec) with estimates of global soil carbon stocks. Geoderma. 2016;269:61–8.

    CAS  Article  Google Scholar 

  54. 54.

    Hengl T, Mendes de Jesus J, Heuvelink GBM, Ruiperez Gonzalez M, Kilibarda M, Blagotić A, et al. SoilGrids250m: global gridded soil information based on machine learning. PLoS ONE. 2017;12:e0169748.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  55. 55.

    Olson DM, Dinerstein E. The Global 200: a representation approach to conserving the earth’s most biologically valuable ecoregions. Conserv Biol. 1998;12:502–15.

    Article  Google Scholar 

  56. 56.

    Kögel-Knabner I. The macromolecular organic composition of plant and microbial residues as inputs to soil organic matter. Soil Biol Biochem. 2002;34:139–62.

    Article  Google Scholar 

  57. 57.

    Fernandez CW, Koide RT. Initial melanin and nitrogen concentrations control the decomposition of ectomycorrhizal fungal litter. Soil Biol Biochem. 2014;77:150–7.

    CAS  Article  Google Scholar 

  58. 58.

    Hemkemeyer M, Dohrmann AB, Christensen BT, Tebbe CC. Bacterial preferences for specific soil particle size fractions revealed by community analyses. Front Microbiol. 2018;9:149.

    PubMed  PubMed Central  Article  Google Scholar 

  59. 59.

    Mills A. Keeping in touch: microbial life on soil particle surfaces. Adv Agron. 2003;78:1–43.

    Article  Google Scholar 

  60. 60.

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

    CAS  Article  Google Scholar 

  61. 61.

    Huang Y, Liang C, Duan X, Chen H, Li D. Variation of microbial residue contribution to soil organic carbon sequestration following land use change in a subtropical karst region. Geoderma. 2019;353:340–6.

    CAS  Article  Google Scholar 

  62. 62.

    Ahrens B, Braakhekke MC, Guggenberger G, Schrumpf M, Reichstein M. Contribution of sorption, DOC transport and microbial interactions to the 14C age of a soil organic carbon profile: insights from a calibrated process model. Soil Biol Biochem. 2015;88:390–402.

    CAS  Article  Google Scholar 

  63. 63.

    Nguyen RT, Harvey HR. Preservation via macromolecular associations during Botryococcus braunii decay: proteins in the Pula Kerogen. Org Geochem. 2003;34:1391–403.

    CAS  Article  Google Scholar 

  64. 64.

    Kallenbach CM, Frey SD, Grandy AS. Direct evidence for microbial-derived soil organic matter formation and its ecophysiological controls. Nat Commun. 2016;7:13630.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  65. 65.

    Puget P, Angers DA, Chenu C. Nature of carbohydrates associated with water-stable aggregates of two cultivated soils. Soil Biol Biochem. 1998;31:55–63.

    Article  Google Scholar 

  66. 66.

    Schmidt MWI, Torn MS, Abiven S, Dittmar T, Guggenberger G, Janssens IA, et al. Persistence of soil organic matter as an ecosystem property. Nature. 2011;478:49–56.

    CAS  PubMed  Article  Google Scholar 

  67. 67.

    Spence A, Simpson AJ, McNally DJ, Moran BW, McCaul MV, Hart K, et al. The degradation characteristics of microbial biomass in soil. Geochim Cosmochim Acta. 2011;75:2571–81.

    CAS  Article  Google Scholar 

  68. 68.

    Drigo B, Anderson IC, Kannangara GSK, Cairney JWG, Johnson D. Rapid incorporation of carbon from ectomycorrhizal mycelial necromass into soil fungal communities. Soil Biol Biochem. 2012;49:4–10.

    CAS  Article  Google Scholar 

  69. 69.

    Wang G, Chen S. A review on parameterization and uncertainty in modeling greenhouse gas emissions from soil. Geoderma. 2012;170:206–16.

    CAS  Article  Google Scholar 

  70. 70.

    Blagodatskaya Е, Blagodatsky S, Khomyakov N, Myachina O, Kuzyakov Y. Temperature sensitivity and enzymatic mechanisms of soil organic matter decomposition along an altitudinal gradient on Mount Kilimanjaro. Sci Rep. 2016;6:22240.

    CAS  Article  Google Scholar 

  71. 71.

    German DP, Weintraub MN, Grandy AS, Lauber CL, Rinkes ZL, Allison SD. Optimization of hydrolytic and oxidative enzyme methods for ecosystem studies. Soil Biol Biochem. 2011;43:1387–97.

