森林径级结构研究: 从统计描述到理论演绎

doi:10.17521/cjpe.2023.0301

摘要/Abstract

摘要：

森林径级结构是树木生长、竞争、死亡等过程的综合反映, 也是估算森林生物量、判断森林演替阶段与健康状态以及预测森林碳汇潜力的基础依据。林学领域早期对径级结构的研究以统计描述为主, 多采用常见的概率分布函数来拟合样地尺度上径级结构的动态变化, 缺乏对其形成机制的阐释。随着宏观生态学的发展, 最大熵原理、中心极限定理等被用于解释大尺度上发现的相对一致的森林径级结构, 但这类模型侧重概率统计, 对具体生态学过程的分析仍然欠缺。2000年以来, 在原始成熟森林中发现的径级结构的幂律特征催生了一系列理论研究, 包括代谢尺度理论、林窗演替理论等。这些理论尝试从树木个体大小和资源利用之间的关系, 以及树木对资源的竞争过程来演绎径级结构达到稳态时幂律特征的形成机制。种群统计平衡理论为稳态径级结构的分析提供了一般性框架, 揭示了不同的树木生长速率和死亡率如何导致径级结构特征的变化; 在此基础上, 种群统计最优性假设为径级结构的分析提供了新的视角。数学层面上, 转移矩阵、积分投影、偏微分方程等都是径级结构动力学分析的有力工具, 但由于这类数学模型的时间动态解析求解较为困难, 研究中通常预先假定森林处于理想的结构平衡状态。而在实际情况下, 结构非平衡往往是森林的常态, 也是森林碳库变化与碳汇潜力估算的基础。为了更好预测全球变化背景下的森林动态趋势, 应明确环境因子对径级相关的树木生长速率、死亡率的影响, 并发展径级结构动态特征的解析方法。

关键词: 森林径级结构, 资源竞争, 树木生长和死亡

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

周建, 王焓. 森林径级结构研究: 从统计描述到理论演绎. 植物生态学报, 2024, 48(6): 675-689. DOI: 10.17521/cjpe.2023.0301

ZHOU Jian, WANG Han. A review of forest size structure studies: from statistical description to theoretical deduction. Chinese Journal of Plant Ecology, 2024, 48(6): 675-689. DOI: 10.17521/cjpe.2023.0301

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链接本文: https://www.plant-ecology.com/CN/10.17521/cjpe.2023.0301

https://www.plant-ecology.com/CN/Y2024/V48/I6/675

图/表 4

图1 Weibull分布在径级结构拟合中的应用。 A, 不同森林样地的径级结构示例(数据来自Coomes和Allen, 2007)。B, 双参数Weibull分布的不同参数取值对应的不同分布特征。C, 常数; k, 形状参数; l, 尺度参数。

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.

图2 同生群自疏过程中的个体大小数量关系(A)和大小个体混合的森林中的径级结构对比(B)。 t1、t2、t3代表自疏的不同阶段。D, 树木径级; N, 个体数量。

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.

图3 各径级生长速率相同时径级结构不发生变化(A), 各径级生长速率不同时径级结构发生变化(B)。 D, 树木径级; N, 个体数量。G1、G2分别代表径级1、2的生长速率。

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.

图4 巴罗科罗拉多岛(BCI) 50 hm2森林大样地2010年清查数据呈现的径级结构(蓝色圆圈): 中间部分符合幂律特征(红色直线), 头部和尾部偏离幂律特征(红色圆圈标记区域)。绿色虚线代表在恒定生长速率和死亡率条件下, 森林径级结构应该呈现的负指数分布特征。

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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