Abstract
The bases and the principles of modeling in microbial community ecology and biogeochemistry are presented and discussed. Several examples are given. Among them, the fermentation process is largely developed, thus demonstrating how the model allows determining the microbial population growth rate, the death rate, and the maintenance rate. More generally, these models have been used to increase the development of bioenergetic formulations which are presently used in biogeochemical models (Monod, Droop, DEB models). Different types of interactions (competition, predation, and virus–bacteria) are also developed. For each topic, a complete view of the models used in the literature cannot be presented. Consequently, the focus has been done on the demonstration how to build a model instead of providing a long list of existing models. Some recent results in sediment biogeochemistry are provided to illustrate the application of such models.
Coordinator
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bailey DJ, Otten W, Gilligan CA (2000) Saprotrophic invasion by the soil-borne fungal plant pathogen Rhizoctonia solani and percolation thresholds. New Phytol 146:535–544
Becks L, Hilker FM, Malchow H, Jürgens K, Arndt H (2005) Experimental demonstration of chaos in a microbial food web. Nature 435:1226–1229
Beretta E, Kuang Y (1998) Modeling and analysis of a marine bacteriophage infection. Math Biosci 149:57–76
Boer MP, Kooi BW, Kooijman SALM (1998) Food chain dynamics in the Chemostat. Math Biosci 150:43–62
Bonkowski M (2004) Protozoa and plant growth: the microbial loop in soil revisited. New Phytol 162:617–631
Boswell GP, Jacobs H, Davidson FA, Gadd GM, Ritz K (2003) Growth and function of fungal mycelia in heterogeneous environments. Bull Math Biol 65:447–477
Boudreau PB (1997) Diagenetic models and their implementation: modelling transport and reactions in aquatic sediments. Springer, Berlin/Heidelberg/New York
Brauer F, Castillo-Chavez C (2000) Mathematical models in population biology and epidemiology, vol 40, Texts in applied mathematics. Springer-Verlag, New York
Coleman D, Fu SL, Hendrix P, Crossley D (2002) Soil foodwebs in agroecosystems: impacts of herbivory and tillage management. Eur J Soil Biol 38:21–28
Costerton JW, Lewandowski Z, De Beer D, Caldwell D, Korber D, James G (1994) Biofilms, the customized microniche. J Bacteriol 176:2137–2142
Couteaudier Y, Steinberg C (1990) Biological and mathematical description of growth pattern of Fusarium oxysporum in sterilized soil. FEMS Microbiol Ecol 74:253–259
Cunningham A, Maas P (1978) Time lag and nutrient storage effects in the transient growth response of Chlamydomonas reinhardtii in nitrogen limited batch and continuous culture. J Gen Microbiol 104:227–231
Dantigny P (2004) Predictive mycology. In: McKellar RC, Lu X (eds) Modeling microbial responses in food. CRC Press, Boca Raton, pp 313–320
Dassonville F, Renault P (2002) Interactions between microbial processes and geochemical transformations under anaerobic conditions: a review. Agronomie 22:51–68
De Wit R, Van den Ende FP, Van Gemerden H (1995) Mathematical simulation of the interactions among cyanobacteria, purple sulfur bacteria and chemotrophic sulfur bacteria in microbial mat communities. FEMS Microbiol Ecol 17:117–136
Decker KLM et al (2005) Mathematical simulation of the diel O, S, and C biogeochemistry of a hypersaline microbial mat. FEMS Microbiol Ecol 52:377–395
Droop MR (1968) Vitamin B12 and marine ecology. IV. The kinetics of uptake, growth and inhibition in Monochrysis lutheri. J Mar Biol Assoc UK 48:689–733
Fu SL, Cabrera ML, Coleman DC, Kisselle KW, Garrett CJ, Hendrix PF, Crossley DA (2000) Soil carbon dynamics of conventional tillage and no-till agroecosystems at Georgia Piedmont – HSB-C models. Ecol Model 131:229–248
