Size Relative Density Research Articles

Toward a metabolic theory of catchments: Scaling of water and carbon fluxes with size

Allometric scaling relations are widely used to link biological processes to body size in nature. Several studies have shown that such scaling laws hold also for natural ecosystems, including individual trees and forests, riverine metabolism, and river network organization. However, the derivation of scaling laws for catchment-scale water and carbon fluxes has not been achieved so far. Here, we focus on scaling relations of catchment green metabolism, defined as the set of ecohydrological and biogeochemical processes through which vegetation assemblages in catchments maintain their structure and react to the surrounding environment. By revising existing plant size-density relationships and integrating them across large-scale domains, we show that the ecohydrological fluxes occurring at the catchment scale are invariant with respect to the above-ground vegetation biomass per unit area of the basin, while they scale linearly with catchment size. We thus demonstrate that the sublinear scaling of plant metabolism results in an isometric scaling at catchment and regional scales. Deviations from such predictions are further shown to collapse onto a common distribution, thus incorporating natural fluctuations due to resource limitations into a generalized scaling theory. Results from scaling arguments are supported by hyperresolution ecohydrological simulations and remote sensing observations.

Ecological succession shapes size–density scaling relationships of trees and soil invertebrates

Abstract The widely observed negative scaling relationship between organism size and abundance is predicted to have a universal −0.75 scaling exponent across all life forms. However, factors influencing frequently observed deviations from this exponent, such as ecosystem succession and organism traits, remain poorly understood. We explore the dependence of size–density scaling on ecosystem succession and organism traits by analysing size–density relationships in trees and soil invertebrates across 183 temperate forest plots comprising urban secondary forests, urban old‐growth forests and non‐urban natural forests. Exponents of scaling relationships in urban tree and invertebrate communities progressively steepened with increasing restored (planted) forest stand age as small organisms increased in abundance. In contrast, non‐urban tree scaling relationships flattened during succession with exponents veering away from −0.75, whereas urban tree and invertebrate communities converged towards this prediction in later successional stages. Our results shed light on how the body size structure of tree and soil invertebrate communities spanning multiple trophic levels shift over successional time as the relative abundances of large versus small‐bodied organisms increase. This study emphasises the fundamental influence of organismal traits and ecosystem succession on scaling relationships of organism body size and abundance. Read the free Plain Language Summary for this article on the Journal blog.

Thirty years of forest productivity in a mountainous landscape: The Yin and Yang of topography

AbstractWe measured light‐related patterns of primary productivity within a topographically complex Oregon watershed over a 30‐year period. Second‐growth conifer densities were experimentally altered in 1981. Plots receiving at least 3434 MJ m−2 over a 6‐month growing season averaged 40% greater aboveground net primary productivity (ANPP) than those receiving less light (p = 0.000). Unthinned stands potentially built enough LAI to compensate for low light, but risked mortality that exceeded resilience. The two light levels acted as basins of attraction for other physiological and ecological processes, including size–density relationships and limiting foliar nutrients. Initial (1981) LAI and the irradiation step (above or below 3434 MJ m−2) explained 60% of variation in a 30‐year ANPP. Irradiation within each light group did not affect ANPP. At high irradiation, foliar N/Ca and slope steepness (both negative) explained 58% of the variation in residuals from the initial models, while at low irradiation on north, east, and west aspects, 83% of residual variation was explained by foliar Mg (+), understory cover (+), and 30‐year mortality (−). Light use efficiency (LUE) of fully stocked stands correlated with LAI and foliar N/K. Results suggest that understory influence on tree foliar N (+ or −) enhances ANPP by regulating critical nutrient ratios. Mortality reduced or eliminated differences among thinning levels, which did not vary at low light and only between unthinned and heavily thinned at high light. Values associated with relatively open forests (biodiversity, resilience) may be attained without large sacrifice of long‐term carbon sinks. In our study, light interacts with topography to produce nonlinear dynamics in which small changes in irradiation can have large consequences. Reduced sunlight has been suggested as a geoengineering option to combat global warming. Ecological changes out of proportion to lowered irradiation are a distinct possibility, including sharp reductions in terrestrial carbon sinks.

Effects of species mixing on maximum size-density relationships in Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.)-dominated mixed forests converted from even-aged pure stands.

