Volkov Igor, Tovo Anna, Anfodillo Tommaso, Rinaldo Andrea, Maritan Amos, Banavar Jayanth R
Department of Physics, The George Washington University, 20052 Washington, DC, USA.
Dipartimento di Fisica "G. Galilei", Università di Padova, 35131 Padova, Italy.
PNAS Nexus. 2022 Mar 10;1(1):pgac008. doi: 10.1093/pnasnexus/pgac008. eCollection 2022 Mar.
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, , of a tree is close to 3, whereas a mature forest has approaching 1. We discuss the energy equivalence rule and show that the metabolic rate-mass relationship is a power law with an exponent /( + 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.
我们证明，当个体树木以及森林中出现幂次缩放时，尽管在许多大小尺度上表征该系统的潜在复杂性很高，但最终会产生极大的简单性。我们的缩放框架统一了森林中看似不同的趋势，并提供了一种简单却有前景的方法，用于定量理解一个具有不完全已知相互作用的极其复杂的多体系统。我们表明，一棵树的有效维度 (d) 接近3，而成熟森林的 (d) 接近1。我们讨论了能量等效规则，并表明在这两种情况下，代谢率与质量的关系都是幂律，指数为 (\beta/(\beta + 1))，这导致树的克莱伯指数为3/4，森林的为1/2。我们的工作对理解碳固存和气候科学具有启示意义。
