The Development of Fungal Networks in Complex Environments

  • Graeme P. BoswellEmail author
  • Helen Jacobs
  • Karl Ritz
  • Geoffrey M. Gadd
  • Fordyce A. Davidson
Original Article


Fungi are of fundamental importance in terrestrial ecosystems playing important roles in decomposition, nutrient cycling, plant symbiosis and pathogenesis, and have significant potential in several areas of environmental biotechnology such as biocontrol and bioremediation. In all of these contexts, the fungi are growing in environments exhibiting spatio-temporal nutritional and structural heterogeneities. In this work, a discrete mathematical model is derived that allows detailed understanding of how events at the hyphal level are influenced by the nature of various environmental heterogeneities. Mycelial growth and function is simulated in a range of environments including homogeneous conditions, nutritionally-heterogeneous conditions and structurally-heterogeneous environments, the latter emulating porous media such as soils. Our results provide further understanding of the crucial processes involved in fungal growth, nutrient translocation and concomitant functional consequences, e.g. acidification, and have implications for the biotechnological application of fungi.


Hybrid cellular automata Fungal mycelia Modelling 


  1. Alexander, M. 1964. Biochemical ecology of soil microorganisms. Ann. Rev. Microbiol. 18, 217–252.CrossRefGoogle Scholar
  2. Anderson, A.R.A. 2003. A hybrid discrete-continuum technique for individual-based migration models. In Alt, W., Chaplain, M., Griebel, M., Lenz, J. (Eds.), Polymer and Cell Dynamics—Multiscale Modelling and Numerical Simulations. Birkhauser, Switzerland, pp. 251–259.Google Scholar
  3. Anderson, A.R.A., Chaplain, M.A.J., 1998. Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Biol. 60, 857–899.zbMATHCrossRefGoogle Scholar
  4. Anderson, A.R.A., Sleeman, B.D., Young, I.M., Griffiths, B.S., 1997. Nematode movement along a chemical gradient in a structurally heterogeneous environment. 2. Theory. Fundam. Appl. Nematol. 20, 165–172.Google Scholar
  5. Bailey, D.J., Otten, W., Gilligan, C.A., 2000. Saprotrophic invasion by the soil-borne fungal plant pathogen Rhizoctonia solani and percolation thresholds. New Phytol. 146, 535-544.CrossRefGoogle Scholar
  6. Barnsley, M., 1988. Fractals Everywhere. Academic Press, London.zbMATHGoogle Scholar
  7. Bell, A.D., 1986. The simulation of branching patterns in modular organisms. Phil. Trans. R. Soc. London Ser. B. Biol. Sci. 313, 143–160.CrossRefGoogle Scholar
  8. Boddy, L., 1999. Saprotrophic cord-forming fungi: Meeting the challenge of heterogeneous environments. Mycologia 91, 13–32.CrossRefGoogle Scholar
  9. Boswell, G.P., Britton, N.F., Franks, N.R., 1998. Habitat fragmentation, percolation theory and the conservation of a keystone species. Proc. R. Soc. Lond. B 265, 1921–1925.Google Scholar
  10. Boswell, G.P., Jacobs, H., Davidson, F.A., Gadd, G.M., Ritz, K., 2002. Functional consequences of nutrient translocation in mycelial fungi. J. Theor. Biol. 217, 459–477.CrossRefMathSciNetGoogle Scholar
  11. Boswell, G.P., Jacobs, H., Davidson, F.A., Gadd, G.M., Ritz, K., 2003a. Growth and function of fungal mycelia in heterogeneous environments. Bull. Math. Biol. 65, 447–477.CrossRefGoogle Scholar
