Leaf nitrogen distribution and whole canopy photosynthetic carbon gain in herbaceous stands

The amount of photosynthetically-active photon flux density incident upon a leaf and the nitrogen content of that leaf strongly affect the photosynthetic carbon gain of that leaf. Therefore, the canopy structure of a stand, affecting the light climate in the canopy, and the leaf nitrogen distribution pattern in the canopy, affect the carbon gain of the whole canopy. This review discusses the results of studies directed to this problem and obtained so far in open and in dense canopies of stands of herbaceous, monocotyledonous or dicotyledonous, plants in their growing or flowering stages. It is found that the leaf nitrogen distribution pattern in the canopy is vertically non-uniform, and in dense stands more strongly so than in open stands. The leaf nitrogen distribution pattern in most canopies closely approaches an optimal pattern in that it maximizes whole canopy potential carbon gain as calculated for the actual total leaf nitrogen content and leaf area index of the stand. The resulting increase in potential carbon gain as compared to a uniform leaf nitrogen distribution pattern is considerable and it is larger in dense stands than in open stands. For at least some dense stands simulation studies show that with the available total leaf nitrogen content, whole canopy carbon gains could still be considerable higher had a lower leaf area index been developed.     

The vertical distribution of nitrogen and photosynthetic activity at different plant densities in Carex acutiformis

Shoots of the monocotyledonous perennial Carex acutiformis were grown in open (28 shoots m⁻²) and dense stands (280 shoots m⁻²). For fully grown stands the distribution of relative PPFD and leaf nitrogen per unit leaf area over canopy depth was determined. Light response of photosynthesis was measured on leaf segments sampled at various heights in the stands. Relations between parameters of these curves and leaf nitrogen were investigated. Simulations showed that in the open stand daily canopy photosynthesis was not affected by nitrogen redistribution in the canopy. For the dense stand however, a uniform nitrogen distribution would lead to only 73% of the maximum net carbon gain by the stand under optimal nitrogen distribution. The actual canopy photosynthesis was only 7% less than this theoretical maximum; the actual nitrogen distribution of the dense stand clearly tended to the optimal distribution. The vertical pattern of the nitrogen distribution was to a large extent determined by the minimum leaf nitrogen content. The relatively high minimum leaf nitrogen content found for Carex leaves may perhaps be necessary to maintain the physiological function of the basal parts of the leaves.     

Maximizing daily canopy photosynthesis with respect to the leaf nitrogen allocation pattern in the canopy

Summary A model of daily canopy photosynthesis was constructed taking light and leaf nitrogen distribution in the canopy into consideration. It was applied to a canopy of Solidago altissima. Both irradiance and nitrogen concentration per unit leaf area decreased exponentially with increasing cumulative leaf area from the top of the canopy. The photosynthetic capacity of a single leaf was evaluated in relation to irradiance and nitrogen concentration. By integration, daily canopy photosynthesis was calculated for various canopy architectures and nitrogen allocation patterns. The optimal pattern of nitrogen distribution that maximizes the canopy photosynthesis was determined. Actual distribution of leaf nitrogen in the canopy was more uniform than the optimal one, but it realized over 20% more photosynthesis than that under uniform distribution and 4.7% less photosynthesis than that under the optimal distribution. Redeployment of leaf nitrogen to the top of the canopy with ageing should be more effective in increasing total canopy photosynthesis in a stand with a dense canopy than in a stand with an open canopy.     

Canopy structure and nitrogen distribution in dominant and subordinate plants in a dense stand of Amaranthus dubius L. with a size hierarchy of individuals

