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Abstract
We demonstrate that when power scaling occurs for an individual tree and in a forest, there is great resulting simplicity notwithstanding the underlying complexity characterizing the system over many size scales. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions. We show that the effective dimension, Dtree, of a tree is close to 3, whereas a mature forest has Dforest approaching 1. We discuss the energy equivalence rule and show that the metabolic rate–mass relationship is a power law with an exponent D/(D + 1) in both cases leading to a Kleiber's exponent of 3/4 for a tree and 1/2 for a forest. Our work has implications for understanding carbon sequestration and for climate science.

Questions: Is there any theoretical model enabling predictions of the optimal tree size distribution in tropical communities? Can we use such a theoretical framework for quantifying the degree of disturbance?. Location: Reserve of Yangambi, northeast region of the Democratic Republic of Congo. Methods: We applied an allometric model based on the assumption that a virtually undisturbed forest uses all available resources. In this condition, the forest structure (e.g. the tree size distribution) is theoretically predictable from the scaling of the tree crown with tree height at an individual level. The degree of disturbance can be assessed through comparing the slopes of the tree size distribution curves in the observed and predicted conditions. We tested this tool in forest stands subjected to different degrees of disturbance. We inventoried trees >1.3 m in height by measuring the DBH in three plots of 1 ha each, and measured tree height, crown radius and crown length in a sub-sample of trees. Results: All tree species, independently of the site, shared the same exponents of allometric relationships: tree height vs tree diameter, crown radius vs tree height, crown length vs tree height and consequently crown volume vs tree height, suggesting that similar trajectories of biomass allocation have evolved irrespective of species. The observed tree size distributions appeared to be power laws (excluding the finite size effect) and, as predicted, the slope was steeper in the less disturbed forest (−2.34) compared to the most disturbed (−1.99). The difference in the slope compared to the theoretical fully functional forest (−2.65) represents the metric for assessing the degree of disturbance. Conclusions: We developed a simple tool for operationalizing the concept of 'disturbance' in tropical forests. This approach is species-independent, needs minimal theoretical assumptions, the measurement of only a few structural traits and requires a low investment in equipment, time and computer skills. Its simple ...