  12. Boswell, G.P., Jacobs, H., Davidson, F.A., Gadd, G.M., Ritz, K., 2003b. A positive numerical scheme for a mixed-type partial differential equation model for fungal growth. Appl. Math. Comput. 138, 321–340.zbMATHCrossRefMathSciNetGoogle Scholar
  13. Carroll, G.C., Wicklow, D.T., (Eds.) 1992. The Fungal Community: its Organisation and Role in the Ecosystem. Marcel-Decker, New York.Google Scholar
  14. Cartwright, D.K., Spurr, H.W., 1998. Biological control of Phytophthora parasitica var. nicotianae on tobacco seedling with non-pathogenic binucleate Rhizoctonia fungi. Soil Biol. Biochem. 30, 1879–1884.CrossRefGoogle Scholar
  15. Caswell, H., Etter, R.J., 1993. Ecological interactions in patchy environments: from patch-occupancy models to cellular automata. In: Levin, S.A., Powell, T.M., Steele, J. (Eds.), Patch Dynamics, Volume 96 of Lecture Notes in Biomathematics. Springer, New York, pp. 176–183.Google Scholar
  16. Chen, C., Stotzky, G., 2002. Interactions between microorganisms and soil particles: An overview. In: Huang, P.M., Bollag, J.-M., Senesi, N. (Eds.), Interactions Between Soil Particles and Microorganisms: Impact on the Terrestrial Ecology. Wiley, New York, pp. 3–40.Google Scholar
  17. Cohen, D., 1967. Computer simulation of biological pattern generation processes. Nature 216, 246–248.CrossRefGoogle Scholar
  18. Davidson, F.A., 1998. Modelling the qualitative response of fungal mycelia to heterogeneous environments. J. Theor. Biol. 195, 281–292.CrossRefGoogle Scholar
  19. Dix, N.J., Webster, J., 1995. Fungal Ecology. Chapman and Hall, London.Google Scholar
  20. Durrett, R., Levin, S., 1994. Stochastic spatial models: A user's guide to ecological applications. Phil. Trans. R. Soc. Lond. B 259, 329–350.CrossRefGoogle Scholar
  21. Edelstein, L., 1982. The propagation of fungal colonies: A model for tissue growth. J. Theor. Biol. 98, 679–701.CrossRefMathSciNetGoogle Scholar
  22. Edelstein, L., Segel, L.A., 1983. Growth and metabolism in mycelial fungi. J. Theor. Biol. 104, 187–210.CrossRefGoogle Scholar
  23. Ermentrout, G.B., Edelstein-Keshet, L., 1993. Cellular automata approaches to biological modelling. J. Theor. Biol. 160, 97–133.CrossRefGoogle Scholar
  24. Fisher-Parton, S., Parton, R.M., Hickey, P.C., Dijksterhuis, J., Atkinson, H.A., Read, N.D., 2000. Confocal microscopy of FM4-64 as a tool for analysing endocytosis and vesicle trafficking in living fungal hyphae. J. Microsc. 198, 246–259.CrossRefGoogle Scholar
  25. Fomina, M., Ritz, K., Gadd, G.M., 2000. Negative fungal chemotropism to toxic metals. FEMS Microbiol. Lett. 193, 207–211.CrossRefGoogle Scholar
  26. Fomina, M., Ritz, K., Gadd, G.M., 2003. Nutritional influence on the ability of fungal mycelia to penetrate toxic metal-containing domains. Mycol. Res. 107, 861–871.CrossRefGoogle Scholar
  27. Gadd, G.M., 1988. Carbon nutrition and metabolism. In: Berry, D.R. (Ed.), Physiology of Industrial Fungi. Blackwell Scientific, Oxford, UK, pp. 21–57.Google Scholar
  28. Gadd, G.M., 1999. Fungal production of citric and oxalic acid: Importance in metal speciation, physiology and biogeochemical processes. Adv. Microb. Physiol. 41, 47–92.CrossRefGoogle Scholar
  29. Gadd, G.M. (Ed.), 2001. Fungi in Bioremediation. Cambridge University Press, Cambridge, p. 481, ISBN: 0-521-78119-1.Google Scholar
  30. Gadd, G.M., Ramsay, L., Crawford, J.W., Ritz, K., 2001. Nutritional influence on fungal colony growth and biomass distribution in response to toxic metals. FEMS Microbiol. Lett. 204, 311–316.CrossRefGoogle Scholar
