Variance in tree growth rates provides a key link for completing the theory of forest size structure formation

In natural forests at a demographic equilibrium state, the size frequency distribution (SFD) of trees is linked with their size-dependent growth and mortality rates. While the mean growth rate (MGR) of each size class is generally used for determining the SFD, the variance in the growth rate (VGR) has always been ignored. Here, based on the analyses with Kolmogorov forward equation, we show that in general, the VGR can flatten the slope of the SFD and, in particular, can address the contradiction between the size-dependent MGR and the similar to 2 power-law SFD in the metabolic scaling theory. We traced the origin of the VGR to the intrinsic stochasticity in the allometric growth coefficients of trees and deduced its functional form based on variance propagation. Using the forest censuses data from Barro Colorado Island, we verified the prediction of the VGR and indicated its indispensability in the theory of forest size-structure formation. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study explores the relationship between the size frequency distribution of trees in natural forests and their size-dependent growth and mortality rates, showing that the variance in growth rate can flatten the slope of the distribution and address contradictions in metabolic scaling theory. The origin of this variance is traced to intrinsic stochasticity in allometric growth coefficients, with the functional form deduced based on variance propagation. Evidence from forest censuses data supports the prediction of variance in growth rate and its essential role in the theory of forest size-structure formation.