Natural Computing

, Volume 8, Issue 2, pp 349–385 | Cite as

Competition and evolution in virtual plant communities: a new modeling approach

  • Stefan BornhofenEmail author
  • Claude Lattaud


This article presents studies on plants and their communities through experiments with a multi-agent platform of generic virtual plants. Based on Artificial Life concepts, the model has been designed for long-term simulations spanning a large number of generations while emphasizing the most important morphological and physiological aspects of a single plant. The virtual plants combine a physiological transport-resistance model with a morphological model using the L-system formalism and grow in a simplified 3D artificial ecosystem. Experiments at three different scales are carried out and compared to observations on real plant species. At the individual level, single virtual plants are grown in order to examine their responses to environmental constraints. A number of emerging characteristics concerning individual plant growth can be observed. Unifying field observation, mathematical theory and computer simulation, population level experiments on intraspecific and interspecific competition for resources are related to corresponding aggregate models of population dynamics. The latter provide a more general understanding of the experiments with respect to long-term trends and equilibrium conditions. Studies at the evolutionary level aim at morphogenesis and the influence of competition on plant morphology. Among other results, it is shown how the struggle for resources induces an arms race that leads to the evolution of elongated growth in contrast to rather ample forms at ground-level when the plants evolve in isolation.


Artificial evolution Artificial life Multi-agent system Plant modeling Population dynamics 


  1. Aerts R, Chapin FS (2000) The mineral nutrition of wild plants revisted: a reevaluation of processes and patterns. Adv Ecol Res 30:1–67CrossRefGoogle Scholar
  2. Allen M, Prusinkiewicz P, DeJong T (2005) Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. New Phytol 166:869–880CrossRefGoogle Scholar
  3. Alsweis M, Deussen O (2005) Modeling and visualization of symmetric and asymmetric plant competition. Eurographics workshop on natural phenomena, pp 83–88Google Scholar
  4. Alsweis M, Deussen O (2006) Efficient simulation of vegetation using light and nutrition competition. In: Proceedings of the 17th conference on simulation and visualization, pp 35–48Google Scholar
  5. AMAP website, April 2008
  6. Berryman A (2002) Population: a central concept for ecology? Oikos 97(3):439–442CrossRefMathSciNetGoogle Scholar
  7. Bidel LPR, Pagès L, Rivière LM, Pelloux G, Lorendeau JY (2000) MassFlowDyn I: a carbon transport and partitioning model for root system architecture. Ann Bot 85:869–886CrossRefGoogle Scholar
  8. Bornhofen S, Lattaud C (2006a) Evolutionary design of virtual plants. In: Proceedings of CGVR. Las Vegas, USA, pp 28–34Google Scholar
  9. Bornhofen S, Lattaud C (2006b) Life history evolution of virtual plants: trading off between growth and reproduction. In: Proceedings of PPSN IX. Reykjavik, Iceland, pp 808–817Google Scholar
  10. Bornhofen S, Lattaud C (2007) Evolution of virtual plants interacting with their environment. In: Proceedings of VRIC. Laval, France, pp 172–176Google Scholar
  11. Bornhofen S, Lattaud C (2008) On hopeful monsters, neutral networks and junk code in evolving L-systems. In: Proceedings of GECCO. Atlanta, USA (to be published)Google Scholar
  12. Boullard B (1999) Guerre et paix dans le règne végétal. Edition EllipseGoogle Scholar
  13. Chelle M, Andrieu B (2007) Modelling the light environment of virtual crop canopies. In: Vos J, Marcelis LFM, de Visser PHB, Struik PC, Evers JB (eds) Functional–structural plant modelling in crop production. Springer, Netherlands, pp 75–89CrossRefGoogle Scholar
  14. Chomsky N (1957) Syntactic structures. Mouton, The HagueGoogle Scholar