Density management is a key silvicultural tool in management programs that enhances compositional and structural diversity and hence forest growth during the conversion of even-aged pure stands into mixed forests. To determine the optimum stand density, a model of maximum size-density relationships was employed to explore the relationship of the self-thinning trajectory with growth, species mixing, latitude, and site conditions during the transition of even-aged pure Chinese fir stands to Chinese fir-dominated mixed forests using stochastic frontier analysis. Data were obtained from a total of 591 permanent plots located in Fujian, Jiangxi, Zhejiang, and Anhui provinces in southern China. The results showed that (1) the slope of the maximum size-density relationship of Chinese fir-dominated mixed forests increased and plateaued over time; (2) the slope of the maximum size-density relationship of Chinese fir-dominated mixed forests did not deviate from Reineke's assumed universal slope of -1.605; and (3) mixing proportion had a positive effect on maximum size-density relationships, and latitude and site conditions had the opposite effect on maximum size-density relationships. Our findings will provide valuable guidance for the forest management of areas in which even-aged pure stands are being converted to mixed forests (i.e., when broadleaved tree species are planted after thinning to improve overall stand density and promote stand growth).

The strength of density dependence on body size of young‐of‐the‐year masu salmon, Oncorhynchus masou, varies over ontogeny in Horokashubuto stream, Hokkaido, northern Japan

AbstractThe relationships between body size and density of salmonids in natural streams have been well studied, and density‐dependent growth (somatic growth) is interpreted as the principal mechanism responsible for the relationship. Moreover, the body size–density relationship is known to vary over ontogeny. However, the relationship has been studied mostly by experimental procedures (e.g. stocking fish into streams), and knowledge about the relationship in natural populations (e.g. no human‐induced input of fish) is still inadequate. In this study, we compared the relationships between body size and density of young‐of‐the‐year (YOY) masu salmon, Oncorhynchus masou, between different ontogenetic stages, that is, fry (spring) and juveniles (autumn). We used the monitoring data of YOY body sizes and densities across three study sites collected from Horokashubuto stream in Hokkaido, northern Japan, from 2014 to 2022. In the juvenile stage, YOY body size correlated negatively with increasing density. This pattern is typical of the density dependence of salmonid growth demonstrated in many previous studies. In the fry stage, however, YOY body size correlated positively with increasing density. This study suggested that the patterns of density dependence vary as functions of the ontogenetic stages of salmonids.

A Density Management Diagram for Pitch Pine to Illustrate Tradeoffs between Carbon and Wildfire Risk

Abstract Pitch pine (Pinus rigida Mill.) can be found across a broad range in eastern North America but assumes local dominance only on poor soils in the northeastern United States. Contemporary management goals in the Northeast for areas dominated by pitch pine are focused on noncommercial benefits of forests, such as carbon density, reduced wildfire risk, habitat for rare species, and water provisioning. We present a density management diagram that empirically articulates the size-density limits of even-aged pitch pine stands. Included in the diagram are wildfire risk and carbon density, which are inversely related for most stand sizes. Maximum possible aboveground live tree carbon begins to decline at a quadratic mean diameter greater than 9 in., while crown fire risk remains high along the size-density limit until a quadratic mean diameter above 12 in. is achieved. Study Implications: Modern silvicultural tools that illustrate forest stand conditions have not been developed for pitch pine, but this species occurs in a region with much public attention on forests. We develop and present a density management diagram to show the interplay of different social goals for the forest and how they relate to the maximum size-density relationship. Pitch pine stands with high levels of aboveground live carbon are at high risk of crown fire, particularly in the smaller size classes.

Disentangling contributions of allometry, species composition and structure to high aboveground biomass density of high-elevation forests

The high elevation forests of the Central Himalayas include stands with an exceptional abundance of aboveground biomass, standing as some of the most carbon-rich forests in the entire Himalayan range and beyond. National or regional models, however, are inadequate in capturing this extreme concentration of biomass observed in select forest inventory plots. We aimed to identify factors contributing to the significant variability of biomass and thus, aboveground forest carbon in the high mountain forests of Nepal. By comparing the utilization of pantropical and Nepali allometric equations, we evaluated whether the elevational gradients in forest biomass were robust to changes in the allometric models used to predict plot biomass. Irrespective of the model employed, the highest biomass values were found in high elevation plots. The diverse distribution of forest biomass reinforces established size-density relationships, attributing observed variations to the interplay between tree size and density. Our results contribute valuable insights into these high biomass forests, affirming observed elevational gradients, quantifying the impact of tree species and structure, and elucidating factors influencing biomass sites concerning allometric models.

