Math. Model. Nat. Phenom.
Volume 6, Number 2, 2011Modelling of plant growth
|Page(s)||54 - 81|
|Published online||11 October 2010|
- M. T. Allen, P. Prusinkiewicz, T. M. DeJong. Using L-systems for modeling source-sink interactions, architecture and physiology of growing tree: The L-Peach model. New Phytologist., 166, 2005, No. 3, 869–880. [CrossRef]
- R. Aratsui. Leonardo was wise: Trees conserve cross-sectional area despite vessel structure. J. Young Investigators, 1, 1998, 1-23.
- J. K. Bailey, R. K. Bangert, J. A. Schweitzer, R. T. Trote. III, S. M. Shuster, T. G. Whitman. Fractal geometry is heritable in trees. Evolution, 58, 2004, No. 9, 2100–2102. [PubMed]
- D. Barthélémy, Y. Caraglio. Plant architecture: A dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny. Annals of Botany, 99, 2007, No. 3, 375–407. [CrossRef] [PubMed]
- F. S. Berezovskava, G. P. Karev, O. S. Kisliuk., R. G. Khlebopros, Y. L. Tsel’niker. A fractal approach to computer-analytical modeling of tree crowns. Trees, 11, 1997, 323–327. [CrossRef]
- N. Bessonov, V. Volpert. Dynamic models of plant growth. Mathematics and Mathematical Modelling. Editions Publibook Universite, Paris, France, 2008.
- L. Breiman. Reflections after refereeing papers for NIPS. In David Wolpert, Ed., The Mathematics of Generalization. Santa Fe Institute Studies in the Sciences of Complexity Volume XX. Addison-Wesley: Reading, MA, 1995.
- J. L. Casti. Would-Be worlds: How simulation is changing the frontiers of science. John Wiley and Sons: New York, NY, 1997.
- J. E. Cohen. Mathematics is biology’s next microscope, only better; Biology is mathematics next physics, only better. Public Library of Science Biology, 2 (2004), No. 12, 2017–2023.
- O. Deussen, B. Lintermann. Digital design of nature: Computer generated plants and organics. New York: Springer-Verlag, 2005.
- A. E. Dimond. Pressure and flow relations in vascular bundles of the tomato plant. Plant Physiology, 41, 1966, 119–131. [CrossRef] [PubMed]
- J. Elkins. The object stares back: On the nature of seeing. Harcourt Brace and Company: San Diego, CA, 1996.
- B. J. Enquist, K. J. Niklas. Global allocation rules for patterns of biomass partitioning in seed plants. Science, 295, 2002, No. 5559, 1517–1520. [CrossRef] [PubMed]
- B. Enquist, J. Sperry, P. Reich, V. Savage. Combining theories for plant architecture, allometry, and traits to develop the next generation of scaling theory. NSF Emerging Frontiers Award #0742800. Start Date: December 1, 2007 - Expires: November 30, 2010 (Estimated); NSF Program: THEORETICAL BIOLOGY, 2007.
- FSPM07. Fifth international workshop on functional structural plant models. Napier, New Zealand, 4–9 November, 2007.
- J. Fisher, H. Honda. Branch geometry and effective leaf area: A study of Terminalia-branching pattern: Theoretical ideas. American J. Botany, 66, 1979, 633–644. [CrossRef]
- C. Godin, O. Puech, F. Boudon, H. Sinoquet. Space occupation by tree crowns obey fractal laws: Evidence from 3D digitized plants. In Godin, C. Hanan, J. Kurth, W. Lacointe, A. Takenaka, A. Prusinkiewicz, P. DeJong, T. M. Beveridge, C. Andrieu, B., Eds. Proceedings of Proceedings of the 4th International Workshop on Functional-Structural Plant Models. Montpellier, 2004, 79–83. Proceedings of the 4th International Workshop on Functional-Structural Plant Models, 7-11/06/2004, Montpellier.
- C. Godin, E. Costes, H. Sinoquet. A method for describing plant architecture which integrates topology and geometry. Annals of Botany, 84, 2004, 343–357. [CrossRef]
- Y. Grossman, T. De Jong, Peach. In Jungck , Eds., The BioQUEST Library, Academic Press: San Diego, 2003.
