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 -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.