Fuhrman JA (1999) Marine viruses and their biogeochemical and ecological effects. Nature 399:541–548
Fujikawa H, Yano K, Morozumi S (2006) Characteristics and modeling of Escherichia coli growth in pouched food. Shokuhin Eiseigaku Zasshi 47:95–98
Fussmann GF, Blasius B (2005) Community response to enrichment is highly sensitive to model structure. Biol Lett 1:9–12
Fussmann GF, Ellner SP, Shertzer KW, Hairston NG Jr (2000) Crossing the Hopf bifurcation in a live predator-prey system. Science 290:1358–1360
Gabrielle B, Laville P, Henault C, Nicoullaud B, Germon JC (2006) Simulation of nitrous oxide emissions from wheat-cropped soils using CERES. Nut Cycl Agroecosyst 74:133–146
Gause GF (1935) Vérifications expérimentales de la théorie mathématique de la lutte pour la vie. Actual Scient Ind 277
Ghosh S, Bhattacharyya S, Bhattacharya DK (2007) The role of viral infection in pest control: a mathematical study. Bull Math Biol 69:2649–2691
Holling CS (1959) Some characteristics of simple types of predation and parasitism. Can Entomol 80:274–287
Holling CS (1965) The functional response of predators to prey density and its role in mimicry and population regulation. Mem Entomol Soc Can 45:1–60
Kooijman SALM (2010) Dynamic energy and mass budgets in biological systems, 3rd edn. Cambridge University Press, Cambridge
Kreft JU (2004) Biofilms promote altruism. Microbiology 150:2751–2760
Kreft JU, Picioreanu C, Wimpenny JWT, Van Loosdrecht MCM (2001) Individual-based modelling of biofilms. Microbiology 147:2897–2912
Lejeune R, Baron GV (1998) Modelling the exponential growth of filamentous fungi during batch cultivation. Biotech Bioeng 60:169–179
Li H, Xie GH, Edmondson A (2007) Evolution and limitations of primary mathematical models in predictive microbiology. Br Food J 109:608–626
Maynard-Smith J (1978) Models in ecology. Cambridge University Press, Cambridge
Mchich R, Auger P, Poggiale J-C (2007) Effect of predator density dependent dispersal of prey on stability of a predator-prey system. Math Biosci 206:343–356
Middelboe M (2000) Bacterial growth rate and marine virus-host dynamics. Microb Ecol 40:114–124
Middelboe M, Hagstrom A, Blackburn N, Sinn B, Fischer U, Borch NH, Pinhassi J, Simu K, Lorenz MG (2001) Effects of bacteriophages on the population dynamics of four strains of pelagic marine bacteria. Microb Ecol 42:395–406
Mitra A, Davidson K, Flynn KJ (2003) The influence of changes in predation rates on marine microbial predator/prey interactions: a modelling study. Acta Oecol Int J Ecol 24:S359–S367
Monti GE, Frankena K, De Jong MCM (2007) Transmission of bovine leukaemia virus within dairy herds by simulation modelling. Epidemiol Infect 135:722–732
Morales SE, Holben WE (2011) Linking bacterial identities and ecosystem processes: can ‘omic’ analyses be more than the sum of their parts? FEMS Microbiol Ecol 75:2–16
Mulder MM (1988) Energetic aspects of bacterial growth: a mosaic non – equilibrium thermodynamic approach. PhD thesis, Amsterdam Universiteit
Patwardhan PR, Srivastava AK (2004) Model-based fed-batch cultivation of R. eutropha for enhanced biopolymer production. Biochem Eng J 20:21–28
Pavé A (2006) By way of introduction: modelling living systems, their diversity and their complexity: some methodological and theoretical problems. C R Biol 329:3–12
Pavé A (2007) Necessity of chance: biological roulettes and biodiversity. C R Biol 330:189–198
Picioreanu C (1999) Multidimensional modeling of biofilm structure. PhD thesis, Department of Biotechnology, TU Delft. ISBN 90-90133110-0
Picioreanu C, Van Loosdrecht MCM, Heijnen J (1998) Mathematical modelling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng 58:101–116
