Construindo árvores filogenéticas com o uso de caminhadas aleatórias e geometria fractal

Abstract

The purpose of this study is to propose an alternative method to build phylogenetic trees using the fractal dimension calculated from (pseudo) random walks on mitochondrial DNA and ribosomal RNA of some species of living beings. The walks are are performed attributing coordinates to each of the nitrogenous bases of DNA or RNA. The generated figures show complex morphologies and therefore we use parameters such as fractal dimension to characterize the different morphologies found. The obtained fractal dimensions of these figures are grouped to generate distance trees (dendograms) using the method of hierarchical clustering. We use the software Mathematica 6.0 to program the routines that build the random walks and calculates the values of fractal dimension and we also use the routine of the software that does the clustering and generates the dendograms. We have chosen ten eukaryotic species for the study: Anopheles gambiae (malaria mosquito), Arabidopsis thaliana (a plant), Danio rerio (zebra fish), Drosophila melanogaster (the fruit fly), Homo sapiens (human), Mus musculus (mouse), Pan troglodytes (chimpanzee), Rattus norvegicus (laboratory rat), Strongylocentrotus purpuratus (sea hedgehog), Xenopus laevis (a species of frog). We found that for these organisms our method can distinguish kingdoms, e.g. the plant from the animals. Among the animals, it distinguishes vertebrates from invertebrates. Among invertebrates, it distinguishes insects (fly and mosquito) from echinoderms (hedgehog). Among the vertebrates, it distinguishes the amphibian from mammals and fish. We conclude that the method generates results consistent with those predicted by the traditional phylogeny.