I think the investigation of fractal dimension in phylogeny is very interesting and this paper is a novel effort towards that. Congratulations.
But may I suggest that you perform your analyses on better source data?
Both the NCBI tree & Catalogue of Life trees you performed your analyses on are taxonomy trees. They are not true phylogenetic trees.
See this post by David Morrison for a fuller explanation:
These taxonomy trees have many artefactual features e.g. they contain zero fossil taxa, and thus your results do not really measure the fractal dimension of phylogeny.
If you want large phylogenetic trees to test may I suggest you look at re-using data from treebase.org or datadryad.org they have many real phylogenies to choose from.
A large example phylogenetic tree would be the 55,473 tip phylogeny from:
Smith SA, Beaulieu JM, Stamatakis A, Donoghue MJ (2011) Understanding angiosperm diversification using small and large phylogenetic trees. American Journal of Botany 98(3): 404-414. doi:10.3732/ajb.1000481 data available from Dryad
Also, this 73,060 tip phylogeny would be suitably large:
Goloboff, P. A., Catalano, S. A., Mirande, J. M., Szumik, C. A., Arias, J. S., Källersjö, M., and Farris, J. S. 2009. Phylogenetic analysis of 73 060 taxa corroborates major eukaryotic groups. Cladistics 25:211-230. link to paper
As an additional exploratory analysis, it might also be interesting to test if there is a difference in fractal dimension between 'supermatrix' approaches to phylogeny reconstruction and 'supertree' approaches.
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