Poggiale J-C, Auger P, Nérini D, Manté C, Gilbert F (2005) Global production increased by spatial heterogeneity in a population dynamics model. Acta Biotheor 53:359–370
Poggiale J-C, Baklouti M, Queguiner B, Kooijman SALM (2010) How far details are important in ecosystem modelling: the case of multi-limiting nutrients in phytoplankton – zooplankton interactions. Philos Trans R Soc Lond B Biol Sci 365:3495–3507
Ponciano JM, Vandecasteele FPJ, Hess TF, Forney LJ, Crawford RL, Joyce P (2005) Use of stochastic models to assess the effect of environmental factors on microbial growth. Appl Environ Microbiol 71:2355–2364
Ronn R, McCaig AE, Griffiths BS, Prosser JI (2002) Impact of protozoan grazing on bacterial community structure in soil microcosms. Appl Environ Microbiol 68:6094–6105
Rosenzweig ML (1971) The paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171:385–387
Rosenzweig ML, MacArthur RH (1963) Graphical representation and stability conditions of predator-prey interactions. Am Nat 97:209–223
Rosso L, Lobry JR, Bajard S, Flandrois JP (1993) An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. J Theor Biol 162:447–463
Sloan WT, Woodcock S, Lunn M, Head IM, Curtis TP (2007) Modeling taxa-abundance distributions in microbial communities using environmental sequence data. Microb Ecol 53:443–455
Smith LH (1997) The periodically forced Droop model for phytoplankton growth in a chemostat. J Math Biol 35:545–556
Solomon E (1949) The natural control of animal populations. J Anim Ecol 18:1–35
Steinberg C, Whipps JM, Wood DA, Fenlon J, Alabouvette C (1999) Effects of nutritional sources on growth of one non-pathogenic strain and four strains of Fusarium oxysporum pathogenic on tomato. Mycol Res 103:1210–1216
Stelling J (2004) Mathematical models in microbial systems biology. Curr Opin Microbiol 7:513–518
Takeuchi Y, Adachi N (1983) Existence and bifurcation of stable equilibrium in two-prey-one-predator communities. Bull Math Biol 45:877–900
Tam VH, Schilling AN, Nikolaou M (2005) Modelling time-kill studies to discern the pharmacodynamics of meropenem. J Antimicrob Chemother 55:699–706
Torsvik V, Ovreas L (2002) Microbial diversity and function in soil: from genes to ecosystems. Curr Opin Microbiol 5:240–245
van den Berg HA, Kiselev YN, Kooijman SALM, Orlov MV (1998) Optimal allocation between nutrient uptake and growth in a microbial trichome. J Math Biol 37:28–48
Van Impe JF, Poschet F, Geeraerd AH, Vereecken KM (2005) Towards a novel class of predictive microbial growth models. Int J Food Microbiol 100:97–105
Vayenas DV, Pavlou S (1999) Chaotic dynamics of a food web in a chemostat. Math Biosci 162:69–84
Woese CR (1987) Bacterial evolution. Microbiol Rev 51:221–271
Wood JC, McKendrick IJ, Gettinby G (2006) A simulation model for the study of the within-animal infection dynamics of E. coli O157. Prev Vet Med 74:180–193
Zhang XS, Holt J, Colvin J (2000) A general model of plant-virus disease infection incorporating vector aggregation. Plant Pathol 49:435–444
Zwietering MH, Witjes T, de Wit JC, van’t Riet K (1992) A decision support system for prediction of the microbial spoilage in foods. J Food Protect 12:973–979
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Poggiale, JC., Dantigny, P., De Wit, R., Steinberg, C. (2015). Modeling in Microbial Ecology. In: Bertrand, JC., Caumette, P., Lebaron, P., Matheron, R., Normand, P., Sime-Ngando, T. (eds) Environmental Microbiology: Fundamentals and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9118-2_19
Download citation
DOI: https://doi.org/10.1007/978-94-017-9118-2_19
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-9117-5
Online ISBN: 978-94-017-9118-2
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)