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.

在处于人口平衡状态的天然林中，树木的大小频率分布 (SFD) 与其大小相关的生长和死亡率有关。虽然每个尺寸等级的平均增长率 (MGR) 通常用于确定 SFD，但增长率 (VGR) 的方差一直被忽略。在这里，基于对 Kolmogorov 前向方程的分析，我们表明，总的来说，VGR 可以拉平 SFD 的斜率，特别是可以解决尺寸相关 MGR 和 -2 幂律 SFD 之间的矛盾代谢标度理论。我们将 VGR 的起源追溯到树木异速生长系数的内在随机性，并基于方差传播推导出其函数形式。使用来自巴罗科罗拉多岛的森林普查数据，