  31. Gadd, G.M., Sayer, J., 2000. Fungal transformations of metals and metalloids. In: Lovley, D.R. (Ed.), Environmental Microbe-Metal Interactions. American Society for Microbiology, Washington, pp. 237–256.Google Scholar
  32. Gooday, G.W., 1975. Chemotaxis and chemotrophism in fungi and algae. In: Carlile, M.J. (Ed.), Primitive Sensory and Communication Systems, Academic Press, London, pp. 155-204.Google Scholar
  33. Gooday, G.W., 1995. The dynamics of hyphal growth. Mycol. Res. 99, 385–394.Google Scholar
  34. Gow, N., Gadd, G.M., (Eds.) 1995. The Growing Fungus. Chapman and Hall, London.Google Scholar
  35. Halley, J.M., Comins, H.N., Lawton, J.H., Hassell, M.P., 1994. Competition, succession and pattern in fungal communities—towards a cellular automata model. Oikos 70, 435–442.CrossRefGoogle Scholar
  36. Harris, K., Crabb, D., Young, I.M., Weaver, H., Gilligan, C.A., Otten, W., Ritz, K., 2002. In situ visualisation of fungi in soil thin sections: Problems with crystallisation of the fluorochrome FB 28 (Calcofluor M2R) and improved staining by SCRI Renaissance 2200. Mycol. Res. 106, 293–297.Google Scholar
  37. Harris, K., Young, I.M., Gilligan, C.A., Otten, W., Ritz, K., 2003. Effect of bulk density on the spatial organisation of the fungus Rhizoctonia solani in soil. FEMS Microbiol. Ecol. 44, 45–56.CrossRefGoogle Scholar
  38. Hillen, T., Othmer, H.G., 2000. The diffusion limit of transport equations derived from velocity-jump processes. SIAM J. Appl. Math. 61, 751–775.zbMATHCrossRefMathSciNetGoogle Scholar
  39. Hutchinson, S.A., Sharma, P., Clark, K.R., MacDonald, I., 1980. Control of hyphal orientation in colonies of Mucor hiemalis. Trans. Br. Mycol. Soc. 75, 177–191.CrossRefGoogle Scholar
  40. Jacobs, H., Boswell, G.P., Harper, F.A., Ritz, K., Davidson, F.A., Gadd, G.M., 2002. Solubilization of metal phosphates by Rhizoctonia solani. Mycol. Res. 106, 1468–1479.CrossRefGoogle Scholar
  41. Jacobs, H., Boswell, G.P., Ritz, K., Davidson, F.A., Gadd, G.M., 2002. Solubilization of calcium phosphate as a consequence of carbon translocation by Rhizoctonia solani. FEMS Microbiol. Ecol. 40, 65–71.CrossRefGoogle Scholar
  42. Jacobs, H., Boswell, G.P., Scrimgeour, C.M., Davidson, F.A., Gadd, G.M., Ritz, K., 2004. Translocation of glucose-derived carbon by Rhizoctonia solani in nutritionally heterogeneous environments. Mycol. Res. 108, 453–461.CrossRefGoogle Scholar
  43. Jennings, D.H., Thornton, J.D., Galpin, M.F.J., Coggins, C.R., 1974. Translocation in fungi. Symp. Soc. Exp. Biol. 28, 139–156.Google Scholar
  44. Kotov, V., Reshetnikov, S.V., 1990. A stochastic model for early mycelial growth. Mycol. Res. 94, 577–586.Google Scholar
  45. LeVeque, R.J., 1992. Numerical Methods for Conservation Laws. Lectures in Mathematics, ETH Zürich. Basel: Birkhäuser.Google Scholar
  46. :1968a Lindenmayer, A., 1968a. Mathematical models for cellular interactions in development I. Filaments with one-sided inputs. J. Theor. Biol. 18, 280–299.CrossRefGoogle Scholar
  47. :1968b Lindenmayer, A., 1968b. Mathematical models for cellular interactions in development II. Simple and branching filaments with two-sided inputs. J. Theor. Biol. 18, 300–315.CrossRefGoogle Scholar
  48. Littlefield, L.J., Wilcoxson, R.D., Sudia, T.W., 1965. Translocation of phosphorus-32 in Rhizoctonia solani. Phytopathology 55, 536–542.Google Scholar