  15. Colasanti RL, Hunt R (1997) Resource dynamics and plant growth: a self-assembling model for individuals, populations and communities. Funct Ecol 11(2):133–145CrossRefGoogle Scholar
  16. Colasanti RL, Hunt R, Askew AP (2001) A self-assembling model of resource dynamics and plant growth incorporating plant functional types. Funct Ecol 15(5):676–687CrossRefGoogle Scholar
  17. Cosby BJ, Hornberger GM, Rastetter EB, Galloway JN, Wright RF (1986) Estimating catchment water quality response to acid deposition using mathematical models of soil ion exchange processes. Geoderma 38:77–95CrossRefGoogle Scholar
  18. Cousens R, Mortimer M (1995) Dynamics of weed populations. Cambridge University Press, New YorkGoogle Scholar
  19. Damer B, Marcelo K, Revi F (1998) Nerve garden: a public terrarium in cyberspace. In: Heudin JC (ed) Virtual worlds. Springer-Verlag, Berlin, pp 177–185CrossRefGoogle Scholar
  20. Dansereau P (1992) Repères pour une éthique de l’environnement avec une méditation sur la paix. In: Bélanger R, Plourde S (eds) Actualiser la morale: mélanges offerts à René Simon. Les Éditions Cerf, ParisGoogle Scholar
  21. Darwin C (1859) On the origin of species. John Murray, LondonGoogle Scholar
  22. Davidson RL (1969) Effect of root/leaf temperature differentials on root/shoot ratios in some pasture grasses and clover. Ann Bot 33:561–569Google Scholar
  23. Dawkins R (1986) The blind watchmaker. WW Norton, New YorkGoogle Scholar
  24. Dawkins R, Krebs JR (1979) Arms races between and within species. Proc R Soc Lond 205:489–511CrossRefGoogle Scholar
  25. Deleuze C, Houllier F (1997) A transport model for tree ring width. Silva Fenn 31:239–250Google Scholar
  26. De Reffye Ph, Edelin C, Francon J, Jaeger M, Puech C (1988) Plant models faithful to botanical structure and development. Comput Graph 22:151–158CrossRefGoogle Scholar
  27. Deussen O, Hanrahan P, Lintermann B, Mech R, Pharr M, Prusinkiewicz P (1998) Realistic modeling and rendering of plant ecosystems. Proc SIGGRAPH 98:275–286Google Scholar
  28. Ebner M (2003) Evolution and growth of virtual plants. In Banzhaf W, Christaller T, Dittrich P, Kim JT, Ziegler J (eds) Advances in artificial life—proceedings of the 7th European conference on artificial life (ECAL). Dortmund, Germany, pp 228–237Google Scholar
  29. Ebner M, Grigore A, Heffner A, Albert J (2002) Coevolution produces an arms race among virtual plants. In: Foster JA, Lutton E, Miller J, Ryan C, Tettamanzi AGB (eds) Proceedings of the fifth European conference on genetic programming (EuroGP 2002). Kinsale, Ireland, pp 316–325Google Scholar
  30. Edelstein-Keshet L (1988) Mathematical models in biology. Random House, New YorkzbMATHGoogle Scholar
  31. Escuela G, Ochoa G, Krasnogor N (2005) Evolving L-systems to capture protein structure native conformations. LNCS 3447:73–83Google Scholar
  32. Ferber J (1995) Les systèmes multi-agents. InterEdition, Paris.Google Scholar
  33. Fick A (1855) Über diffusion. Ann Phys (Leipzig) 170:59–86Google Scholar
  34. Filleur S, Walch-Liu P, Gan Y, Forde BG (2005) Nitrate and glutamate sensing by plant roots. Biochem Soc Trans 33:283–286CrossRefGoogle Scholar
  35. Firbank LG, Watkinson AR (1985) A model of interference within plant monocultures. J Theor Biol 166:291–311CrossRefGoogle Scholar
  36. Firn R (1994) Phototropism. In: Kendrick RE, Kronenberg GHM (eds) Photomorphogensis in plants. Kluwer Academic Publishers, Dordrecht, pp 659–681Google Scholar
  37. FVS website, April 2008
  38. FSPM07 (5th International Workshop on Functional Structural Plant Models) website, April 2008
  39. Gause GF (1934) The struggle for existence. Williams and Wilkins, BaltimoreGoogle Scholar
  40. Génard M, Pagès L, Kervella J (1998) A carbon balance model of peach tree growth and development for studying the pruning response. Tree Physiol 18:351–362Google Scholar
