Simple models for scaling in phylogenetic trees

Details Simple models for scaling in phylogenetic trees Simple models for scaling in phylogenetic trees

2008-10-21

arxiv.org/abs/0810.3877v2

International Journal of Bifurcation and Chaos 20, 805-811 (2010)

Biology

Quantitative Biology

Quantitative Methods

7 pages, 4 figures. A new figure, with example trees, has been added. To appear in Int. J. Bifurcation and Chaos

Scientific paper

10.1142/S0218127410026095

Many processes and models --in biological, physical, social, and other contexts-- produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this motivation, we analyze numerically two branching models leading to non-logarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.

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