Abstract¶

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.

These results may help reveal when communities of individuals have maximized their potential to cycle energy through an ecosystem or when they have been disturbed by exogenous forces.

The manuscript table of contents, the supporting notebooks and the author list are on the Part II landing page.