- M. Hiratsuka, T. Toma, M. Yamada, I. Heriansyah, Y. Morikawa. A general allometric equation for estimating biomass in Acacia mangium plantations. In Proceedings of the 2003 International Conference on Tropical Forests and Climate Change, University of the Philippines Los Banos, Laguna, Philippines 2003, 212–218.
- P. Hogeweg, B. Hesper. A model study on biomorphological description. Pattern Recognition, 6, 1974, 165–179. [CrossRef]
- H. Honda. Description of the form of trees by the parameters of a tree-like body: Effects of the branching angle and branch length on the shape of the tree-like body. J. Theoretical Biology, 31, 1971, 331–338. [CrossRef]
- H. S. Horn. Adaptive geometry of trees. Princeton University Press: Princeton, NY, 1971.
- J. R. Jungck. Ten equations that changed biology. Bioscene: Journal of College Biology Teaching, 23, 1997, No. 1, 11–36.
- J. R. Jungck, E. D. Stanley, S. J. Everse, V. Vaughan, Eds. The BioQUEST Library. Academic Press: North Reading, MA, 2003.
- J. R. Jungck. The biological ESTEEM collection: Excel simulations and tools for exploratory, experiential mathematics. BioQUEST Notes, 14, 2005, No. 1, 1–2.
- J. R. Jungck. Challenges, connections, complexities: Educating for collaboration. Chapter in Lynn Steen, Ed., Math & Bio2010: Linking Undergraduate Disciplines. The Mathematical Association of America: Washington, DC., 2005, 1–12.
- J. R. Jungck. Fostering figuring and fascination: Engaging learners through alternative aesthetics. In J. R. Jungck, Er. Mazur, Wi. Schmidt, T. Schuller, Eds., Criticism of Contemporary Issues: Education. Serralves Museum of Art, Fundacao Serralves: Porto, Portugal, 2008, 19–54 and 93–126.
- C. E. Knapp. Review of Last child in the woods: Saving our children from nature-deficit disorder (Revised edition), by Richard Louv. 2008. Chapel Hill, NC: Algonquin Books. 390 pages. Paperback. $14.95. ISBN13: 978-1-56512-605-3. Journal of Environmental Education, 40 2009, No. 2, 63–64.
- A. Lindenmayer. Developmental systems without cellular interaction, their languages and grammars. J. Theoretical Biology, 30, 1971, 455–484. [CrossRef]
- A. Lindenmayer. Developmental systems and languages in their biological context. In G. T. Herman & G. Rozenberg, Eds., Developmental systems and languages. Amsterdam: North-Holland Publishing, 1975, 1–40. 0-7204-2806-8
- A. Lindenmayer. Growing fractals and plants. In Heinz-Otto Peitgen, Hartmut Jürgens and Dietmar Saupe, Eds. Chaos and Fractals, Second Edition. New Frontiers of Science. Springer: New York, 2004, 329–376. ISBN 978-0-387-20229-7
- R. Louv. A brief history of the children & nature movement. J. Sci. Educ. Technol, 17, 2008, 217–218. [CrossRef]
- B. Mandelbrot. Fractals: Form, chance and dimension. W. H. Freeman and Co.: San Francisco, 1977.
- K. A. McCulloh, J. S. Sperry, R. F. Adler. Water transport in plants obey Murray’s law. Nature, 401, 2003, 939. [CrossRef] [PubMed]
- K. A. McCulloh, J. S. Sperry, R. F. Adler. Murray’s law and the hydraulic vs mechanical functioning of wood. Functional Ecology, 18, 2004, 931. [CrossRef]
- M. Mesterton-Gibbons, M. J. Childress. Constraints on reciprocity for non-sessile organisms. Bulletin of Mathematical Biology, 58, 1996, No. 5, 861–875. [CrossRef]
- National Research Council. Bio 2010: Transforming undergraduate education for future research biology. National Academies Press: Washington, DC, 2003.
- K. J. Niklas. Computer simulations of branching-patterns and their implications on the evolution of plants. In L. J. Gross, R. M. Miura, Eds. Some Mathematical Questions in Biology: Plant Biology, Lectures on Mathematics in the Life Sciences, 18, 1986, 1–50 (American Mathematical Society).