  41. Gherini SA, Mok L, Hudson JM, Davis GF, Chen CW, Goldstein RA (1985) The ILWAS model: formulation and application. Water Air Soil Pollut 26:425–460Google Scholar
  42. Godin C (2000) Representing and encoding plant architecture: a review. Ann For Sci 57:413–438CrossRefGoogle Scholar
  43. Godin C, Carglio Y (1998) A multiscale model of plant topological structures. J Theor Biol 191:1–46CrossRefGoogle Scholar
  44. Godin C, Sinoquet H (2005) Functional–structural plant modelling. New Phytol 166:705–708CrossRefGoogle Scholar
  45. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-WesleyGoogle Scholar
  46. Grimm V (1999) Ten years of individual-based modelling in ecology: what we have learned and what could we learn in the future? Ecol Modell 115:129–148CrossRefGoogle Scholar
  47. Grimm V, Railsback SF (2005) Individual-based modeling and ecology. Princeton University Press, PrincetonzbMATHGoogle Scholar
  48. Grossman YL, DeJong TM (1994) PEACH: a simulation model of reproductive and vegetative growth in peach trees. Tree Physiol 14:329–345Google Scholar
  49. Hallé F (1999) Eloge de la plante. Pour une nouvelle biologie. Editions du Seuil, ParisGoogle Scholar
  50. Harper JL, Rosen BR, White J (1986) The growth and form of modular organisms. The Royal Society, LondonGoogle Scholar
  51. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann ArborGoogle Scholar
  52. Honda H (1971) Description of the form of trees by the parameters of the tree-like body: effects of the branching angle and the branch length on the shape of the tree-like body. J Theor Biol 31:331–338CrossRefGoogle Scholar
  53. Hornby GS, Pollack JB (2001) Evolving L-systems to generate virtual creatures. Comput Graph 25(6):1041–1048CrossRefGoogle Scholar
  54. Jacob C (1994) Genetic L-system programming. In: Davudor Y, Schwefel HP, Maenner R (eds) PPSN III. The 3rd international conference on evolutionary computation. Jerusalem, Israel, Berlin, pp 334–343Google Scholar
  55. Jacob C (1996a) Evolution programs evolved. In: Voigt HM, Ebeling W, Rechenberg I, Schwefel HP (eds) PPSN IV. The 4th international conference on evolutionary computation. Berlin, Germany, Berlin, pp 42–51Google Scholar
  56. Jacob C (1996b) Evolving evolution programs: genetic programming and L-systems. In: Koza JR, Goldberg DE, Fogel DB, Riolo RL (eds) Proceedings of the 1st annual conference on genetic programming. Cambridge, MA, pp 107–115Google Scholar
  57. Katok A, Hasselblatt B (1995) Introduction to the modern theory of dynamical systems. Cambridge University Press, New YorkzbMATHGoogle Scholar
  58. Kókai G, Tóth Z, Ványi R (1999) Modelling blood vessels of the eye with parametric L-systems using evolutionary algorithms. In: Proc joint European conference on artificial intelligence in medicine and medical decision making, AIMDM’99, LNCS, vol 1620, pp 433–442Google Scholar
  59. Kurth W (1994a) Morphological models of plant growth: possibilities and ecological relevance. Ecol Modell 75–76:299–308CrossRefGoogle Scholar
  60. Kurth W (1994b) Growth grammar interpreter GROGRA 2.4. A software tool for the 3-dimensional interpretation of stochastic, sensitive growth grammars in the context of plant modelling, Introduction and reference manual. In: Berichte des Fortschungszentrums Waldökosysteme, Ser. B38, Göttingen, Germany, p 192Google Scholar
  61. Lacointe A (2000) Carbon allocation among tree organs: a review of basic processes and representation in functional–structural models. Ann For Sci 57:521–534CrossRefGoogle Scholar
  62. Landsberg JJ, Gower ST (1997) Applications of physiological ecology to forest management. Academic Press, LondonGoogle Scholar
  63. Lane B, Prusinkiewicz P (2002) Generating spatial distributions for multilevel models of plant communities. In: Proceedings of graphics interface, pp 69–80Google Scholar
  64. Le Dizès S, Cruiziat P, Lacointe A, Sinoquet H, Le Roux X, Balandier Ph, Jacquet P (1997) A model for simulating structure-function relationships in walnut tree growth processes. Silva Fenn 31:313–328Google Scholar
