Vietnam Journal of Mathematics

, Volume 43, Issue 4, pp 801–817 | Cite as

Simulating Biological Dynamics Using Partial Differential Equations: Application to Decomposition of Organic Matter in 3D Soil Structure

  • Babacar Lèye
  • Doanh Nguyen-NgocEmail author
  • Olivier Monga
  • Patricia Garnier
  • Naoise Nunan


The majority of carbon on earth is in the form of soil organic matter. And its degradation by microorganisms leads to the remineralization of carbon as carbon dioxide. The microbial activity causes a reduction of soil carbon and increases atmospheric carbon. However, most models of organic matter do not explicitly take into account this reality. We try to answer these questions by developing and validating a model describing the action of microorganisms on degradation of organic matter. We use simulation domain as the pores in the soil modeled by a network of balls. The model is solved numerically in the balls by the finite element method with the solver of partial differential equations (PDEs) Freefem3d. We compare the numerical results with experimental data on the mineralization of soil carbon.


Model Partial differential equations Soil Organic matter 3D computed tomography image Validation 

Mathematics Subject Classification (2010)

35Q92 35K57 78M10 80M10 



This work was done while the second author was at Vietnam Institute for Advanced Study in Mathematics (VIASM). The work was partially supported by the project VAST.DLT.01/12-13. The authors would like to thank anonymous referees for their valuable comments.


  1. 1.
    Allison, S.D.: Cheaters, diffusion and nutrients constrain decomposition by microbial enzymes in spatially structured environments. Ecol. Lett. 8, 626–635 (2005)CrossRefGoogle Scholar
  2. 2.
    Coucheney, E.: Effets Combinés de Facteurs Climatiques et de la Diversité sur le Fonctionnement de Communautés Bactériennes: Respiration et Métabolomique. Université Pierre et Marie Curie (2009)Google Scholar
  3. 3.
    Del Pino, S., Pironneau, O.: Asymptotic analysis and layer decomposition for the couplex exercise. Comput. Geosci. 8, 149–162 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Dobrzynski, C., Frey, P.J., Mohammadi, B., Pironneau, O.: Fast and accurate simulations of air-cooled structures. Comput. Methods Appl. Mech. Eng. 195, 3168–3180 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Falconer, R.E., Bown, J.L., White, N.A., Crawford, J.W.: Biomass recycling: a key to efficient foraging by fungal colonies. OIKOS 116, 1558–1568 (2007)CrossRefGoogle Scholar
  6. 6.
    Fang, C., Smith, P., Smith, J.U., Monrieff, J.B.: Incorporating microorganisms as decomposers into models to simulate soil organic matter decomposition. Geoderma 129, 139–146 (2005)CrossRefGoogle Scholar
  7. 7.
    Ingwersena, J., Pollb, C., Strecka, T., Kandelerb, E.: Micro-scale modelling of carbon turnover driven by microbial succession at a biogeochemical interface. Soil Biol. Biochem. 40, 864–878 (2008)CrossRefGoogle Scholar
  8. 8.
    George, P.L., Borouchaki, H.: Premières expériences de maillage automatique par une méthode de Delaunay anisotrope en trois dimensions. RT-027, Inria (2002)Google Scholar
  9. 9.
    Gignoux, J., House, J., Hall, D., Masse, D., Nacro, H.B., Abbadie, L.: Design and test of a generic cohort model of soil organic matter decomposition: the SOMKO model. Glob. Ecol. Biogeogr. 10, 639–660 (2001)CrossRefGoogle Scholar
  10. 10.
    Killham, K., Amato, M., Ladd, J.N.: Effect of substrate location in soil and soil pore-water regime on carbon turnover. Soil Biol. Biochem. 25, 57–62 (1993)CrossRefGoogle Scholar
  11. 11.
    Long, T., Or, D.: Aquatic habitats and diffusion constraints affecting microbial coexistence in unsaturated porous media. Water Resour. Res. 41 (2005). doi: 10.1029/2004WR003796
  12. 12.
    Marilleau, N., Cambier, C., Drogoul, A., Chotte, J.L., Perrier, E., Blanchart, E.: Multiscale MAS modelling to simulate the soil environment: Application to soil ecology. Simul. Model. Pract. Theory 16, 736–745 (2008)CrossRefGoogle Scholar
  13. 13.
    Manzoni, S., Porporato, A.: Soil carbon and nitrogen mineralization: theory and models across scales. Soil Biochem. 41, 1355–1379 (2009)CrossRefGoogle Scholar
  14. 14.
    Monga, O., Bousso, M., Garnier, P., Pot, V.: 3D geometric structures and biological activity: Application to microbial soil organic matter decomposition in pore space. Ecol. Model. 216, 291–302 (2008)CrossRefGoogle Scholar
  15. 15.
    Monga, O., Bousso, M., Garnier, P., Pot, V.: Using pore space 3D geometrical modelling to simulate biological activity: impact of soil structure. Comput. Geosci. 35, 1789–1801 (2009)CrossRefGoogle Scholar
  16. 16.
    Monga, O., Ngom, N.F., Delerue, J.F.: Representing geometric structures in 3D tomography soil images: Application to pore-space modeling. Comput. Geosci. 33, 1140–1161 (2007)CrossRefGoogle Scholar
  17. 17.
    Murray, J.D.: Mathematical Biology. I. An Introduction. Springer, New York (2003)Google Scholar
  18. 18.
    Schimel, J.P., Weintraub, M.N.: The implications of exoenzyme activity on microbial carbon and nitrogen limitation in soil: a theoretical model. Soil Biol. Biochem. 35, 549–563 (2003)CrossRefGoogle Scholar
  19. 19.
    Semenov, M.A., Halford, N.G.: Identifying target traits and molecular mechanisms for wheat breeding under a changing climate. J. Exp. Bot. 60, 2791–2804 (2009)CrossRefGoogle Scholar
  20. 20.
    Tartakovsky, A.M, Scheibe, T.D, Meakin, P.: Pore-scale model for reactive transport and biomass growth. J. Porous Media 12, 417–434 (2009)CrossRefGoogle Scholar
  21. 21.
    Treves, D.S., Xia, B., Zhou, J., Tiedje, J.M.: A two-species test of the hypothesis that spatial isolation influences microbial diversity in soil. Microb. Ecol. 45, 20–28 (2003)CrossRefGoogle Scholar
  22. 22.
    Vetter, Y.A, Deming, J.W., Jumars, P.A, Krieger-Brockett, B.B.: A predictive model of bacterial foraging by means of freely released extracellular enzymes. Microb. Ecol. 36, 75–92 (1998)CrossRefGoogle Scholar

Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  • Babacar Lèye
    • 1
  • Doanh Nguyen-Ngoc
    • 2
    Email author
  • Olivier Monga
    • 3
  • Patricia Garnier
    • 4
  • Naoise Nunan
    • 5
  1. 1.Laboratoire d’Analyse Numérique et Informatique(LANI), Ummisco UMI 209 IRDUniversité Gaston BergerSaint-LouisSenegal
  2. 2.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam
  3. 3.International Joint Unity (UMI 209) UMMISCO, IRDBondy CedexFrance
  4. 4.INRA, UMR EcoSysThiverval GrignonFrance
  5. 5.CNRS, UMR 7618, Institute of Ecology and Environmental ScienceThiverval-GrignonFrance

Personalised recommendations