Abstract
There is a renaissance in forest modelling due to the application of mathematics and physics. There are some classical theories including pipe model theory, Metzger’s theory, self-thinning rule, Da Vinci’s tree form concept, Logarithmic spiral technique, etc., which have greater significance in forestry science. With advanced computational tools from the IT revolution at disposal, a better understanding of the above-mentioned theories is now possible. In meantime, plants’ architecture and design have been a source of inspiration for biomechanists, as mechanics is an inseparable part of the abiotic realm. It is based on one important principle “all structures, whether engineered or natural, must obey the laws of physics”. Trees grow, adapt and acclimate to maintain their stability. This demands a trade-off between their mechanical stability and other physiological functions. It is also vivid that mechanical forces can manipulate the tree architecture and root architecture and influence thigomorphogensis. For this reason, it is important to understand the impact of mechanical forces on tree growth. Forest modelling can take a leap forward by infusing these theories and biomechanics. The present chapter narrates some of the classical theories in forestry and simultaneously showcases the relevance of these theories based on research work done. Furthermore, it deliberates on the utilization of modelling to provide greater impetus in forest science in order to explore prudent silvicultural practice for enhancing forest productivity and product quality.
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References
Ali, F. (2010). Use of vegetation for slope protection: Root mechanical properties of some tropical plants. International Journal of Physical Sciencies, 5(5), 496–506.
Avani, N., Lateh, H., & Bibalani, G. H. (2015). Root distribution of Acacia mangium Willd. and Macaranga tanarius L. of rainforest. Bangladesh Journal of Botany, 43, 141–145.
Bentley, L. P., Stegen, J. C., Savage, V. M., Smith, D. D., Allmen, E. I., Sperry, J. S., et al. (2013). An empirical assessment of tree branching networks and implications for plant allometric scaling models. Ecological Letters, 16, 1069–1078.
Bézivin, J. (2005). On the unification power of models. Software and Systematic Modelling, 4(2), 171–188.
Bhimappa, K. (2014). Bamboo based agroforestry systems in Kerala, India: performance of turmeric (Curcumalonga L.) in the subcanopy of differentially spaced seven year-old bamboo stand. Agroforestry Systems, 90(2), 237–250.
Bohm, W. (1979). Methods of studying root systems (p. 188p). Berlim: Springer-Verlag.
Boudaoud, A. (2010). An introduction to the mechanics of morphogenesis for plant biologists. Trends in Plant Science, 15, 353–360.
Bronzino, J. D. & Peterson, D. R. (2014). Biomechanics: Principles and practices (pp. 352). CRC Press.
Divakara, B. N., Kumar, B. M., Balachandran and P. V, Kamalam, N. V. (2001). Bamboo hedgerow systems in Kerala, India: Root distribution and competition with trees for phosphorus. Agroforestry Systems, 51, 189–200.
Eloy, C. (2011). Leonardo’s rule, self-similarity, and wind-induced stresses in trees. Physical Review Letters, 107(25), 258101.
Eloy, C., Fournier, M., Lacointe, A., & Moulia, B. (2017). Wind loads and competition for light sculpt trees into self-similar structures. Nature Communications, 8, 1014.
Ennos, A. (1997). Wind as an ecological factor. Trends in Ecology & Evolution, 12, 108–111.
Enquist, B. J., & Niklas, K. J. (2002). Global allocation rules for patterns of biomass partitioning in seed plants. Science, 80(295), 1517–1520.
Fernández, J. E., Moreno, F., Cabrera, F., Arrue, J. L., & Martín-Aranda, J. (1991). Drip irrigation, soil characteristics and the root distribution and root activity of olive trees. Plant and Soil, 133, 239–251.
Fourcaud, T., & Lac, P. (2003). Numerical modelling of shape regulation and growth stresses in trees. Trees, 17, 23–30.
Fourcaud, T., Zhang, X., Stokes, A., Lambers, H., & Körner, C. (2008). Plant growth modelling and applications: the increasing importance of plant architecture in growth models. Annals of Botany, 101, 1053–1063.
Fournier, M., Stokes, A., Coutand, C., Fourcaud, T., & Moulia, B. (2006). Tree biomechanics and growth strategies in the context of forest functional ecology. Ecology and Biomechanics—a mechancial approach to ecology of animals and plants (pp. 1–33). Boca Raton: CRC Press.
Hübner, K., Sahle, S., & Kummer, U. (2011). Applications and trends in systems biology in biochemistry. The FEBS Journal, 278, 2767–2857.