The Importance of Using Permanent Plots Data to Fit the Self-Thinning Line: An Example for Maritime Pine Stands in Portugal

Density-dependent mortality occurs in the evolution of even-aged populations when these approach crown closure age. This density-dependent mortality is regulated by the so-called “3/2 power law of self-thinning” that assumes a constant slope for the line relating the log of stand density with the log of the average tree size, the self-thinning line or maximum size–density relationship, MSDR. A good estimate of the self-thinning line is therefore an essential component to any forest growth model. Two concepts for the MSDR have emerged: (1) a static upper limit for the species; and (2) a dynamic self-thinning line influenced by several factors (e.g., management techniques, site quality and/or genetics). The objective of this study was to estimate a new static self-thinning line based on the quadratic mean diameter at breast height (Reineke’s self-thinning line) for the generalized use in maritime pine growth models in Portugal. Data from 41 observations obtained in nine long-term permanent experimental trials of maritime pine species were carefully selected from a data set of 186 plots as being under self-thinning. Two methods were used: OLS and mixed linear models. An exploratory analysis on the impact of each environmental variable on the slope and intercept of the self-thinning line led to the selection of a subset of environmental variables later used in an all possible regressions algorithm to find the subsets leading to the lowest values of Akaike information criterion (AIC). The OLS procedure showed that the differences between the plots could be explained by site index, by climate variables (e.g., evaporation or climatic indices) and the use of more than one covariable slightly improved the fit. Nevertheless, the best MSDR line fitted with mixed linear models (ln N = 12.97158 − 1.83926 ln dg) having the plot random effect in the intercept, largely outperformed the best OLS model and is therefore recommended for generalized use in forest growth models.

Aridity index and quantile regression influences on the maximum size-density relationship for coniferous and broad-leaved mixed forests

The maximum size-density relationship (MSDR) of mixed stands is of great significance for optimizing stand structural components and increasing stand productivity. However, model structure, climatic factors and parameter estimation methods affect the prediction accuracy of MSDR for multi-species mixed stands with complex structures, emphasizing the need to improve MSDR prediction methods. This study applied likelihood analysis to 333 sample plots of larch (Larix principis-rupprechtii Mayr.) and birch (Betula platyphylla Suk.) coniferous and broad-leaved mixed forests in Saihanba, Hebei Province, China to determine the structure of MSDR. Nonlinear least squares and nonlinear quantile regression were used to construct the MSDR of mixed stands, including the Martonne aridity index (M) which is a composite index that responds to temperature and precipitation. The results indicate that the optimal model form for predicting the MSDR of mixed stands is a nonlinear additive error structure. When considering M and using a quantile q = 0.95, the MSDR can accurately describe the variation in stand density of mixed larch-birch coniferous and broad-leaved forests.

The grain size distribution of matrix in primitive chondrites

AbstractThe matrix of primitive chondrites is composed of submicron crystals embedded in amorphous silicates. These grains are thought to be the remains of relatively unprocessed dust from the inner regions of the protoplanetary disk. The matrix of primitive meteorites is often compared to chondritic porous interplanetary dust particles (CP‐IDPs) which are believed to be of cometary origin, having accreted in the outermost regions of the solar nebula. Crystalline grains in CP‐IDPs show evidence of a size–density relationship between the silicates and sulfides suggesting that these components experienced sorting prior to accretion. Here, we investigate whether such evidence of sorting is also present in the matrix constituents of primitive chondrites. We report findings from our study of grain size distributions of discrete silicate and opaque (sulfide and metal) grains within the matrix of the primitive meteorites Acfer 094 (C2‐ung.), ALHA77307 (CO3), MIL 07687 (C3‐ung.), and QUE 99177 (CR2). Mean radii of matrix silicate grains range from 103 nm in QUE 99177 to 2018 nm in MIL 07687. The opaque grains show a wider variation, with average radii ranging from 15 nm in QUE 99177 to 219 nm in MIL07687. Our results indicate that, in contrast to CP‐IDPs, the size distribution of matrix components of these primitive meteorites cannot be explained by aerodynamic sorting that took place prior to accretion. We conclude that any evidence of sorting is likely to have been lost due to a greater variety and degree of processing experienced on these primitive chondrites than on cometary parent bodies.