The objective was to investigate how nitrogen allocation patterns in plants are affected by their vertical position in the vegetation (i.e. being either dominant or subordinate). A garden experiment was carried out with Amaranthus dubius L., grown from seed, in dense stands in which a size hierarchy of nearly equally aged individuals had developed. A small number of dominant plants had most of their leaf area in the highest layers of the canopy while a larger number of subordinate plants grew in the shade of their dominant neighbours. Canopy structure, vertical patterns of leaf nitrogen distribution and leaf photosynthetic characteristics were determined in both dominant and subordinate plants. The light distribution in the stands was also measured. Average N contents per unit leaf area (total canopy nitrogen divided by the total leaf area) were higher in the dominant than in the subordinate plants and this was explained by the higher average MPA (leaf dry mass per unit area) of the dominant plants. However, when expressed on a weight basis, average N contents (LNC_av; total canopy N divided by the total dry weight of leaves) were higher in the subordinate plants. It is possible that these higher LNC_av values reflect an imbalance between carbon and nitrogen assimilation with N uptake exceeding its metabolic requirement. Leaf N content per unit area decreased more strongly with decreasing relative photon flux density in the dominant than in the subordinate plants showing that this distribution pattern can be different for plants which occupy different positions in the light gradient in the canopy. The amount of N which is reallocated from the oldest to the younger, more illuminated leaves higher up in the vegetation may depend on the sink strength of the younger leaves for nitrogen. In the subordinate plants, constrained photosynthetic activity caused by shading might have reduced the sink intensity of these leaves.     

Importance of the gradient in photosynthetically active radiation in a vegetation stand for leaf nitrogen allocation in two monocotyledons

Carex acutiformis and Brachypodium pinnatum were grown with a uniform distribution of photosynthetic photon flux density (PFD) with height, and in a vertical PFD gradient similar to the PFD gradient in a leaf canopy. Distribution of organic leaf N and light-saturated rates of photosynthesis were determined. These parameters were also determined on plants growing in a natural vegetation stand. The effect of a PFD gradient was compared with the effect of a leaf canopy. In Brachypodium, plants growing in a vegetation stand had increasing leaf N with plant height. However, distribution of leaf N was not influenced by the PFD gradient treatment. The gradient of leaf N in plants growing in a leaf canopy was not due to differences within the long, mostly erect, leaves but to differences between leaves. In Carex, however, the PFD gradient caused a clear increase of leaf N with height in individual leaves and thus also in plants. The leaf N gradient was similar to that of plants growing in a leaf canopy. Leaf N distribution was not affected by nutrient availability in Carex. In most cases, photosynthesis was positively related to leaf N. Hence, lightsaturated rates of photosynthesis increased towards the top of the plants growing in leaf canopies in both species and, in Carex, also in the PFD gradient, thus contributing to increased N use efficiency for photosynthesis of the whole plant. It is concluded that in Carex the PFD gradient is the main environmental signal for leaf N allocation in response to shading in a leaf canopy, but one or more other signals must be involved in Brachypodium.     

Light acquisition and use by individuals competing in a dense stand of an annual herb, Xanthium canadense

The importance of light acquisition and utilization by individuals in intraspecific competition was evaluated by determining growth and photosynthesis of individual plants in a dense monospecific stand of an annual, Xanthium canadense. Photosynthesis of individual plants in the stand was calculated using a canopy photosynthesis model in which leaf photosynthesis was assumed to be function of leaf nitrogen content and light availability. The estimated photosynthetic rates of individuals were strongly correlated with the measured growth rates. Photosynthetic rates per unit aboveground mass (RPR, relative photosynthetic rate) increased with increasing aboveground mass, suggesting asymmetric (one-sided) competition in the stand. However, larger individuals had similar RPRs, suggesting symmetric (two-sided) competition. These results were consistent with the observation that size inequality over the whole stand increased with growth, but it remained stable among the larger individuals. The RPR of an individual was calculated as the product of absorbed photon flux per unit aboveground mass (Φ_mass) and light use efficiency (LUE, photosynthesis per unit absorbed photon flux). Φ_mass indicates the efficiency of light acquisition, and was higher in larger individuals in the stand, while LUE was highest in individuals with intermediate aboveground mass. LUE depends on leaf nitrogen content. At an early stage, leaf nitrogen contents of smaller individuals were similar to those that maximize LUE. Light availability to smaller individuals decreased as they grew, while their nitrogen contents did not change markedly, which decreased their LUE. We concluded that asymmetric competition among individuals in the stand resulted mainly from lower efficiencies in both light acquisition and light use by smaller individuals. Received: 31 January 1998 / Accepted: 12 November 1998     

Canopy structure,nitrogen distribution and whole canopy photosynthetic carbon gain in growing and flowering stands of tall herbs

Using a combination of mathematical modeling and field studies we showed that in dense stands of growing herbaceous plants the vertical pattern of leaf nitrogen distribution resembles the pattern of mean light attenuation in the stand and hence tends to maximize total daily photosynthetic carbon gain of the whole stand. Flowering represents a strong sink of nitrogen away from the photosynthetic apparatus and in herbs like Solidago altissima it induces leaf shedding. We studied both the effect of nitrogen reallocation and leaf shedding on the whole canopy photosynthesis and changes in leaf nitrogen distributions in stands moving from the growing to the flowering stage. Despite a decrease in leaf area index and total nitrogen available for photosynthesis in the flowering stand, the leaf nitrogen distribution here also leads to an almost maximum canopy photosynthesis. In both the growing and the flowering stands the leaf area index was higher than calculated optimum values. It is pointed out that this should not necessarily be interpreted as non-adaptive.     