- K. J. Niklas. Evolutionary walks through a land plant morphoscape. J. Experimental Botany, 50, 1999, No. 330, 39–52. [CrossRef]
- K. J. Niklas, E. D. Cobb. Evidence for “diminishing returns” from the scaling of stem diameter and specific leaf area. Am. J. Botany, 95, 2008, 549–557. [CrossRef]
- K. Ogle, S. W. Pacala. A modeling framework for inferring tree growth and allocation from physiological, morphological and allometric traits. Tree Physiol., 29, 2009, 587–605. [CrossRef] [PubMed]
- R. W. Pearcy, H. Muraoka, F. Valladares. Crown architecture in sun and shade environments: Assessing function and trade-offs with a three-dimensional simulation model. New Phytologist, 166, 2005, No. 3, 791–800. [CrossRef]
- C. A. Price, B. J. Enquist, V. M. Savage. A general model for allometric covariation in botanical form and function. PNAS, 104, 2007, 13204–13209. [CrossRef]
- P. Przemyslaw, J. Hanan. Lindenmayer systems, fractals, and plants. Lecture Notes in Biomathematics, volume 79. Springer-Verlag, New York, 1989.
- P. Prusinkiewicz, A. Lindenmayer. The algorithmic beauty of plants. New York: Springer-Verlag, 1990. (Available on-line in high quality pdf at (http://algorithmicbotany.org/papers/#abop)).
- P. Prusinkiewicz, Y. Erasmus, B. Lane, L. D. Harder, E. Coen. Evolution and development of inflorescence architectures. Science, 316, 2007, No. 5830, 1452–1456. [CrossRef] [PubMed]
- D. M. Raup. Computer as aid in describing form in gastropod shells. Science, 138, 1962, 150–152. [CrossRef] [PubMed]
- P. de Reffye. Computer simulation of plant growth. In Clifford A. Pickover and Stuart K. Tewksbury, Eds. Frontiers of scientific visualization. John Wiley & Sons, Inc.: New York, NY, USA, 1994, 145–179.
- D. Robinson. Implications of a large global root biomass for carbon sink estimates and for soil carbon dynamics. Proc. R. Soc. B, 274, 2007, 2753–2759. [CrossRef]
- A. Szalay, J. Gray. 2020 computing: Science in an exponential world. Nature, 440, 2006, 413–414. [CrossRef] [PubMed]
- R. Sattler, R. Rutishauser. The fundamental relevance of morphology and morphogenesis to plant research. Annals of Botany, 80, 1997, 571–582. [CrossRef]
- Seits, I.S. Antonova. Applying multidimensional statistics to tree architecture analysis. In Godin, C. Hanan, J. Kurth, W. Lacointe, A. Takenaka, A. Prusinkiewicz, P. DeJong, T. M.Beveridge, C. Andrieu, B., Eds. Proceedings of Proceedings of the 4th International Workshop on Functional-Structural Plant Models. Montpellier, 2004, 70–74. Proceedings of the 4th International Workshop on Functional-Structural Plant Models, 7–11/06/2004, Montpellier.
- I. Shlyakhter, M. Rozenoer, J. Dorsey, S. Teller. Reconstructing 3D tree models from instrumented photographs. IEEE Computer Graphics and Animations, xx, 2001, 1–9.
- S. Wegrzyn, J.-C. Gille, P. Vidal. Developmental systems: At the crossroads of system theory, computer science, and genetic engineering. Springer-Verlag: New York, 1990.
- A. Weisstein, Ed. The Biological ESTEEM project (Excel simulations and tools for exploratory, experiential mathematics), 2009. (< http//bioquest.org/esteem >).
- D. Willis, The sand dollar and the slide rule. Addison-Wesley Publishing Co.: North Reading, MA, 232 pp, 1995. ISBN 0-201-63275-6 $23 ($27 postpaid) from
- W. Wimsatt. False models as means to truer theories. Chapter 6 in his book:Re-engineering philosophy for limited beings: Piecewise approximations to reality. Harvard University Press: Cambridge, MA, 2007.
- M. S. Zens, C. O. Webb. Sizing up the shape of life. Science, 295, 2002, No. 5559, 1475. [CrossRef] [PubMed]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.