The case for stand management guidelines as dynamic as global change: Aspen forest stockings of the western Great Lakes

Since the development of contemporary stocking techniques a century ago, the combination of climatic, atmospheric, financial, and social factors that determine forest management strategies have changed, altering aspen stand dynamics in the western Great Lakes, USA. Despite this, aspen management is still informed by 1970s management guides that are based on 1920s inventories; hence, a century exists between the data that underlie current management guidelines and current stand conditions. We hypothesized that current aspen stands may support higher stocking and height growth than nearly a century ago at relatively similar age and site indices, due to increased atmospheric CO2 concentrations and fertilization, intensive coppice harvests, and other factors. To explore this question, we compared historic aspen observations with comparable contemporary data from the USDA Forest Service’s Forest Inventory and Analysis program. The results show increased stand stocking levels as well as increased height growth of aspen throughout the region over the historic inventory data. Although other controlled experimental studies support the hypothesis of increased carbon fertilization altering aspen size-density relationships, our study is the first to examine an empirical application to forest management guides. Our results suggest a comprehensive reevaluation of aspen growth dynamics under contemporary environmental conditions is warranted. We highlight the need to assess the value of current stocking standards in an era of increasingly variable environmental conditions and to reimagine a more dynamic, responsive, and predictive approach to guide forest management for future application as global change may accelerate.

Diverse mangroves deviate from other angiosperms in their genome size, leaf cell size and cell packing density relationships.

While genome size limits the minimum sizes and maximum numbers of cells that can be packed into a given leaf volume, mature cell sizes can be substantially larger than their meristematic precursors and vary in response to abiotic conditions. Mangroves are iconic examples of how abiotic conditions can influence the evolution of plant phenotypes. Here, we examined the coordination between genome size, leaf cell sizes, cell packing densities and leaf size in 13 mangrove species across four sites in China. Four of these species occurred at more than one site, allowing us to test the effect of climate on leaf anatomy. We found that genome sizes of mangroves were very small compared to other angiosperms, but, like other angiosperms, mangrove cells were always larger than the minimum size defined by genome size. Increasing mean annual temperature of a growth site led to higher packing densities of veins (Dv) and stomata (Ds) and smaller epidermal cells but had no effect on stomatal size. In contrast to other angiosperms, mangroves exhibited (1) a negative relationship between guard cell size and genome size; (2) epidermal cells that were smaller than stomata; and (3) coordination between Dv and Ds that was not mediated by epidermal cell size. Furthermore, mangrove epidermal cell sizes and packing densities covaried with leaf size. While mangroves exhibited coordination between veins and stomata and attained a maximum theoretical stomatal conductance similar to that of other angiosperms, the tissue-level tradeoffs underlying these similar relationships across species and environments were markedly different, perhaps indicative of the unique structural and physiological adaptations of mangroves to their stressful environments.

Estimating maximum stand density for mixed-hardwood forests among various physiographic zones in the eastern US

Quantifying maximum stand density is important to evaluate the potential stand density of the target population in forest management. However, most of the past research in the eastern US was mainly focused on planted monocultures, coniferous forests, a few commercially important species at the stand level, or in a particular geographic region. This study aimed to estimate the maximum stand density for mixed-hardwood forests across physiographic zones in the eastern US between two decades (1996–2009 and 2010–2021). Data used in analyses were collected from the US national forest inventory established and maintained by the USDA Forest Service’s Forest Inventory and Analysis (FIA) program.Results showed that the slope of the self-thinning lines varied among forest types. Estimating maximum stand density index (SDImax) from size-density relationships produced more precise estimates than using SDI-size curves. Among all forest types, elm-ash-cottonwood (Ulmus-Fraxinus-Populus) showed consistent SDImax estimates whereas other forest types varied by regions. New England had considerably higher SDImax in aspen-birch (Populus-Betula), oak-hickory (Quercus-Carya) and oak-pine (Quercus-Pinus) forests than other physiographic zones. Most of the combinations showed consistent SDImax between two time periods. Only six combinations showed a significant gain (4–14% increase), which was likely driven by the growth of the same dominant species groups. The findings of this work provided not only additional insights of maximum stand density in the region, but also a methodology for forest ecologists and managers to quantify SDImax for a variety of forest types.