  49. Lopez-Franco, R., Bartnicki-Garcia, S., Bracker, C.E., 1994. Pulsed growth of fungal hyphal tips. Proc. Natl. Acad. Sci. U.S.A. 91, 12228–12232.Google Scholar
  50. Meěkauskas, A., McNulty, L.J., Moore, D., 2004a. Concerted regulation of all hyphal tips generates fungal fruit body structures: Experiments with computer visualizations produced by a new mathematical model of hyphal growth. Mycol. Res. 108, 341–353.CrossRefGoogle Scholar
  51. Meěkauskas, A., Fricher, M.D., Moore, D., 2004b. Simulating colonial growth of fungi with the neighbour-sensing model of hyphal growth. Mycol. Res. 108, 1241–1256.CrossRefGoogle Scholar
  52. Morley, G.F., Sayer, J.A., Wilkinson, S.C., Gharieb, M.M., Gadd, G.M., 1996. Fungal sequestration, solubilization and transformation of toxic metals. In: Frankland, J.C., Magan, N., Gadd, G.M. (Eds.), Fungi and Environmental Change, Cambridge University Press, Cambridge, pp. 235–256.Google Scholar
  53. Ogoshi, A., 1987. Ecology and pathology of anastomosis and intraspecific groups of Rhizoctonia solani Kühn. Ann. Rev. Phytopathol. 25, 125–143.Google Scholar
  54. Olsson, S., 1994. Uptake of glucose and phosphorus by growing colonies of Fusarium oxysporum as qualified by image analysis. Exp. Mycol. 18, 33–47.CrossRefGoogle Scholar
  55. Olsson, S., 1995. Mycelial density profiles of fungi on heterogeneous media and their interpretation in terms of nutrient reallocation patterns. Mycol. Res. 99, 143–153.Google Scholar
  56. Olsson, S., 1999. Nutrient translocation and electric signalling in mycelia. In: Gow, N.A.R., Robson, G.D., Gadd, G.M. (Eds.), The Fungal Colony, Cambridge University Press, Cambridge.Google Scholar
  57. Olsson, S., Gray, S.N., 1998. Patterns and dynamics of 32P-phosphate and labelled 2-aminoisobutyric acid (14C-AIB) translocation in intact basidiomycete mycelia. FEMS Microbiol. Ecol. 26, 109–120.CrossRefGoogle Scholar
  58. Othmer, H.G., Stevens, A., 1997. Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks. SIAM J. Appl. Math. 57, 1044–1081.zbMATHCrossRefMathSciNetGoogle Scholar
  59. Otten, W., Hall, D., Harris, K., Ritz, K., Young, I.M., Gilligan, C.A., 2001. Soil physics, fungal epidemiology and the spread of Rhizoctonia solani. New Phytol. 151, 459–468.CrossRefGoogle Scholar
  60. Paul, E.A., Clark, F.E., 1989. Soil Microbiology and Biochemistry, Academic Press, San Diego.Google Scholar
  61. Persson, C., Olsson, S., Jansson, H.-B., 2000. Growth of Arthrobotrys superba from a birch wood food base into soil determined by radioactive tracing. FEMS Microbiol. Ecol. 31, 47–51.CrossRefGoogle Scholar
  62. Plank, M.J., Sleeman, B. 2004. Lattice and non-lattice models for tumour angiogenesis. Bull. Math. Biol. 66, 1785–1819.CrossRefMathSciNetGoogle Scholar
  63. Rayner, A.D.M., Franks, N.R., 1987. Evolutionary and ecological parallels between ants and fungi. Trends Ecol. Evol. 2, 127–132.CrossRefGoogle Scholar
  64. Rayner, A.D.M., Watkins, Z.R., Beeching, J.R., 1999. Self-integration—an emerging concept from the fungal mycelium. In: Gow, N.A.R., Robson, G.D., Gadd, G.M. (Eds.), The Fungal Colony, Cambridge University Press, Cambridge, pp. 1–24.Google Scholar
  65. Regalado, C.M., Crawford, J.W., Ritz, K., Sleeman, B.D., 1996. The origins of spatial heterogeneity in vegetative mycelia: A reaction-diffusion model. Mycol. Res. 100, 1473-1480.CrossRefGoogle Scholar