  65. Le Roux X, Lacointe A, Escobar-Gutiérrez A, LeDizès S (2001) Carbon-based models of individual tree growth: a critical appraisal. Ann For Sci 58:469–506CrossRefGoogle Scholar
  66. Lindenmayer A (1968) Mathematical models for cellular interaction in development, I and II. J Theor Biol 18:280–315CrossRefGoogle Scholar
  67. Lo E, Zhang MW, Lechowicz M, Messier C, Nikinmaa E, Perttunen J (2000) Adaptation of the LIGNUM model simulations of growth and light response in jack pine. For Ecol Manag 150:279–291CrossRefGoogle Scholar
  68. Lotka AJ (1924) Elements of physical biology. Williams and Wilkins, Baltimore, Maryland, USA. Reprinted in 1956 by Dover Publications, New York as Elements of Mathematical BiologyGoogle Scholar
  69. Marschner H (1995) Mineral nutrition of higher plants, Second edn. Academic Press, LondonGoogle Scholar
  70. Mech R, Prusinkiewicz P (1996) Visual models of plants interacting with their environment. In: Proceedings of SIGGRAPH’96 (New Orleans). ACM Press, New York, pp 397–410Google Scholar
  71. Mercer L, Prusinkiewicz P, Hanan J (1990) The concept and design of a Virtual Laboratory. In: Proceedings of graphics interface, pp 149–155Google Scholar
  72. Mock KJ (1998) Wildwood: the evolution of L-system plants for virtual environments. In: International conference on evolutionary computation. Anchorage, AK, pp 476–480Google Scholar
  73. Münch E (1930) Die Stoffbewegungen in der Pflanze. Gustav Fischer, JenaGoogle Scholar
  74. Niklas KJ (1986) Computer-simulated plant evolution. Sci Am 254:68–75CrossRefGoogle Scholar
  75. Ochoa G (1998) On genetic algorithms and Lindenmayer systems. In: Parallel problem solving from nature—PPSN V. Berlin, pp 335–344Google Scholar
  76. OGRE website, April 2008
  77. ODE website, April 2008
  78. Pagès L, Doussan C, Vercambre G (2000) An introduction on below-ground environment and resource acquisition, with special reference on trees. Simulation models should include plant structure and function. Ann For Sci 57:513–520CrossRefGoogle Scholar
  79. Pearl R, Reed LJ (1920) On the rate of growth of the population of United States since 1790 and its mathematical representation. Proc Natl Acad Sci USA 6:275–288CrossRefGoogle Scholar
  80. Peng C (2000) Growth and yield models for uneven-aged stands: past, present and future. For Ecol Manag 132:259–279CrossRefGoogle Scholar
  81. Perttunen J, Sievänen R, Nikinmaa E, Salminen H, Saarenmaa H, Väkevä J (1996) LIGNUM: a tree model based on simple structural units. Ann Bot 77:87–98CrossRefGoogle Scholar
  82. Perttunen J, Sievänen R, Nikinmaa E (1998) LIGNUM: a model combining the structure and functioning of trees. Ecol Modell 108:189–198CrossRefGoogle Scholar
  83. Perttunen J, Nikinmaa E, Lechowicz MJ, Sievänen R, Messier C (2001) Application of the functional–structural tree model LIGNUM to sugar maple saplings (Acer saccharum Marsh) growing in forest gaps. Ann Bot 88:471–481CrossRefGoogle Scholar
  84. Pigliucci M (2001) Phenotypic plasticity: beyond nature and nurture. The John Hopkins University Press, BaltimoreGoogle Scholar
  85. Prusinkiewicz P (1998) Modeling of spatial structure and development of plants: a review. Sci Hortic 74:113–149CrossRefGoogle Scholar
  86. Prusinkiewicz P, Hanan JS (1989) Lindenmayer systems, fractals and plants. Lecture notes in biomathematics. Springer-Verlag, New YorkGoogle Scholar
  87. Prusinkiewicz P, Lindenmayer A (1990) The algorithmic beauty of plants. Springer-Verlag, BerlinzbMATHGoogle Scholar
  88. Prusinkiewicz P, Hammel M, Hanan J, Mech R (1997) Visual models of plant development. In: Rozenberg G, Salomaa A (eds) Handbook of formal languages, vol 3. Springer-Verlag, Berlin, pp 535–597Google Scholar
  89. Radosevich SR, Holt J, Ghersa CM (1997) Weed ecology, implications for management. Wiley, New YorkGoogle Scholar