Carbon balance in a monospecific stand of an annual herb <Emphasis Type="Italic">Chenopodium album</Emphasis> at an elevated CO<Subscript>2</Subscript> concentration

Elevated CO₂ enhances carbon uptake of a plant stand, but the magnitude of the increase varies among growth stages. We studied the relative contribution of structural and physiological factors to the CO₂ effect on the carbon balance during stand development. Stands of an annual herb Chenopodium album were established in open-top chambers at ambient and elevated CO₂ concentrations (370 and 700 μmol mol⁻¹). Plant biomass growth, canopy structural traits (leaf area, leaf nitrogen distribution, and light gradient in the canopy), and physiological characteristics (leaf photosynthesis and respiration of organs) were studied through the growing season. CO₂ exchange of the stand was estimated with a canopy photosynthesis model. Rates of light-saturated photosynthesis and dark respiration of leaves as related with nitrogen content per unit leaf area and time-dependent reduction in specific respiration rates of stems and roots were incorporated into the model. Daily canopy carbon balance, calculated as an integration of leaf photosynthesis minus stem and root respiration, well explained biomass growth determined by harvests (r ² = 0.98). The increase of canopy photosynthesis with elevated CO₂ was 80% at an early stage and decreased to 55% at flowering. Sensitivity analyses suggested that an alteration in leaf photosynthetic traits enhanced canopy photosynthesis by 40–60% throughout the experiment period, whereas altered canopy structure contributed to the increase at the early stage only. Thus, both physiological and structural factors are involved in the increase of carbon balance and growth rate of C. album stands at elevated CO₂. However, their contributions were not constant, but changed with stand development.     

Spatial heterogeneity of photosynthetic photon flux density in the canopy ofMiscanthus sinensis

Spatial variation in photosynthetic photon flux density (PPFD) was investigated in detail at different heights within the canopy of aMiscanthus sinensis grassland to evaluate the light environment of microsites for establishment of heliophilic tree seedlings. Highly heterogeneous patterns of light distribution were revealed within the apparently uniform grass canopies, especially under direct light. The frequency distribution patterns of relative PPFD (RPFD) were compared among different solar and sky conditions. With increasing height in the canopy, the mean RPFD value and standard deviation (SD) increased, while the skewness and kurtosis of the distribution decreased. The mean RPFD and SD were higher, especially at higher solar elevation angles, under direct light than those under diffuse light conditions. The frequency distribution of RPFD was more platykurtic under direct light and at higher solar elevation angles.     

Light field heterogeneity among tussock grasses: Theoretical considerations of light harvesting and seedling establishment in tussocks and uniform tiller distributions

Although the tussock growth form of caespitose graminoids is widespread, the effect of this growth form on light interception and carbon gain of tillers has received little attention. Daily incident photosynthetic photon flux density (PFD_inc) and carbon gain in monospecific stands of tussock grasses were compared with those of a hypothetical distribution with the equivalent tiller density per total ground area, but evenly distributed rather than clumped in tussocks. This was computed for two tussock grasses Pseudoroegneria spicata (Pursh) A. Löve (bluebunch wheatgrass) and Agropyron desertorum (Fisch, ex Link) Schult. (creasted wheatgrass) at different plant densities. Daily PFD_inc and net photosynthesis (A) were greater if tillers were distributed uniformly rather than clumped in tussocks, except when the density of tussocks was so great as to approach a uniform canopy. When tussock density per ground area was low, much of the difference between tussock and uniform tiller densities in PFD_inc and A was due to shading within the tussocks; up to 50–60% of the potential carbon gain was lost in A. desertorum due to shading within tussocks. In a matrix of tussocks, the light field for establishing seedlings was very heterogeneous; potential A ranged from 7 to 96% relative to an isolated seedling. The mean of daily PFD_inc and A for seedlings in a tussock stand were nearly identical to the values in corresponding stands of uniform tiller distributions. It is hypothesized that the loss of A resulting from clumping tillers into tussocks is offset by benefits of protecting sequestered belowground resources from invasion by seedlings of competitors.     