Huguet, J. G. (1973). Nouvelle methode d’etude de l’enracinement des vegetaux perennes a partir d’une trachee spirale. Annales Agronomiques, 24(6), 707–731.
Humphrey, J. D., & O’Rourke, S. L. (2015). An introduction to biomechanics (p. 692). New York: Springer New York.
Jackson, L. J., Trebitz, A. S., & Cottingham, K. L. (2000). An introduction to the practice of ecological modeling. BioScience, 50(8), 694–706.
Jirasek, C., Prusinkiewicz, P., & Moulia, B. (2000). Integrating biomechanics into developmental plant models expressed using L-systems. Plant Biomechanics, 19, 615–624.
King, D., & Loucks, O. L. (1978). The theory of tree bole and branch form. Radiation and Environmental Biophysics, 15, 141–165.
Lanza, A. M., Crook, N. C., & Alper, H. S. (2012). Innovation at the intersection of synthetic and systems biology. Current Opinion in Biotechnology, 23, 712–717.
Lateh, H., Avani, N., & Bibalani, G. H. (2012). Investigation of root distribution and tensile strength of Acaciamangium willd (Fabaceae) in the rainforest. Greener Journal of Biological Sciences, 4, 45–52.
Lateh, H., Avani, N., & Bibalani, H. (2013). Effect of Acaciamangium root properties on shallow landslide and slope stability. Journal of Life Science and Technology, 1, 127–131.
Lockwood, E. H. (1967). A book of curves (p. 690). Cambridge University Press.
Mattheck, C. (2006). Teacher tree: The evolution of notch shape optimization from complex to simple. Engineering Fracture Mechanics, 73, 1732–1742.
McMahon, T. A., & Kronauer, R. E. (1976). Tree structures: Deducing the principle of mechanical design. Journal of Theoretical Biology, 59, 443–466.
Morgan, J., & Cannell, M. G. R. (1994). Shape of tree stems—a re-examination of the uniform stress hypothesis. Tree Physiology, 14, 49–62.
Niklas, K. J., & Spatz, H. C. (2012). Plant physics (p. 426) University of Chicago Press.
Oppelt, A. L., Kurth, W., & Godbold, D. L. (2001). Topology, scaling relations and Leonardo’s rule in root systems from African tree species. Tree Physiology, 21, 117–128.
Sellier, D., Fourcaud, T., & Lac, P. (2006). A finite element model for investigating effects of aerial architecture on tree oscillations. Tree Physiology, 26, 799–806.
Snowdon, P., Keith, H., & Raison, R. J. (2001). Protocol for sampling tree and stand biomass. Technical Report No. 31, Australian Greenhouse Office, Canberra.
Sone, K., Suzuki, A. A., Miyazawa, S. I., Noguchi, K., & Terashima, I. (2009). Maintenance mechanisms of the pipe model relationship and Leonardo da Vinci’s rule in the branching architecture of Acer rufinerve trees. Journal of Plant Research, 122, 41–52.
Srinivasan, K., Kunhamu, T. K., & Mohankumar, B. (2004). Root excavation studies in a mature rubber (Heveabrasiliensis Muell. Arg.) plantation. Natural Rubber Research, 17, 18–22.
Thakur, S., Kumar, B. M., & Kunhamu, T. K. (2015). Coarse root biomass, carbon, and nutrient stock dynamics of different stem and crown classes of silver oak (Grevillearobusta A. Cunn. ex. R. Br.) plantation in central Kerala, India. Agroforestry Systems, 89, 869–883.
Tomlinson, H., Traore, A., & Teklehaimanot, Z. (1998). An investigation of the root distribution of Parkia biglobosa in Burkina Faso, West Africa, using a logarithmic spiral trench. Forest and Ecology Management, 107, 173–182.
Torres, N. V., & Santos, G. (2015). The mathematical modeling process in biosciences. Frontiers in Genetics, 6, 354.
Voottipruex, P., Bergado, D. T., Mairaeng, W., Chucheepsakul, S., & Modmoltin, C. (2008). Soil reinforcement with combination roots system: a case study of Vetiver grass and Acacia Mangium Wild. Lowland Technology International, 10, 56–67.
Wainwright, J., & Mulligan, M. (2005). Environmental modelling: finding simplicity in complexity (p. 494). John Wiley and Sons.
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Ramanan, S.S., Kunhamu, T.K., Namgyal, D., Gupta, S.K. (2020). Fusing Classical Theories and Biomechanics into Forest Modelling. In: Chandra, G., Nautiyal, R., Chandra, H. (eds) Statistical Methods and Applications in Forestry and Environmental Sciences. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1476-0_9
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