Forest demography and biomass accumulation rates are associated with transient mean tree size vs. density scaling relations

Abstract

Linking individual and stand-level dynamics during forest development reveals a scaling relationship between mean tree size and tree density in forest stands, which integrates forest structure and function. However, the nature of this so-called scaling law and its variation across broad spatial scales remain unquantified, and its linkage with forest demographic processes and carbon dynamics remains elusive. In this study, we develop a theoretical framework and compile a broad-scale dataset of long-term sample forest stands (n = 1,433) from largely undisturbed forests to examine the association of temporal mean tree size vs. density scaling trajectories (slopes) with biomass accumulation rates and the sensitivity of scaling slopes to environmental and demographic drivers. The results empirically demonstrate a large variation of scaling slopes, ranging from -4 to -0.2, across forest stands in tropical, temperate, and boreal forest biomes. Steeper scaling slopes are associated with higher rates of biomass accumulation, resulting from a lower offset of forest growth by biomass loss from mortality. In North America, scaling slopes are positively correlated with forest stand age and rainfall seasonality, thus suggesting a higher rate of biomass accumulation in younger forests with lower rainfall seasonality. These results demonstrate the strong association of the transient mean tree size vs. density scaling trajectories with forest demography and biomass accumulation rates, thus highlighting the potential of leveraging forest structure properties to predict forest demography, carbon fluxes, and dynamics at broad spatial scales.

Keywords: biomass accumulation rates; forest demography; forest structure and function; mean tree size vs. density scaling trajectory.

Fig. 1.

A conceptual framework on the transient mean tree size vs. density scaling law: the scaling trajectory and its association with forest demography and biomass accumulation rates. A) The mean tree size (aboveground biomass) vs. density scaling law is initially proposed and applied in an even-sized community, whereby trees compete for the constant space and/or resources. At macroecology scales (i.e. by using large-scale and spatial data of mean tree size and density), the scaling law predicts a scaling exponent (α) of −3/2 (Euclidean scaling) or −4/3 (fractal scaling), whereby the isometric model considers plants as 3D solids (Euclidean scaling) and the allometric model considers the geometric structure of the plant as a fractal. As such, this spatial approach does not allow to link the demography with α at forest stand or local scales. B) The transient mean tree size vs. density scaling trajectory or temporal α is expected to be linked with forest demography—growth and mortality at forest stand or local scales. Here, the transient mean tree size vs. density scaling trajectory is temporally fitted using temporal series of data on mean tree size and density within each forest stand. As conceptualized based on demographic processes, when the mortality rate remains constant, a higher forest growth would lead to a higher mean size and thus a steeper mean tree size vs. density scaling trajectory with a more negative value of the scaling exponent and a higher biomass accumulation rate. By comparison, a lower growth rate would lead to a less negative value of the scaling exponent. Similarly, in a scenario of assuming a constant forest growth, a higher mortality rate would reduce the time to reach the decreased tree density (i.e. 200 ind ha⁻¹), thus leading to a lower mean size, a less negative value of the scaling exponent, and a lower biomass accumulation rate. By comparison, a lower mortality rate would lead to a more negative value of the scaling exponent. See the conceptual model for mathematic derivations in detail in Materials and methods.

Fig. 2.

The transient mean tree size vs. density scaling exponents (or slopes) over time within and among forest biomes. A) The scaling slopes across forest stands within tropical (n = 31), temperate (n = 800), and boreal (n = 602) forest biomes. The solid vertical line refers to the Euclidean scaling law (−3/2), while the dashed vertical line refers to the fractal scaling law (−4/3). B) The probability distribution of the mean value of the transient mean tree size vs. density scaling slopes using a bootstrapped (1,000 iterations) approach by randomly selecting 95% of stands across forest biomes.

Fig. 3.

The environmental controls on the transient mean tree size vs. density scaling over time in North America forests. A) Standardized coefficient estimates (mean ± 95% CIs) for the effects of forest age, basal area, size variation, precipitation in the warmest quarter, rainfall seasonality, SOC, and pH on the slopes of the transient mean tree size vs. density scaling. The environmental variables were standardized (z-score) before analysis. B) Mean decrease in accuracy (%IncMSE, mean, and SD) estimated from 1,000 simulations of random forests in evaluating the importance of environmental conditions in the slopes of the transient mean tree size vs. density scaling. C) Partial feature contributions of primary environmental variable interactions (age vs. rainfall seasonality) to the slopes of the transient mean tree size vs. density scaling. D) The relationship between forest mean age and the slopes of the transient mean tree size vs. density scaling across temperate and boreal forests in North America. Data were binned over 30 points across forest mean age range.

Fig. 4.

The association of transient mean tree size vs. density scaling slopes with the demographic drivers—growth and biomass loss from mortality and biomass accumulation rate across forest biomes. A) Coefficient estimates (mean ± 95% CIs) for the effects of growth and biomass loss from mortality on the slopes of the transient mean tree size vs. density scaling across forest biomes, quantified by the SEMs. B) The relationships between transient mean tree size vs. density scaling slopes and biomass accumulation rate (kg m⁻² year⁻¹) across forest biomes. Both growth and biomass loss from mortality are with units kg m⁻² year⁻¹. The tails with slope >−1 describe zones of the carbon sources. These results are robust to account for stand area and data source using linear-mixed models (see SI Appendix, Fig. S5).