Coexistence, Energy, and Trophic Cascade in a Three-Level Food Chain Integrating Body Sizes

Predation is a biological interaction that influences demographic patterns by modifying community structure. In the current ecological crisis, there is a need to better understand the conditions of coexistence between predators, prey and their resources. The body size is considered a key feature to explain community-scale phenomena, energetic, and evolutionary constraints. This raises the question of how species body size directly or indirectly affects the demographic patterns that enable coexistence. Considering the above, we conducted a theoretical study that implements a Rosenzweig-MacArthur type model, which represents a three-level chain that integrates body sizes and includes a Holling type I functional response. In this model, we characterize coexistence through body size-dependent net reproductive rates. Our results suggest that the body sizes of consumer species strongly affect the size-density relations and energy requirements. We obtain the negative relationship between body size and density of intermediate consumers and discuss the energy equivalence rule. Furthermore, larger predators have a more significant impact on the intensity of the trophic cascade than smaller predators. Finally, we discuss potential extensions and applications of our modeling approach.

Climate, site conditions, and stand characteristics influence maximum size-density relationships in Korean red pine (Pinus densiflora) and Mongolian oak (Quercus mongolica) stands, South Korea

This study examines the effects of climate, site index and structural diversity on maximum size-density relationships (MSDRs) for Korean red pine (Pinus densiflora Siebold & Zucc.) and Mongolian oak (Quercus mongolica Fisch. ex Ledeb.) which are widely distributed and abundant across South Korea. We used data collected between 2006 and 2015 from the Korean National Forest Inventory and stochastic frontier function regression to develop static self-thinning lines (STLs) for pure pine, pure oak, and pine-oak mixed-species stands. Climate variables, site condition (e.g., site index), and stand characteristics (e.g., structural diversity and pine proportion) were applied to the STLs to examine the factors affecting MSDRs and the effects of climate on MSDRs. Our results indicate that the slope and intercept values differed significantly between the three stand types, with the pine STL being steeper than other STLs. Degree days above 18 °C in spring (DD18_sp), degree days above 5 °C in spring (DD5_sp), and annual heat moisture index (AHM) mainly influenced the position of STLs. Increases in these climate variables (e.g., warmer and drier conditions) reduce maximum densities owing to increased evapotranspiration and water stress in stands. Increasing site index (SI) was associated with an upward shift in the position of the STL for pine, and the result shows that better site quality can improve carrying capacity and increase stand stocking. However, high stand stocking can encourage tree competition with increasing dryness and reduce maximum stocking. Higher stand structural diversity caused an upward shift in all STLs, and the effect of climate on the STLs of different structural diversities varied with stand type. Structurally diverse stands can stock more trees in their stands owing to efficient space use, especially with respect to shade tolerant species. Nonetheless, under drier conditions, trees in dense stands experience severe competition, and their carrying capacity decreases. Our results suggest that it is important to include stand density control in forest management plans to prepare for global warming in South Korea.

Relative density of United States forests has shifted to higher levels over last two decades with important implications for future dynamics

Tree size-density dynamics can inform key trends in forest productivity along with opportunities to increase ecosystem resiliency. Here, we employ a novel approach to estimate the relative density (RD, range 0–1) of any given forest based on its current size-density relationship compared to a hypothetical maximum using the coterminous US national forest inventory between 1999 and 2020. The analysis suggests a static forest land area in the US with less tree abundance but greatly increased timber volume and tree biomass. Coupled with these resource trends, an increase in RD was identified with 90% of US forest land now reaching a biologically-relevant threshold of canopy closure and/or self-thinning induced mortality (RD > 0.3), particularly in areas prone to future drought conditions (e.g., West Coast). Notably, the area of high RD stands (RD > 0.6) has quintupled over the past 20 years while the least stocked stands (RD < 0.3) have decreased 3%. The evidence from the coterminous US forest RD distribution suggest opportunities to increase live tree stocking in understocked stands, while using density management to address tree mortality and resilience to disturbances in increasingly dense forests.

Site carrying capacity of Norway spruce and Scots pine stands has increased in Germany and northern Europe

The maximum size-density relationship describes site carrying capacity, i.e., the maximum number of trees of a given size that can be stocked per unit area (self-thinning line). We analysed whether the self-thinning lines of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) have remained unchanged over time in South Germany, Norway and Finland, i.e., over a wide climatic gradient from Central Europe up to the Arctic circle. The analyses are based on long-term growth and yield experiments measured on individual tree basis over several decades, the oldest experiments established during the early 20th century. The stochastic frontier analysis was used to analyse changes in the species-specific self-thinning lines. The results show that the self-thinning lines have shifted upwards over time in all the regions. Thus, currently stands sustain higher stand densities than in the past. The increase of the maximum density for a given average stem size was more pronounced for pine than for spruce, but similar in all studied geographical regions. In addition, increasing site index was associated with increasing site carrying capacity for spruce and pine in all regions. The results imply that environmental changes have altered site properties in similar fashion across the whole study region. In practical forestry, increased site carrying capacity will reduce mortality and loss of growing stock.

