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

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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.

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References

  • Aerts R, Chapin FS (2000) The mineral nutrition of wild plants revisted: a reevaluation of processes and patterns. Adv Ecol Res 30:1–67

    Article  Google Scholar 

  • 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 166:869–880

    Article  Google Scholar 

  • Alsweis M, Deussen O (2005) Modeling and visualization of symmetric and asymmetric plant competition. Eurographics workshop on natural phenomena, pp 83–88

  • 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 35–48

  • AMAP website, http://amap.cirad.fr. April 2008

  • Berryman A (2002) Population: a central concept for ecology? Oikos 97(3):439–442

    Article  MathSciNet  Google Scholar 

  • 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 85:869–886

    Article  Google Scholar 

  • Bornhofen S, Lattaud C (2006a) Evolutionary design of virtual plants. In: Proceedings of CGVR. Las Vegas, USA, pp 28–34

  • 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 808–817

  • Bornhofen S, Lattaud C (2007) Evolution of virtual plants interacting with their environment. In: Proceedings of VRIC. Laval, France, pp 172–176

  • 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)

  • Boullard B (1999) Guerre et paix dans le règne végétal. Edition Ellipse

  • 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 75–89

    Chapter  Google Scholar 

  • Chomsky N (1957) Syntactic structures. Mouton, The Hague

    Google Scholar 

  • Colasanti RL, Hunt R (1997) Resource dynamics and plant growth: a self-assembling model for individuals, populations and communities. Funct Ecol 11(2):133–145

    Article  Google Scholar 

  • 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):676–687

    Article  Google Scholar 

  • 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 38:77–95

    Article  Google Scholar 

  • Cousens R, Mortimer M (1995) Dynamics of weed populations. Cambridge University Press, New York

    Google Scholar 

  • Damer B, Marcelo K, Revi F (1998) Nerve garden: a public terrarium in cyberspace. In: Heudin JC (ed) Virtual worlds. Springer-Verlag, Berlin, pp 177–185

    Chapter  Google Scholar 

  • 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, Paris

    Google Scholar 

  • Darwin C (1859) On the origin of species. John Murray, London

    Google Scholar 

  • Davidson RL (1969) Effect of root/leaf temperature differentials on root/shoot ratios in some pasture grasses and clover. Ann Bot 33:561–569

    Google Scholar 

  • Dawkins R (1986) The blind watchmaker. WW Norton, New York

    Google Scholar 

  • Dawkins R, Krebs JR (1979) Arms races between and within species. Proc R Soc Lond 205:489–511

    Article  Google Scholar 

  • Deleuze C, Houllier F (1997) A transport model for tree ring width. Silva Fenn 31:239–250

    Google Scholar 

  • De Reffye Ph, Edelin C, Francon J, Jaeger M, Puech C (1988) Plant models faithful to botanical structure and development. Comput Graph 22:151–158

    Article  Google Scholar 

  • Deussen O, Hanrahan P, Lintermann B, Mech R, Pharr M, Prusinkiewicz P (1998) Realistic modeling and rendering of plant ecosystems. Proc SIGGRAPH 98:275–286

    Google Scholar 

  • 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 228–237

  • 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 316–325

  • Edelstein-Keshet L (1988) Mathematical models in biology. Random House, New York

    MATH  Google Scholar 

  • Escuela G, Ochoa G, Krasnogor N (2005) Evolving L-systems to capture protein structure native conformations. LNCS 3447:73–83

    Google Scholar 

  • Ferber J (1995) Les systèmes multi-agents. InterEdition, Paris.

  • Fick A (1855) Über diffusion. Ann Phys (Leipzig) 170:59–86

    Google Scholar 

  • Filleur S, Walch-Liu P, Gan Y, Forde BG (2005) Nitrate and glutamate sensing by plant roots. Biochem Soc Trans 33:283–286

    Article  Google Scholar 

  • Firbank LG, Watkinson AR (1985) A model of interference within plant monocultures. J Theor Biol 166:291–311

    Article  Google Scholar 

  • Firn R (1994) Phototropism. In: Kendrick RE, Kronenberg GHM (eds) Photomorphogensis in plants. Kluwer Academic Publishers, Dordrecht, pp 659–681

    Google Scholar 

  • FVS website, http://www.fs.fed.us/fmsc/fvs. April 2008

  • FSPM07 (5th International Workshop on Functional Structural Plant Models) website, http://algorithmicbotany.org/FSPM07. April 2008

