Part V: Research Framework and Testable Hypotheses¶

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Spectral Geometry and Metabolic Scaling in Forest Canopy Architecture: A Preregistration Framework

Keywords: spectral geometry, fractal dimension, lacunarity, Riemann Zeta distribution, self-organized criticality, GUE statistics, canopy structure, metabolic scaling, complex dimensions, old-growth forest

Do old-growth forests at self-organized criticality carry geometric and spectral signatures that distinguish them from disturbed or managed stands? Treating the LiDAR canopy height model as a stochastic surface, the framework predicts that optimal space packing and metabolic scaling produce characteristic fractal dimension \( D \) and lacunarity \( \Lambda \) curves, that canopy gap sizes follow a zeta (power-law) distribution with exponent near 2, and that the spacing of dominant tree crowns follows Wigner-Dyson (GUE) repulsion statistics, like the zeros of the Riemann zeta function, rather than Poisson randomness. Five primary hypotheses (optimal filling, scale invariance, zeta gap distribution, universal repulsion and biotic decoupling) and four spatial hypotheses from fractal string theory are each given null and alternative forms together with the statistical tests (ANOVA, regression, likelihood-ratio and chi-squared tests) that will decide them.

Contents¶

1. Abstract
2. Introduction
3. Methods
4. Expected Results
5. Discussion
6. Conclusion
7. References

Implementation path¶

The measurements this framework calls for (normalised canopy height models, differential box-counting, gliding-box lacunarity, gap-size distributions and tree-apex spacing) are being implemented in the 3DEP canopy height model notebooks, which build canopy height models for a set of United States forest sites from USGS 3DEP LiDAR. The Part II notebook Canopy Dimensions & Statistical Validation shows the differential box-counting workflow on canopy height models.