Macroecological patterns of forest structure and allometric scaling in mangrove forests

AbstractAimMangrove wetlands span broad geographical gradients, resulting in functionally diverse tree communities. We asked whether latitudinal variation, allometric scaling relationships and species composition influence mangrove forest structure and biomass allocation across biogeographical regions and distinct coastal morphologies.LocationGlobal.Time periodPresent.Major taxa studiedMangrove ecosystems.MethodsWe built the largest field‐based dataset on mangrove forest structure and biomass to date (c. 2,800 plots from 67 countries) to address macroecological questions pertaining to structural and functional diversity of mangroves spanning biogeographical and coastal morphology gradients. We used frequentist inference statistics and machine learning models to determine environmental drivers that control biomass allocation within and across mangrove communities globally.ResultsAllometric scaling relationships and forest structural complexity were consistent across biogeographical and coastal morphology gradients, suggesting that mangrove biomass is controlled by regional forcings rather than by latitude or species composition. For instance, nearly 40% of the global variation in biomass was explained by regional climate and hydroperiod, revealing nonlinear thresholds that control biomass accumulation across broad geographical gradients. Furthermore, we found that ecosystem‐level carbon stocks (average 401 ± 48 MgC/ha, covering biomass and the top 1 m of soil) varied little across diverse coastal morphologies, reflecting regional bottom‐up geomorphic controls that shape global patterns in mangrove biomass apportioning.Main conclusionsOur findings reconcile views of wetland and terrestrial forest macroecology. Similarities in stand structural complexity and cross‐site size–density relationships across multiscale environmental gradients show that resource allocation in mangrove ecosystems is independent of tree size and invariant to species composition or latitude. Mangroves follow a universal fractal‐based scaling relationship that describes biomass allocation for several other terrestrial tree‐dominated communities. Understanding how mangroves adhere to these universal allometric rules can improve our ability to account for biomass apportioning and carbon stocks in response to broad geographical gradients.

A macroecological perspective on the fluctuations of exploited fish populations

The natural variability of fish populations is increased by exploitation, but the specific mechanisms driving this variability are still debated. We propose a macroscopic approach combining the size-density relationship and Taylor’s law to predict the temporal variance of exploited and unexploited fish populations. Using information from 11 years of fishery-independent abundance surveys, we showed that the body-size dependence of the variance of exploited (targeted) and unexploited (non-targeted or bycatch) fish populations can be accurately predicted. Targeted fish populations showed a variability that was 2 orders of magnitude greater than that of non-targeted fish populations. Such variability was explained solely by the higher relative abundance of the former, regardless of their specific trophic position, while aggregated community fluctuation was lower in a high trophic position group. This study showed the usefulness of the macroscopic approach to predict fish variability and fishing effect in the whole community. This approach is complementary to other modeling strategies and seems to be useful in tackling the problem of variability in population fluctuations of exploited fish, particularly in cases where specific details of the interacting species are lacking.

Rethinking maximum stand basal area and maximum SDI from the aspect of stand dynamics

The maximum stand basal area (BA) and maximum stand density index (SDI) are often used to express stand carrying capacity in forestry. But their definitions are inconsistent in the literature. The maximum stand BA in most previous studies is associated with an upper boundary for a population of stands and is commonly derived from maximum size-density relationships (MSDRs). The maximum stand BA implied by MSDRs, under the assumption that stands attain maximum BA while attaining maximum SDI, is non-decreasing and divergent. We defined the maximum stand BA and maximum SDI for individual stands based on their BA and SDI development behaviors. Based on the mathematical relationships among stand BA, SDI, thinning, and quadratic mean diameter trajectories and their observed full trajectories in 551 unthinned plots selected from six long-term loblolly pine experimental studies, we theoretically and empirically proved that stands would achieve their maximum BA only after reaching their maximum SDI. The general mean maximum stand BA and maximum SDI for loblolly pine in the southern US were 46.2 m2 ha−1 and 1002 trees ha−1, respectively, and both showed significant variation (30.2–61.7 m2 ha−1 and 600–1410 trees ha−1, respectively). With the information of site quality, initial density and silvicultural treatments, our developed models could estimate the magnitude and timing of maximum stand BA for loblolly pine stands. Insights into individual stand BA and SDI trajectories provide more information for developing site specific silvicultural prescriptions.