A review of forest size structure studies: from statistical description to theoretical deduction

doi:10.17521/cjpe.2023.0301

Abstract

Abstract:

Forest size structure (the diameter distribution of trees in a forest) is a comprehensive indicator of forest demographic processes. It is the basis for determining forest successional stage and the state of forest health, estimating forest biomass and predicting forest carbon sink potential. Studies of forest size structure began with statistical descriptions before progressing to theoretical and mathematical deduction. In early statistical studies of forestry, many common probability distribution functions were used to fit plot-scale variations in size structure, but most of these functions were not derived from biological processes and therefore lack clear biological meaning. With the development of macroecology, the principle of maximum entropy and the central limit theorem have been used to explain the relatively consistent forest size structure at large spatial scales. Such models mainly focus on probabilistic statistics rather than ecological processes. Reports of a power-law size structure in natural mature forests in the early 2000s spawned a series of theoretical studies, including metabolic scaling theory and the theory of gap succession, among others. These theories have proposed that the observed power-law size structure results from the relationship between tree size and resource use on the individual scale and tree competition for resources on the community scale. Demographic equilibrium theory provides a general framework for analyzing the relationship between the steady state forest size structure and tree growth and mortality. Under this equilibrium framework, the hypothesis of demographic optimality further provides a new perspective for the analysis of forest size structure. Mathematical models including transition matrices, integral projections, and partial differential equations are powerful tools for analyzing forest size structure dynamics. However, due to the difficulty of identifying time-varying solutions to the mathematical models, most studies have been confined to the framework of forest demographic equilibrium. To understand dynamic variations of forest size structure and predict forest carbon sink potential in a rapidly changing climate, it is essential both to find general time-varying solutions to the mathematical models and to tighten empirical constraints on the effects of climatic factors on forest growth and mortality rates.

Key words: forest size structure, resource competition, tree growth and mortality

ZHOU Jian, WANG Han. A review of forest size structure studies: from statistical description to theoretical deduction[J]. Chin J Plant Ecol, 2024, 48(6): 675-689.

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Figures/Tables 4

Fig. 1 Application of Weibull distribution in studies of forest size structure. A, Different patterns of forest size structure in different forest plots (data from Coomes & Allen, 2007). B, Varying shape and scale parameters for the Weibull distribution leads to different patterns of the probability distribution function. C, constant value; k, shape parameter; l, scale parameter.

Fig. 2 Evolution of the size-density relationship associated with self-thinning in an even-sized cohort (A) and tree size structure in a mixed sized forest (B). t1, t2, t3 represent different stages of self-thinning. D, size class; N, individual number.

Fig. 3 Forest size structure remains constant when the same growth rate applies to each size class (A) and changes when the growth rate varies across different size classes (B). D, size class; N, individual number. G1 and G2 represent the growth rates of size class 1 and 2, respectively.

Fig. 4 Forest size structure based on data from the Barro Colorado Island (BCI) 50 hm2 forest plot inventory in 2010 (blue circles): a power-law distribution at intermediate sizes (red solid line) breaks down in the head and tail (marked by red circles). Green dashed line shows a negative exponential distribution assuming constant growth rate and mortality.

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