  90. Rauscher HM, Isebrands JG, Host GE, Dickson RE, Dickmann DI, Crow TR, Michael DA (1990) ECOPHYS: an ecophysiological growth process model for juvenile poplar. Tree Physiol 7:255–281Google Scholar
  91. Ricklefs R (1990) Ecology, 3rd edn. Freeman, New YorkGoogle Scholar
  92. Room P, Hanan J, Prusinkiewicz P (1996) Virtual plants: new perspectives for ecologists, pathologists and agricultural scientists. Trends Plant Sci 1:33–38CrossRefGoogle Scholar
  93. Schwinning S, Weiner J (1998) Mechanisms determining the degree of size-asymmetry in competition among plants. Oecologia 113:447–455CrossRefGoogle Scholar
  94. Shinozaki K, Yoda K, Hozumi K, Kiro T (1964) A quantitative analysis of plant form—the pipe model theory, I. basic analysis. Jpn J Ecol 14:97–105Google Scholar
  95. Sievanen R, Makela A, Nikinmaa E (1997) Preface to the collection of papers on functional–structural tree models. Silva Fenn 31(3):237–238Google Scholar
  96. Sievanen R, Nikinmaa E, Nygren P, Ozier-Lafontaine H, Perttunen J, Hakula H (2000) Components of functional–structural tree models. Ann For Sci 57:399–412CrossRefGoogle Scholar
  97. Sims K (1991) Artificial evolution for computer graphics. Comput Graph 25(4):319–328. ACM SIGGRAPH ‘91 conference proceedings. Las Vegas, NevadaGoogle Scholar
  98. Sperry JS, Adler FR, Campbell GS, Comstock JP (1998) Limitation of plant water use by rhizosphere and xylem conductance: results from a model. Plant Cell Environ 21:347–360CrossRefGoogle Scholar
  99. Stearns SC (1992) The evolution of life histories. Oxford University Press, UKGoogle Scholar
  100. Steinberg D, Sikora S, Lattaud C, Fournier C, Andrieu B (1999) Plant growth simulation in virtual worlds : towards online artificial ecosystems, In: Proceedings of the first workshop on artificial life integration in virtual environment. Lausanne, SwitzerlandGoogle Scholar
  101. Thornley JHM (1972a) A model to describe the partitioning of photosynthate during vegetative plant growth. Ann Bot 36:419–430Google Scholar
  102. Thornley JHM (1972b) A balanced quantitative model for root:shoot ratios in vegetative plants. Ann Bot 36:431–441Google Scholar
  103. Thornley JHM (1998) Modelling shoot:root relations: the only way forward? Ann Bot 81:165–171CrossRefGoogle Scholar
  104. Tilman GD (1984) Plant dominance along an experimental nutrient gradient. Ecology 65:1445–1453CrossRefGoogle Scholar
  105. Ulam S (1962) On some mathematical properties connected with patterns of growth of figures. In: Proceedings of symposia on applied mathematics, vol 14. Am. Math. Soc., pp 215–224Google Scholar
  106. Vanclay JK (1994) Modelling forest growth and yield: applications to mixed tropical forests. CAB International, UKGoogle Scholar
  107. Van Dyck M (2001) Keyword reference guide for the forest vegetation simulator. . WO-TM Service Center, USDA Forest Service, Fort CollinsGoogle Scholar
  108. Van Valen L (1973) A new evolutionary law. Evol Theory 1:1–30Google Scholar
  109. Verhulst PF (1838) Notice sur la loi que la population suit dans son accroissement. Corr Math Phys 10:113–121Google Scholar
  110. Volterra V (1926) Fluctuations in the abundance of a species considered mathematically. Nature 118:558–560zbMATHCrossRefGoogle Scholar
  111. Weinstein DA, Yanai RD, Beloin R, Zollweg CG (1992) The response of plants to interacting stresses: TREGRO Version 1.74—description and parameter requirements. Electric Power Res. Institute, Palo AltoGoogle Scholar
  112. Westoby M, Falster DS, Moles AT, Vesk PA, Wright IJ (2002) Plant ecological strategies: some leading dimensions of variation between species. Annu Rev Ecol Syst 33:125–159CrossRefGoogle Scholar
  113. Yoda K, Kira T, Ogawa H, Hozumi K (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions. J Biol 14:107–129Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Laboratoire d’Intelligence Artificielle de Paris 5 LIAP5Université Paris DescartesParisFrance

Personalised recommendations