    CAS  Article  Google Scholar 

  72. 72.

    Wu J, Xiao H. Measuring the gross turnover time of soil microbial biomass C under incubation. Acta Pedol Sin. 2004;41:401–7.

    CAS  Google Scholar 

  73. 73.

    Cheng W. Rhizosphere priming effect: Its functional relationships with microbial turnover, evapotranspiration, and C–N budgets. Soil Biol Biochem. 2009;41:1795–801.

    CAS  Article  Google Scholar 

  74. 74.

    Luo Z, Tang Z, Guo X, Jiang J, Sun OJ. Non-monotonic and distinct temperature responses of respiration of soil microbial functional groups. Soil Biol Biochem. 2020;148:107902.

    CAS  Article  Google Scholar 

  75. 75.

    de Graaff M-A, Classen AT, Castro HF, Schadt CW. Labile soil carbon inputs mediate the soil microbial community composition and plant residue decomposition rates. New Phytol. 2010;188:1055–64.

    PubMed  Article  CAS  PubMed Central  Google Scholar 

  76. 76.

    Paul EA. The nature and dynamics of soil organic matter: plant inputs, microbial transformations, and organic matter stabilization. Soil Biol Biochem. 2016;98:109–26.

    CAS  Article  Google Scholar 

  77. 77.

    Crowther TW, Sokol NW, Oldfield EE, Maynard DS, Thomas SM, Bradford MA. Environmental stress response limits microbial necromass contributions to soil organic carbon. Soil Biol Biochem. 2015;85:153–61.

    CAS  Article  Google Scholar 

  78. 78.

    Ding X, Chen S, Zhang B, He H, Filley TR, Horwath WR. Warming yields distinct accumulation patterns of microbial residues in dry and wet alpine grasslands on the Qinghai-Tibetan Plateau. Biol Fertil Soils. 2020;56:881–92.

    CAS  Article  Google Scholar 

  79. 79.

    Mao D, Luo L, Wang Z, Zhang C, Ren C. Variations in net primary productivity and its relationships with warming climate in the permafrost zone of the Tibetan Plateau. J Geogr Sci. 2015;25:967–77.

    Article  Google Scholar 

  80. 80.

    Wu J, Feng Y, Zhang X, Wurst S, Tietjen B, Tarolli P, et al. Grazing exclusion by fencing non-linearly restored the degraded alpine grasslands on the Tibetan Plateau. Sci Rep. 2017;7:15202.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  81. 81.

    Li J, Wang G, Mayes MA, Allison SD, Frey SD, Shi Z, et al. Reduced carbon use efficiency and increased microbial turnover with soil warming. Glob Change Biol. 2019;25:900–10.

    Article  Google Scholar 

  82. 82.

    Chen G, Ma S, Tian D, Xiao W, Jiang L, Xing A, et al. Patterns and determinants of soil microbial residues from tropical to boreal forests. Soil Biol Biochem. 2020;151:108059.

    CAS  Article  Google Scholar 

  83. 83.

    Wang YP, Chen BC, Wieder WR, Leite M, Medlyn BE, Rasmussen M, et al. Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition. Biogeosciences. 2014;11:1817–31.

    CAS  Article  Google Scholar 

  84. 84.

    Soares M, Rousk J. Microbial growth and carbon use efficiency in soil: links to fungal-bacterial dominance, SOC-quality and stoichiometry. Soil Biol Biochem. 2019;131:195–205.

    CAS  Article  Google Scholar 

  85. 85.

    Liang C, Cheng G, Wixon DL, Balser TC. An Absorbing Markov Chain approach to understanding the microbial role in soil carbon stabilization. Biogeochemistry. 2011;106:303–9.

    Article  Google Scholar 

  86. 86.

    Fan Z, Liang C. Significance of microbial asynchronous anabolism to soil carbon dynamics driven by litter inputs. Sci Rep. 2015;5:9575.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

Download references


This study was funded by the National Key R&D Program of China (2019YFA0607301), the National Natural Science Foundation of China (No. 41971058), and the National Program for Support of Top-notch Young Professionals (to EB).

Author information




XF and EB designed the study and analyzed the experiments and wrote and edited the paper. XF collected and organized the data and built and run the model. DG, CZ, CW, YQ, and JZ contributed to the discussion of results and revision of the paper.

Corresponding author

Correspondence to Edith Bai.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fan, X., Gao, D., Zhao, C. et al. Improved model simulation of soil carbon cycling by representing the microbially derived organic carbon pool. ISME J 15, 2248–2263 (2021).

Download citation


Quick links