Part II: Metabolic Scaling Theory and Biological Fractals

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Abstract

Much of the scientific literature describes the fractal-like hierarchical branching networks of vascular organisms as 'self-similar'. Here we examine papers where fractal-like self-similarity is incorrectly described. We also link why the hierarchical branching networks in vascular organisms are 'self-affine' rather than self-similar by linking metabolic scaling theory to these structural traits. Last, we propose a mechanistic theory of fractal dimensions for single cell through multicellular life forms.

In our supplemental materials, we provide empirical explanations for the fractal-like structures of single cell colonies and autotrophs including primitive algae, vascular organisms including lichens and bryophytes, and higher order terrestrial plants.

We also describe how self-affinity arises in heterotrophs as related to metabolic and circulatory networks.

Key Findings

1. Dimensional analysis with appropriate self-affine mass dimension shows that many reported fractal dimensions in ecology are either incorrect or inappropriately reported.

2. A technique for testable predictions, including a mechanistic explanation for how individual branching networks grow and fill space and how communities of organisms emerge with fractal dimensions based on MST predictions.

3. Self-affine vs self-similar: The distinction between these concepts has significant implications for how we measure and interpret fractal dimensions in biological systems.

Authors

Tyson Lee Swetnam Institute for Computation and Data-enabled Insight, University of Arizona

Jon D Pelletier Department of Geosciences, University of Arizona

Brian J. Enquist Department of Ecology and Evolutionary Biology, University of Arizona