Theoretical and experimental approach of scale relations and fractality of vegetation on a seasonally flooded area in the Amazon Forest

Authors

DOI:

https://doi.org/10.5902/1980509839420

Keywords:

Alometria, Lei de potência, Modelo WBE

Abstract

The relationship between plant physiology and metabolism, as well as energy flows mediated by vegetation, is poorly understood today. According to the West, Brown and Enquist (WBE) theory, some plant parameters, such branch diameters, are expected to obey power law distributions. In this work, we tried to approach the relations of scale and fractality in two seasonally flooded areas of the Amazon Forest. Specifically, the aim was to answer if there is a relationship of power law type (free of scale) for the distribution of the diameters of the trunks in the study areas, if there is a similar relationship with respect to the distribution of the branch diameters in some species in these same areas, and there is still a similarity with the distribution of the trunks, in such a way that we can say that the tree ‘imitates’ the forest in which it is contained. We also present a way to measure the fractality in the studied trees based on the relationships between the branch diameters of the subsequent generations (β) coefficient of variation. It was observed that some exponents differ from those predicted by the WBE theory and that the trunk distributions are of the power law-type, but with expressive variations of R². For the branches, the results indicate that the parameters really follow power laws, but with variations in between the studied species. It has also been shown that at least one species is more self-similar (fractal) than others. Finally, there was a brief discussion about what is the role of this pattern in the adaptation and evolution of plants.

Downloads

Download data is not yet available.

Author Biographies

Adriano Pereira Guilherme, Universidade Federal do Amazonas, Coari, AM

Físico, Dr., Professor do Instituto de Saúde e Biotecnologia, Universidade Federal do Amazonas, Estrada Coari-Mamiá, 305, CEP 69460-000, Coari (AM), Brasil. 

Deniz dos Santos Mota, Universidade Federal do Amazonas, Manaus, AM

Físico, Dr., Professor do Departamento de Física, Instituto de Ciências Exatas, Universidade Federal do Amazonas, Av. General Rodrigo Otávio Jordão Ramos, 1200, CEP 69067-005, Manaus (AM), Brasil. 

Iramaia Jorge Cabral de Paulo, Universidade Federal de Mato Grosso, Cuiabá, MT

Física, Dra., Professora do Instituto de Física, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipó, CEP 78060-900, Cuiabá (MT), Brasil. 

Sérgio Roberto de Paulo, Universidade Federal de Mato Grosso, Cuiabá, MT

Físico(a), Dr(a)., Professoro(a) do Instituto de Física, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipó, CEP 78060-900, Cuiabá (MT), Brasil. 

References

AVNIR, D. et al. Is the Geometry of Nature Fractal? Science, Washington, v. 279, p. 39-40, jan. 1998.

BARTHOLOMEW, G. A. A matter of size; An examination of endothermy in insects and terrestrial vertebrates. In: HEINRICH, B. (ed.). Insect thermoregulation. New York: Wiley, 1981.

BEJAN, A. Constructal-theory network of conducting paths for cooling a heat generating volume. International Journal of Heat Mass Transfer, Amsterdam, v. 40, p. 799-816, mar. 1997.

BEJAN, A. Shape and structure, from engineering to nature. Cambridge: Cambridge University Press, 2000.

BRODY, S.; PROCTER, R. C.; ASHWORTH, U. S. Basal metabolism, endogenous nitrogen, creatinine and neutral sulphur excretions as functions of body weight. University of Missouri Agricultural Experiment Station Research Bulletin, Jefferson City, v. 220, p. 1-40, 1934.

CALDER, W. A. Size, function, and life history. Cambridge: Harvard University Press, 1984.

ELOY, C. Leonardo’s rule, self-similarity and Wind-induced stresses in trees. Physical Review Letters,College Park, v. 107, p. 258101, dec. 2011.

ENQUIST B. J.; NIKLAS, K. J. Invariant scaling relations across tree-dominated communities. Nature, Londres, v. 410, p. 655-660, apr. 2001.

FISCH, G. Uma revisão geral sobre o clima da Amazônia. Acta Amazonica, Manaus, v. 28, n. 2, p. 101-101, jun. 1998.

GUILHERME, A. P. Abordagem teórico-experimental das relações de escala e fractalidade: uma aplicação do modelo “WBE” em área de várzea da floresta amazônica. 2017. Tese (Doutorado em Física Ambiental) – Universidade Federal de Mato Grosso, Instituto de Física, Cuiabá, 2017. Disponível em: http://www.pgfa.ufmt.br/index.php/br/utilidades/teses/368-adriano-pereira-guilherme/file>

HALLEY, J. M. et al. Uses and abuses of fractal methodology in ecology. Ecology Letters, Paris, v. 7, p. 254-271, 2004.