Relationships between leaf nitrogen and limitations of photosynthesis in canopies of Solidago altissima

Vertical distribution patterns of light, leaf nitrogen, and leaf gas exchange through canopies of the clonal perennial Solidago altissima were studied in response to mowing and fertilizer application in a field experiment. Consistent with the distribution of light, average leaf nitrogen content followed a `smooth' exponential decline along the fertilized stands both in control and mown plots. The nitrogen profile along the unfertilized stands in mown plots, however, was `disrupted' by high-nitrogen leaves at the top of shorter ramets that only reached intermediate strata of the canopies. Hence, in these stands leaf nitrogen was significantly increased in short ramets compared with tall ramets for a given light environment, suggesting suboptimal stand structure but not necessarily suboptimal single-ramet architecture. However, at least under the climatic conditions observed during measurements, such disrupture had no substantial effect on stand productivity: model calculations showed that vertical distribution patterns of leaf nitrogen along ramets only marginally influenced the photosynthetic performance of ramets and stands. This is explained by the observed photosynthesis-nitrogen relationship: the rate of photosynthesis per unit amount of leaf nitrogen did not increase with leaf nitrogen content even under saturating light levels indicating that leaf photosynthesis was not nitrogen limited during the measurement periods. Nevertheless, our study indicates that consideration of how architecture(s) of adjacent individual plants interact could be essential for a better understanding of the trade-offs between individual and canopy characteristics for maximizing carbon gain. Such trade-offs may end up in a suboptimal canopy structure, which could not be predicted and understood by classical canopy optimization models.     

Biomass Allocation and Light Partitioning Among Dominant and Subordinate Individuals inXanthium canadenseStands

Patterns of above-ground biomass allocation and light captureby plants growing in dense stands or in isolation were studiedin relation to their height. A canopy model was developed tocalculate light absorption by individual plants. This modelwas combined with data on canopy structure and patterns of biomassallocation for solitary plants and for plants of different heightsin dense mono-specific stands of the dicotyledonous annualXanthiumcanadenseMill. There were four stands, and stand height increasedwith age and nutrient availability. The allometric relationshipbetween height and mass differed considerably between plantsin stands and those growing in isolation and also between plantsof different heights within stands. The proportion of shootmass in leaf laminae (LMR) decreased with increasing plant height,but solitary plants had a higher LMR than competing plants ofthe same height. Thus, in contrast to previous assumptions,LMR of competing plants is not strictly determined by biomechanicalconstraints but results from a plastic shift in biomass allocationin response to competition. Average leaf area per unit leafmass (SLA) decreased with increasing photosynthetic photon fluxdensity (PPFD) independent of nutrient availability. Consequently,taller, more dominant plants in stands had a lower leaf arearatio (LAR: LAR=LMRxSLA) than shorter, more subordinate plants.Dominant plants absorbed more light both per unit leaf area(     

Nitrogen use efficiency in instantaneous and daily photosynthesis of leaves in the canopy of a Solidago altissima stand

Photosynthetic capacity was measured on detached leaves sampled in a canopy of Solidago altissima L. Non-rectangular hyperbola fitted the light response curve of photosynthesis and significant correlations were observed between leaf nitrogen per unit area and four parameters which characterize the light-response curve. Using regressions of the parameters on leaf nitrogen, a model of leaf photosynthesis was constructed which gave the relationships between leaf nitrogen, photon flux density (PFD) and photosynthesis. Curvilinear relations were obtained between leaf nitrogen and photosynthetic rate on both an instantaneous and a daily basis. Nitrogen use efficiency (NUE, photosynthesis per unit leaf nitrogen) was calculated against leaf nitrogen under varying PFDs. The optimum nitrogen content per unit leaf area that maximizes NUE shifted to higher values with increasing PFD. Field measurements of PFD showed high positive correlations between the distribution of leaf nitrogen in the canopy and relative PFD. The predicted optimum leaf nitrogen content for each level in the canopy, to achieve maximized NUE during a clear day, was close to the actual nitrogen distribution as found through sampling.     