  • Gause GF (1934) The struggle for existence. Williams and Wilkins, Baltimore

    Google Scholar 

  • Génard M, Pagès L, Kervella J (1998) A carbon balance model of peach tree growth and development for studying the pruning response. Tree Physiol 18:351–362

    Google Scholar 

  • Gherini SA, Mok L, Hudson JM, Davis GF, Chen CW, Goldstein RA (1985) The ILWAS model: formulation and application. Water Air Soil Pollut 26:425–460

    Google Scholar 

  • Godin C (2000) Representing and encoding plant architecture: a review. Ann For Sci 57:413–438

    Article  Google Scholar 

  • Godin C, Carglio Y (1998) A multiscale model of plant topological structures. J Theor Biol 191:1–46

    Article  Google Scholar 

  • Godin C, Sinoquet H (2005) Functional–structural plant modelling. New Phytol 166:705–708

    Article  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley

  • 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 115:129–148

    Article  Google Scholar 

  • Grimm V, Railsback SF (2005) Individual-based modeling and ecology. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Grossman YL, DeJong TM (1994) PEACH: a simulation model of reproductive and vegetative growth in peach trees. Tree Physiol 14:329–345

    Google Scholar 

  • Hallé F (1999) Eloge de la plante. Pour une nouvelle biologie. Editions du Seuil, Paris

    Google Scholar 

  • Harper JL, Rosen BR, White J (1986) The growth and form of modular organisms. The Royal Society, London

    Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • 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 31:331–338

    Article  Google Scholar 

  • Hornby GS, Pollack JB (2001) Evolving L-systems to generate virtual creatures. Comput Graph 25(6):1041–1048

    Article  Google Scholar 

  • 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 334–343

  • 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 42–51

  • 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 107–115

  • Katok A, Hasselblatt B (1995) Introduction to the modern theory of dynamical systems. Cambridge University Press, New York

    MATH  Google Scholar 

  • 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 433–442

  • Kurth W (1994a) Morphological models of plant growth: possibilities and ecological relevance. Ecol Modell 75–76:299–308

    Article  Google Scholar 

  • 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 192

  • Lacointe A (2000) Carbon allocation among tree organs: a review of basic processes and representation in functional–structural models. Ann For Sci 57:521–534

    Article  Google Scholar 

  • Landsberg JJ, Gower ST (1997) Applications of physiological ecology to forest management. Academic Press, London

    Google Scholar 

  • Lane B, Prusinkiewicz P (2002) Generating spatial distributions for multilevel models of plant communities. In: Proceedings of graphics interface, pp 69–80

  • 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 31:313–328

    Google Scholar 

  • Le Roux X, Lacointe A, Escobar-Gutiérrez A, LeDizès S (2001) Carbon-based models of individual tree growth: a critical appraisal. Ann For Sci 58:469–506

    Article  Google Scholar 

  • LIAP5 website, http://www.math-info.univ-paris5.fr/alife. April 2008

  • Lindenmayer A (1968) Mathematical models for cellular interaction in development, I and II. J Theor Biol 18:280–315

    Article  Google Scholar 

  • 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 150:279–291

    Article  Google Scholar 

  • 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 Biology

  • Marschner H (1995) Mineral nutrition of higher plants, Second edn. Academic Press, London

    Google Scholar 

  • 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 397–410

  • Mercer L, Prusinkiewicz P, Hanan J (1990) The concept and design of a Virtual Laboratory. In: Proceedings of graphics interface, pp 149–155

  • Mock KJ (1998) Wildwood: the evolution of L-system plants for virtual environments. In: International conference on evolutionary computation. Anchorage, AK, pp 476–480

  • Münch E (1930) Die Stoffbewegungen in der Pflanze. Gustav Fischer, Jena

    Google Scholar 

  • Niklas KJ (1986) Computer-simulated plant evolution. Sci Am 254:68–75

    Article  Google Scholar 

  • Ochoa G (1998) On genetic algorithms and Lindenmayer systems. In: Parallel problem solving from nature—PPSN V. Berlin, pp 335–344

  • OGRE website, http://www.ogre3d.org. April 2008

  • ODE website, http://www.ode.org. April 2008

  • 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 57:513–520

    Article  Google Scholar 

  • 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 6:275–288

    Article  Google Scholar 

  • Peng C (2000) Growth and yield models for uneven-aged stands: past, present and future. For Ecol Manag 132:259–279

