Get started
Work

What does the tree of life look like as it grows? Evolution and the multifractality of time

Year: 2025
Type: article
Abstract: • We develop a mathematical model of the dynamic tree of life from three principles of phylogeny: nestedness, duality, and randomness. • The resulting structure resembles a Cantor dust, with each branch a distinct fractal, making the whole system multifractal. • Since branch lengths represent time, the length of a time interval depends on the observer's form, so that time is also multifractal. By unifying three foundational principles of modern biology, we develop a mathematical framework to analyze the growing tree of life. Contrary to the static case, where the analogy between phylogenetic trees and the tree that grows in soil is drawn, our framework shows that the living tree of life is analogous to a Cantor dust where each branch is a distinct fractal curve. The system as a whole is therefore multifractal in the sense that it consists of many unique fractals. The three foundational principles for the mathematical framework are that phylogeny is nested, phylogeny is dualistic (i.e., transitive between singularities and populations), and phylogeny is stochastic. Integrating these three principles, we model the dynamic (i.e., living ) tree of life as a random iterated function system that generates unique convexly related sequences of branching random variables (visualized in Animation 1 ). The multifractal nature of this dynamic tree of life implies that, for any two living entities, the time interval from their last common ancestor to the present moment is a distinct fractal curve for each. Thus, the length of a time interval along each distinct branch is unique, so that time is also multifractal and not an ultrametric on the tree of life.
DOI: 10.1016/j.jtbi.2025.112121
Language: English
Open Access status: hybrid
Estimated APC paid: $2,550
OpenAlex ID: W4409375680
FWCI: 3.216
Cites: 58
Cited by: 2
Related to: 10