Population life-cycle and stand structure in dense and open stands of the introduced tall herb <Emphasis Type="Italic">Heracleum mantegazzianum</Emphasis>

Populations of the introduced Heracleum mantegazzianum consist of dense central stands, which gradually give way to open stands towards the margins. To analyse whether open stands are due to unsuitable conditions or represent the invading front for further spread, we studied life-cycle, population dynamics, stand structure and soil conditions of open and dense stands over two transition periods. Populations decreased during the first interval but increased after the extremely dry and warm summer of 2003 during the second interval. Open stands had shorter generation times, lower height, smaller proportions of small individuals and were less in equilibrium with the environment than dense stands. In open stands, growth to higher stages was most important, while in dense stands delayed development (self-loops) had a strong effect on population growth; stasis and fecundity contributed most to the difference in λ between stand types. By petiole extension H. mantegazzianum may raise its leaves just above the resident vegetation. Therefore, younger stages develop faster in open stands, whereas strong competition by conspecific adults leads to longer generation times and a higher proportion of small individuals in dense stands. Disturbance due to extreme climatic conditions in summer 2003 equalised population dynamics of both stand types. Life-cycle variation between stand types makes it difficult to infer simple management rules. However, our data suggest that small and/or open stands of H. mantegazzianum may eventually serve as initials for further spread after land-use changes, whereas dense stands are stable and may represent sources of propagules.     

Optimal leaf area indices in C3 and C4 mono- and dicotyledonous species at low and high nitrogen availability

From an analytical model it was shown that for a given total amount of nitrogen in the canopy, there exists an optimal leaf area index (LAI), and therefore an optimal average leaf introgen content, at which canopy photosynthesis is maximal. If the LAI is increased above this optimum, increased light interception will not compensate for reduction in photosynthetic capacity of the canopy resulting from reduced leaf nitrogen contents. It was further derived from the model that the value of the optimal LAI increases with the photosynthetic nitrogen use efficiency (PNUE) and decreases with the canopy extinction coefficient for light (K_L) and incident photon flux density (PFD) at the top of the canopy. These hypotheses were tested on dense stands of species with different photosynthetic modes and different architectures. A garden experiment was carried out with the C₄ monocot sorghum ( Sorghum bicolor [L.] Moensch cv. Pioneer), the C₃ monocot rice ( Oryza sativa L. cv. Araure 4), the C₄ dicot amaranth ( Amaranthus cruentus L. cv. K113) and the C₃ dicot soybean ( Glycine max [L.] Merr. cv. Williams) at two levels of nitrogen availability.
The C₄ species had higher PNUEs than the C₃ species while the dicots formed stands with higher extinction coefficients for light and had lower PNUEs than the monocots. The C₄ and monocot species were found to have formed more leaf area per unit leaf nitrogen (i.e., had lower leaf nitrogen contents) than the C₃ and dicot species, respectively. These results indicate that the PNUE and the extinction coefficient for light are important factors determining the amount of leaf area produced per unit nitrogen as was predicted by the model.     

Carbon gain in a multispecies canopy: the role of specific leaf area and photosynthetic nitrogen-use efficiency in the tragedy of the commons

Models have been formulated for monospecific stands in which canopy photosynthesis is determined by the vertical distribution of leaf area, nitrogen and light. In such stands, resident plants can maximize canopy photosynthesis by distributing their nitrogen parallel to the light gradient, with high contents per unit leaf area at the top of the vegetation and low contents at the bottom. Using principles from game theory, we expanded these models by introducing a second species into the vegetation, with the same vertical distribution of biomass and nitrogen as the resident plants but with the ability to adjust its specific leaf area (SLA, leaf area:leaf mass). The rule of the game is that invaders replace the resident plants if they have a higher plant carbon gain than those of the resident plants. We showed that such invaders induce major changes in the vegetation. By increasing their SLA, invading plants could increase their light interception as well as their photosynthetic nitrogen-use efficiency (PNUE, the rate of photosynthesis per unit organic nitrogen). By comparison with stands in which canopy photosynthesis is maximized, those invaded by species of high SLA have the following characteristics: (1) the leaf area index is higher; (2) the vertical distribution of nitrogen is skewed less; (3) as a result of the supra-optimal leaf area index and the more uniform distribution of nitrogen, total canopy photosynthesis is lower. Thus, in dense canopies we face a classical tragedy of the commons: plants that have a strategy to maximize canopy carbon gain cannot compete with those that maximize their own carbon gain. However, because of this strategy, individual as well as total canopy carbon gain are eventually lower. We showed that it is an evolutionarily stable strategy to increase SLA up to the point where the PNUE of each leaf is maximized.     