    Article  Google Scholar 

  • Perttunen J, Sievänen R, Nikinmaa E, Salminen H, Saarenmaa H, Väkevä J (1996) LIGNUM: a tree model based on simple structural units. Ann Bot 77:87–98

    Article  Google Scholar 

  • Perttunen J, Sievänen R, Nikinmaa E (1998) LIGNUM: a model combining the structure and functioning of trees. Ecol Modell 108:189–198

    Article  Google Scholar 

  • 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 88:471–481

    Article  Google Scholar 

  • Pigliucci M (2001) Phenotypic plasticity: beyond nature and nurture. The John Hopkins University Press, Baltimore

    Google Scholar 

  • Prusinkiewicz P (1998) Modeling of spatial structure and development of plants: a review. Sci Hortic 74:113–149

    Article  Google Scholar 

  • Prusinkiewicz P, Hanan JS (1989) Lindenmayer systems, fractals and plants. Lecture notes in biomathematics. Springer-Verlag, New York

    Google Scholar 

  • Prusinkiewicz P, Lindenmayer A (1990) The algorithmic beauty of plants. Springer-Verlag, Berlin

    MATH  Google Scholar 

  • 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 535–597

    Google Scholar 

  • Radosevich SR, Holt J, Ghersa CM (1997) Weed ecology, implications for management. Wiley, New York

    Google Scholar 

  • 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 7:255–281

    Google Scholar 

  • Ricklefs R (1990) Ecology, 3rd edn. Freeman, New York

    Google Scholar 

  • Room P, Hanan J, Prusinkiewicz P (1996) Virtual plants: new perspectives for ecologists, pathologists and agricultural scientists. Trends Plant Sci 1:33–38

    Article  Google Scholar 

  • Schwinning S, Weiner J (1998) Mechanisms determining the degree of size-asymmetry in competition among plants. Oecologia 113:447–455

    Article  Google Scholar 

  • 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 14:97–105

    Google Scholar 

  • Sievanen R, Makela A, Nikinmaa E (1997) Preface to the collection of papers on functional–structural tree models. Silva Fenn 31(3):237–238

    Google Scholar 

  • Sievanen R, Nikinmaa E, Nygren P, Ozier-Lafontaine H, Perttunen J, Hakula H (2000) Components of functional–structural tree models. Ann For Sci 57:399–412

    Article  Google Scholar 

  • Sims K (1991) Artificial evolution for computer graphics. Comput Graph 25(4):319–328. ACM SIGGRAPH ‘91 conference proceedings. Las Vegas, Nevada

    Google Scholar 

  • 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 21:347–360

    Article  Google Scholar 

  • Stearns SC (1992) The evolution of life histories. Oxford University Press, UK

    Google Scholar 

  • 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, Switzerland

  • Thornley JHM (1972a) A model to describe the partitioning of photosynthate during vegetative plant growth. Ann Bot 36:419–430

    Google Scholar 

  • Thornley JHM (1972b) A balanced quantitative model for root:shoot ratios in vegetative plants. Ann Bot 36:431–441

    Google Scholar 

  • Thornley JHM (1998) Modelling shoot:root relations: the only way forward? Ann Bot 81:165–171

    Article  Google Scholar 

  • Tilman GD (1984) Plant dominance along an experimental nutrient gradient. Ecology 65:1445–1453

    Article  Google Scholar 

  • 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 215–224

  • Vanclay JK (1994) Modelling forest growth and yield: applications to mixed tropical forests. CAB International, UK

    Google Scholar 

  • Van Dyck M (2001) Keyword reference guide for the forest vegetation simulator. . WO-TM Service Center, USDA Forest Service, Fort Collins

    Google Scholar 

  • Van Valen L (1973) A new evolutionary law. Evol Theory 1:1–30

    Google Scholar 

  • Verhulst PF (1838) Notice sur la loi que la population suit dans son accroissement. Corr Math Phys 10:113–121

    Google Scholar 

  • Volterra V (1926) Fluctuations in the abundance of a species considered mathematically. Nature 118:558–560

    Article  MATH  Google Scholar 

  • 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 Alto

    Google Scholar 

  • 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 33:125–159

    Article  Google Scholar 

  • Yoda K, Kira T, Ogawa H, Hozumi K (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions. J Biol 14:107–129

    Google Scholar 

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Bornhofen, S., Lattaud, C. Competition and evolution in virtual plant communities: a new modeling approach. Nat Comput 8, 349–385 (2009). https://doi.org/10.1007/s11047-008-9089-5

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