HENDRICKS, W. A.; ROBEY, K. W. The Sampling Distribution of the Coefficient of Variation. The Annals of Mathematical Statistics, Beachwood, v. 7, n.3, p. 129-132, 1936. DOI:10.1214/aoms/1177732503

HONDA, H.; FISHER, J. B. Tree Branch Angle: Maximizing Effective Leaf Area. Science, v. 199, p. 888-890, feb. 1978.

JAMES, K. R.; HARITOS, N.; ADES, P. K. Mechanical stability of trees under dynamic loads. American Journal of Botany, San Luis, v. 93, n. 10, p. 1522-1530, 2006.

KANG, H. S.; DENNIS, D.; MENEVEAU, C. Flow over fractals: drag forces and near wakes. Fractals, Singapura, v. 19, n. 4, p. 387-399, 2011.

KLEIBER, M. Body size and metabolism. Hilgardia, Berkeley, v. 6, p. 315-353, 1932.

KOZŁOWSKI, J.; KONARZEWSKI, M. Is West, Brown and Enquist's Model of Allometric Scaling Mathematically Correct and Biologically Relevant? Functional Ecology, London, v. 18, n. 2, p. 283-289, apr. 2004.

LEOPOLD, L. B. Trees and Streams: The Efficiency of Branching Patterns. Journal of theoretical Biology, Amsterdam, v. 31, p. 339-354, 1971.

MULLER-LANDAU, H. C. et al. Comparing tropical forest tree size distributions with the predictions of metabolic ecology and equilibrium models. Ecology Letters, Paris, v. 9, p. 589-602, 2006.

NAÇÕES UNIDAS. Influência humana no aquecimento global é evidente, alerta novo relatório do IPCC. [S. l.], 2014. Disponível em: https://nacoesunidas.org/influencia-humana-no-aquecimento-global-e-evidente-alerta-novo-relatorio-do-ipcc/. Acesso em: 22 jun. 2016.

PETERS, R. H. The ecological implications of body size. Cambridge: Cambridge University Press, 1983.

RIAN, I. M.; SASSONE, M. Tree-inspired dendriforms and fractal-like branching structures in architecture: a brief historical overview. Frontiers of Architectural Research, Beijing, v. 3, p. 298-323, 2014.

RUBNER, M. Uber den Einfluss der Korpergrosse auf Stoff-und Kraftwechsel, Zeitscrift fur Biologie, Munique, v. 19, p. 535-562, 1883.

SALM, R. et al. Cross-scale determinants of palm species distribution. Acta Amazonica, Manaus, v. 37, n. 1, p. 17-26, 2007.

SCHMIDT-NIELSEN, K. Scaling: why is animal size so important? Cambridge: Cambridge University Press, 1984.

SERVIÇO FLORESTAL BRASILEIRO. Florestas do Brasil em resumo- 2010: dados de 2005-2010. Brasília, 2010. 152 p. Disponível em: http://www.mma.gov.br/estruturas/sfb/_arquivos/

SILVA JÚNIOR, M. C.; SILVA, A. F. Distribuição dos diâmetros dos troncos das espécies mais importantes do cerrado na estação florestal de experimentação de Paraopeba (EFLEX)-MG. Acta Botanica Brasilica, Brasília, v. 2, n. 1/2, p. 107-126, 1988.

THOMAS, P. The shapes of trees: a matter of compromise. Arnoldia, [s. l.], v. 61, n. 1, p. 14-21, 2001.

THOMAS, P. The shape of trees. In: TREES: Their Natural History. 2nd ed. Cambridge: Cambridge University Press, 2014.

VANGEL, M. G. Confidence Intervals for a Normal Coefficient of Variation. The American Statistician, Boston, v. 50, n. 1, p. 21-26, 1996.

WANG, X. et al. Tree size distributions in an old-growth temperate forest. Oikos, Lund, v. 118, p. 25-36, 2009.

WEST, G. B.; BROWN, J. H.; ENQUIST, B. J. A general model for the origin of allometric scaling laws in biology. Science, Washington, v. 276, p. 122-126, apr. 1997.

WEST, G.; ENQUIST, B.; BROWN, J. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science, Washington, v. 284, p. 1677-1679, jun. 1999.

WEST, G.; ENQUIST, B.; BROWN, J. A general quantitative theory of forest structure and dynamics. PNAS, Washington, v. 106, n. 17, p. 7040-7045, apr. 2009.

WINDSOR-COLINS, A. et al. The palm – a model for success? In: DESIGN and Information in Biology. Billerica: WIT Press, 2007. p. 303-326.

Published

2020-12-01

How to Cite

Guilherme, A. P., Mota, D. dos S., Paulo, I. J. C. de, & Paulo, S. R. de. (2020). Theoretical and experimental approach of scale relations and fractality of vegetation on a seasonally flooded area in the Amazon Forest. Ciência Florestal, 30(4), 1061–1074. https://doi.org/10.5902/1980509839420

Issue

Section

Articles