Temporal and spatial variations in leaf herbivory within a canopy of<Emphasis Type="Italic"> Fagus crenata</Emphasis>

This study investigated spatio-temporal variation in the leaf area consumed by insect herbivores within a canopy of Fagus crenata, with reference to the light conditions of leaf clusters. There was no clear relationship between photosynthetic photon flux density (PPFD) and consumed leaf area (CLA) in May, immediately after leaf flush, but CLA decreased with an increase in PPFD after June. Leaf mass per area, carbon concentration, C/N ratio, concentration of total phenolics, and condensed tannin concentration were higher in leaves under high light intensity than those of leaves under low light. On the other hand, the nitrogen concentration of leaves decreased as light availability increased. Consequently, within-tree variation in light availability affects the consumption of leaves by insect herbivores through temporal changes in leaf characteristics.     

Acclimation of photosynthesis in canopies: models and limitations

Within a time-scale of several days photosynthesis can acclimate to light by variation in the capacity for photosynthesis with depth in a canopy or by variation in the stoichiometry of photosynthetic components at each position within the canopy. The changes in leaf photosynthetic capacity are usually related to and expressed as changes in leaf nitrogen content. However, photosynthetic capacity and leaf nitrogen never match exactly the photon flux density (PFD) gradient within a canopy. As a result, photosynthetic light use efficiency, i.e. photosynthetic performance per incident PFD, increases considerably from the top of the canopy to the lower shaded part. Many of existing optimisation models fail to express the actual pattern of nitrogen or photosynthetic capacity distribution within a canopy. This failure occurs because these optimisation models do not consider that the quantitative aspect of photosynthesis acclimation is a whole plant phenomenon. Although turnover models, which describe the distribution of the photosynthetic apparatus within a canopy as a dynamic equilibrium between breakdown and regeneration of apparatus with respect to nitrogen availability, photosynthetic rate and export of carbohydrates, produce realistic results, these models require confirmation. The mechanism responsible for changes in the relative share of light-harvesting apparatus as acclimation to irradiance remains unknown. Ability of the photosynthetic apparatus to balance properly the light harvesting capacity with electron transport and biochemical capacities is limited. As a result of this fundamental limitation, photosynthetic light use efficiency always increases with increasing thickness of the photosynthetic apparatus.     

Canopy transpiration in a chronosequence of Central Siberian pine forests

Tree transpiration was measured in 28, 67, 204 and 383‐y‐old uniform stands and in a multicohort stand (140–430 y) of Pinus sylvestris ssp. sibirica Lebed. in Central Siberia during August 1995. In addition transpiration of three codominant trees was monitored for two years in a 130‐y‐old stand. All stands established after fire. Leaf area index (LAI) ranged between 0.6 (28‐y‐old stand) and 1.6 for stands older than 67‐y. Stand xylem area at 1.3 m height increased from 4 cm² m^?2 (28‐y) to 11.5 cm² m^?2 (67‐y) and decreased again to 7 cm² m^?2 in old stands. Above‐ground living biomass increased from 1.5 kg dry weight m^?2 (28‐y) to 14 kg dry weight m^?2 (383‐y). Day‐to‐day variation of tree transpiration in summer was dependent on net radiation, vapour pressure deficit, and soil water stress. Tree‐to‐tree variation of xylem flux was small and increased with heterogeneity in canopy structure. Maximum rates of xylem flux density followed the course of net radiation from mid April when a constant level of maximum rates was reached until mid September when low temperatures and light strongly reduced flux density. Maximum sap flux density (60 g m^?2 s^?1) and canopy transpiration (1.5 mm d^?1) were reached in the 67‐y stand. Average canopy transpiration of all age classes was 0.72 ± 0.3 mm d^?1. Canopy transpiration (E) was not correlated with LAI but related to stand sapwood area SA (E = ? 0.02 + 1.15SA R²) which was determined by stand density and tree sapwood area.