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Networks with side branching in biology

D L Turcotte¹, J D Pelletier, W I Newman

¹Department of Geological Sciences, Cornell University, Ithaca, NY 14853, USA.

Journal of Theoretical Biology

|September 24, 1998

Summary

This study introduces the Tokunaga taxonomy for analyzing branching networks, revealing similar side-branching patterns in biological systems like leaf veins and river networks, and in diffusion-limited aggregation clusters.

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Area of Science:

Network theory
Fractal geometry
Biological systems

Background:

Branching networks are prevalent in biology (plants, cardiovascular, bronchial).
Many biological networks exhibit self-similarity and fractal scaling.
Understanding side-branching patterns is crucial for network analysis.

Purpose of the Study:

Introduce the Tokunaga taxonomy for side branching.
Analyze deterministic and stochastic branching networks.
Explore the universality of side-branching statistics in natural and artificial systems.

Main Methods:

Developed the Tokunaga taxonomy and parameterization for self-similar side-branching.
Examined deterministic branching networks with identical fractal dimensions but different side-branching parameters.
Analyzed stochastic branching in leaf vein structures, river networks, and diffusion-limited aggregation (DLA) clusters.

Main Results:

Deterministic networks with the same fractal dimension can possess distinct side-branching parameters.
Leaf vein networks and river networks share nearly identical side-branching statistics.
DLA clusters also exhibit Tokunaga side-branching statistics, suggesting universal formation principles.

Conclusions:

The Tokunaga taxonomy provides a framework for quantifying side-branching in complex networks.
Similar side-branching statistics in diverse systems (leaves, rivers, DLA) point to common underlying formation mechanisms.
The model shows good agreement with the allometric scaling of metabolic rate and mass, supporting its applicability to biological systems.

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