1. Introduction

Numerous experimental and natural studies show that few large trees (hereafter L-trees) in forests are sensitive to climate change (such as drought and heat) whereas small–medium trees (S-trees) are often considered resistant and resilient (Phillips et al., 2010; Bennett et al., 2015; Lindenmayer and Laurance, 2017; Meakem et al., 2018; de Lima et al., 2023). In forests, few L-trees, as compared to S-trees, are often considered the major reservoir of aboveground carbon stock (AGCS) which impose a dominant influence on environmental resources (Clark and Clark, 1996; Stephenson et al., 2014; Bastin et al., 2018; Lutz et al., 2018; Ali and Wang, 2021). Yet, challenges exist as the general insight is that the overruling effects of tree-based attributes (i.e., tree species richness and size inequality) of a few L-trees versus S-trees on forest functions such as AGCS, aboveground biomass (AGB) stock and productivity. The allometric and metabolic relationships might be justified by the overriding influences because L-trees hold large initial AGB due to their body size growth over time (Enquist et al., 1999; Poorter et al., 2015; Sheil et al., 2017; Lutz et al., 2018; Ali and Wang, 2021; Jucker et al., 2022). However, the functional trait-based attributes (i.e., multi-trait diversity and single-trait dominance) could provide further new insights into the tree-based attributes by linking allometric, physiological and metabolic processes to better understand the species' functional strategies of how and why L-trees overrule the effects of S-trees in regulating forest functions (Barbier et al., 2008; Bartels and Chen, 2013; Díaz et al., 2016; Ali and Wang, 2021).

In the tree-based concept, stand structural complexity (e.g., tree size inequality, stand density and stand structural diversity) is the powerful driver of AGCS or AGB stock compared to tree species diversity, which supports the niche complementarity effect based on the complementarity resource-use of coexisting species based on the individual tree size inequality (van der Plas, 2019). Nevertheless, in the trait-based concept, the functional traits have widely been recognized as the potential drivers of plant species co-occurrence processes by capturing tree species' functional strategies (i.e., resource-conservative versus resource-acquisitive) (Wright et al., 2004; Chave et al., 2009; Reich, 2014; Díaz et al., 2016). However, the bulk of earlier research has revealed that, in contrast to multi-trait diversity, dominant traits (i.e., those measured by the community-weight mean of a single trait) are more effective in driving AGB stock or AGCS, suggesting that the niche complementarity effect may not be as effective as the mass ratio effect (Conti and Díaz, 2013; Finegan et al., 2015; Poorter et al., 2015; Fotis et al., 2018; Aponte et al., 2020). Thus, the strong effects of tree size inequality, stand structural diversity and trait dominance on AGCS or AGB stock as compared to species and multi-trait diversity suggest that different-sized coexisting tree species might have different requirements for resource capture and use which in turn regulate forest functioning (Zhang and Chen, 2015; Fotis et al., 2018; Aponte et al., 2020). In this context, further studies have suggested that overstorey trees regulate AGCS, AGB stock and productivity better than understorey trees because few L-trees (which are mostly resource-acquisitive) are dominant in acquiring available resources in forests (Barbier et al., 2008; Bartels and Chen, 2013; Zhang et al., 2017; Lee et al., 2022). Although functionally and structurally dissimilar species are likely to coexist in a forest community as they have different niches and requirements for available resources, most of the studies have shown that understorey trees or S-trees tend to adopt a resource-conservative strategy to diminish competition with resource-acquisitive overstorey stratum or L-trees on nutrient-poor soils (Baker et al., 2009; Coomes et al., 2009; Bartels and Chen, 2010; Zhang et al., 2017; Lee et al., 2022).

