Abordagem teórico-experimental das relações de escala e fractalidade : uma aplicação do modelo “WBE” em área de várzea da Floresta Amazônica

Abstract

In the context of climate and environmental changes, we can ask how Evolution optimized the grasping and distribution of resources in living beings. Geometric shapes called fractals are apparently present in innumerable situations in nature, seeming to be a kind of structure that leads to some kind of evolutionary advantage. In general, geometry is considered to explain much of the success of living beings, a fact studied by Allometry. The reasons to find models that result in good allometric relationships is such that relations allow, in theory, to extrapolate the properties of individual plants or small forest areas to the Forest as a whole, a reasonable assumption due to the present self-similarity in fractal geometry. This thesis aims to study the following questions: 1) Is there a power-law (scale-free) relation for the distribution of trunk diameters in the study area? If affirmative, is there universality? 2) Is there a similar relationship with respect to the distribution of diameters and lengths of branches in some species in the same area? If so, is there similarity to the distribution of trunks? 3) What the extension of WBE model assumptions to validate the studied structures? 4) Why do trees have the formats they have and what is the role of the branching pattern? Using as a research methodology the measurement of tree branchs of two species (Inga alba and Bocageopsis), from image analysis to leaf venation and literature review, it was possible to partially answer the questions raised: 1) We find a power law in the study area, but this behavior does not appear to be universal. 2) There is also a power law for the diameter of the branches, but not in the same way as the trunks. 3) There are varying degrees of self-similarity, but some degree of fractality can be inferred. There was some agreement between the results and the prediction of certain parameters (β and γ), but nothing could be said about the invariance of the capillaries. 4) Many adjustments between different objectives result in the great diversity of formats, although the optimization in the capture of solar radiation seems to prevail.