  66. Ritz, K., 1995. Growth responses of some soil fungi to spatially heterogeneous nutrients. FEMS Microbiol. Ecol. 16, 269–280.CrossRefGoogle Scholar
  67. Ritz, K., Crawford, J.W., 1990. Quantification of the fractal nature of colonies of Trichoderma viride. Mycol. Res. 94, 1138–1141.Google Scholar
  68. Ritz, K., Crawford, J.W., 1999. Colony development in nutritionally heterogeneous environments. In: Gow, N.A.R., Robson, G.D., Gadd, G.M. (Eds.), The Fungal Colony, Cambridge University Press, Cambridge, pp. 49–74.Google Scholar
  69. Sampson, K., Lew, R.R., Heath, I.B., 2003. Time series analysis demonstrates the absence of pulsatile hyphal growth. Microbiology 149, 3111–3119.CrossRefGoogle Scholar
  70. Sayer, J.A., Gadd, G.M., 1997. Solubilization and transformation of insoluble metal compounds to insoluble metal oxalates by Aspergillus niger. Mycol. Res. 101, 653–661.CrossRefGoogle Scholar
  71. Sayer, J.A., Raggett, S.L., Gadd, G.M., 1995. Solubilization of insoluble metal compounds by soil fungi: Development of a screening method for solubilizing ability and metal tolerance. Mycol. Res. 99, 987–993.Google Scholar
  72. Schack-Kirchner, H., Wilpert, K.V., Hildebrand, E.E., 2000. The spatial distribution of soil hyphae in structured spruce-forest soils. Plant Soil 224, 195–205.CrossRefGoogle Scholar
  73. Soddell, F., Seviour, R., Soddell, J., 1995. Using Lindenmayer systems to investigate how filamentous fungi may produce round colonies. Complexity International 2. Available online: Scholar
  74. Stauffer, D., 1985. Introduction to percolation theory, Taylor & Francis Ltd, London.zbMATHGoogle Scholar
  75. Sun, S., Wheeler, M.F., Obeyesekere, M., Patrick, C.W., 2005. A deterministic model of growth factor-induced angiogenesis. Bull. Math. Biol. 67, 313–337.CrossRefMathSciNetGoogle Scholar
  76. Thornton, C.R., Gilligan, C.A., 1999. Quantification of the effect of the hyperparasite Trichoderma harzianum on the saprotrophic growth dynamics of Rhizoctonia solani in compost using a monoclonal antibody-based ELISA. Mycol. Res. 103, 443–448.CrossRefGoogle Scholar
  77. Tisdall, J.M., 1994. Possible role of soil-microorganisms in aggregation in soils. Plant Soil 159, 115–121.Google Scholar
  78. Webster, J., 1980. Introduction to Fungi, (2nd ed.). Cambridge University Press, Cambridge.Google Scholar
  79. Whipps, J.M., 2001. Microbial interactions and biocontrol in the rhizosphere. J. Exp. Bot. 52, 487–511.Google Scholar
  80. Zheng, X., Wise, S.M., Cristini, V., 2005. Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull. Math. Biol. 67, 211–259.CrossRefMathSciNetGoogle Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • Graeme P. Boswell
    • 1
    • 4
    Email author
  • Helen Jacobs
    • 2
  • Karl Ritz
    • 3
    • 5
  • Geoffrey M. Gadd
    • 2
  • Fordyce A. Davidson
    • 1
  1. 1.Department of MathematicsUniversity of DundeeDundeeUK
  2. 2.Division of Environmental and Applied Biology, Biological Sciences Institute, School of Life SciencesUniversity of DundeeDundeeUK
  3. 3.Soil-Plant Dynamics GroupScottish Crop Research Institute, InvergowrieDundeeUK
  4. 4.Division of Mathematics and Statistics, School of TechnologyUniversity of GlamorganPontypriddUK
  5. 5.National Soil Resources InstituteCranfield UniversitySilsoeUK

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