The global literature review shows that L-trees regulate forest functioning through ecological mechanisms underlying abiotic and biotic conditions (Ali and Wang, 2021). The growing concept is that the tree-based attributes of few L-trees overrule the effects of S-trees (and even the whole-community effects) on forest AGCS, AGB stock and productivity (Ali et al., 2019; Bordin et al., 2021; Yuan et al., 2021). This mechanism might be understandable because L-trees (or overstorey trees in general) can greatly impose several competitive limitations on S-trees due to their high demand for light, water and soil nutrients (Barbier et al., 2008; Yuan et al., 2012; Bartels and Chen, 2013). As such, L-trees are generally considered to be resource-acquisitive in performance as compared to S-trees in a specific forest type (Bartels and Chen, 2013; Ali and Wang, 2021), even though L-trees are globally sensitive to climate change events due to hydraulic failure and carbon starvation (Phillips et al., 2010; Bennett et al., 2015; Meakem et al., 2018). Further recent attempts have been made to understand the dominant effects of L-trees versus S-trees on forest functions through the use of trait-based attributes for capturing tree species' functional strategies (i.e., resource-conservative versus resource-acquisitive) in forests (Bordin et al., 2021; Yuan et al., 2021). Yet, it remains unclear how the tree-based concept versus the trait-based concept advances our understanding of the multidimensional effects of L-trees versus S-trees on AGCS in forests. Also, this question cannot be simply answered as complexity exists in the threshold size quantification approaches for defining L-trees and S-trees in a forest community (Lutz et al., 2018; Ali and Wang, 2021). However, existing challenges for exploring multidimensional tree-based and trait-based BEF relationships in forests are assumed to be explained by taking the mean value of the threshold sizes across three alternative approaches, i.e., the fixed-diameter approach, the percentile approach and the AGC-ranked ordered approach, to defining L-trees and S-trees within each forest plot, i.e., we introduce the mean threshold approach (Fig. 1). In Iran's temperate deciduous forests, we addressed the following particular research questions using data on forest inventory, functional features and abiotic variables collected from 99 standard plots. (1) How are tree-based versus trait-based attributes of L-trees versus S-trees used to define the forest species co-occurrence processes? (2) What matters – L-trees, S-trees, and/or abiotic factors – in explaining variance in AGCS in forests under the tree-based concept versus the trait-based concept? (3) What are the most effective drivers –tree-based and/or tree-based attributes of L-trees and S-trees along with abiotic factors – of AGCS in strength, magnitude, and direction to determine the main underlying ecological mechanism? (4) Which concept – tree-based or trait-based, and which threshold size quantification – mean, percentile, fixed-diameter or AGC-ranked ordered – approach matter substantially in explaining AGCS? We hypothesize that tree species' functional strategies regulate AGCS by tree sizes in temperate deciduous forests across local scale environmental gradients. We expect that: 1) functional strategies, synergies and trade-offs across tree sizes may regulate plant species coexistence, even though L-trees matter considerably more than S-trees due to big-sized trees effects; 2) L-trees directly modulate the magnitude and strength of abiotic drivers, especially soil nutrients, on AGCS, and indirectly regulate S-trees structural attributes (i.e., growth and fitness) due to the big-sized trees, soil fertility, resource availability and heterogeneity effects; 3) nutrient-acquisition strategies of a few L-trees are the major determinant of AGCS due to the big-sized trees and the mass ratio effects; and eventually we expect 4) both tree-based and trait-based attributes of mean threshold approach may provide positive feedback for regulating higher AGCS through non-mutually exclusive ecological mechanisms (i.e., niche complementarity and mass ratio effects) governed by a few L-trees (i.e., big-sized trees effects).

2. Materials and methods 2.1. Research region, field data collection and lab experiments

This forest research was carried out in northwest Iran, which is located between the latitude of 37°36′31˝ to 37°44′40˝ N and the longitude of 48°35′17˝to 48°56′26˝ E) (Fig. S1). A humid temperate zone best describes the region's climate where the range of the annual average contemporary temperature is 5.9–14.5 ℃, while the range of the annual average contemporary precipitation is 676–1630.7 mm. Alfisols and Inceptisols are the two most common soil types (Kazempour Larsary et al., 2021).

To cover local forest communities or types over the studied temperate deciduous forests, 104 plots (each 20 m × 20 m = 400 m²) were designed and established along 28 altitudinal transects (Fig. S1b). Each forest plot's specific position (i.e., latitude and longitude) was determined using a portable Global Positioning System (GPS) whereas the plot's slope and aspect were measured with the SUUNTO clinometer. We calculated two indices of the topographic aspect, i.e., northness = cos (aspect) and eastness = sin (aspect). The elevation (Elev) of each plot was determined through the digital elevation models (DEM) in ArcGIS (v.10.8). The fieldwork and lab experiments were conducted in the summers (i.e., from June to August or September) of the 2018 and 2019 calendar years.

Following the well-defined forest inventory techniques, we measured the tree diameter-at-breast height (DBH), height, and crown dimensions of all known shrub and tree species (i.e., 3084 individuals) with DBH ≥ 1 cm (Cornelissen et al., 2003). In doing so, within each plot, the AGB (Kg) of each individual was quantified using multispecies allometric equations, which is based on DBH (cm), height (m) and species' wood density (g cm⁻³) (Table S1). The AGCS was computed by multiplying the AGB stock of each individual per species with its corresponding conversion factor (calculated through the dry combustion method; see Table S1). Plot-level AGCS (Mg ha⁻¹) was quantified by summing and scaling the AGCS of all individuals.

At the same time, we randomly selected around five healthy individuals from each tree and shrub species (29 species and 150 individuals) along a 1400 m altitudinal range and all individuals were measured for their DBH, height, and crown dimensions. After that, we collected 20–60 completely formed leaves with no obvious physical damage from each selected individual (i.e., approximately 6071 leaf samples). The total number of leaf samples of each specific species is provided in Table S2. In the field, the leaves were kept cool for further measurements in the laboratory (Cornelissen et al., 2003). The fresh leaf areas of 20–60 leaves were measured using ImageJ (http://www.nih.gov/), and then the species' mean leaf area was determined. Leaf dry mass was measured by drying leaf samples at 75 ℃ for 48 h, and then the specific leaf area (sla) and leaf dry matter content (ldmc) were calculated using the data of mean leaf dry mass and mean fresh leaf area. Also, wood samples were cut from the same five individuals per species, and then the ratio of the oven-dry mass to the volume of the wood sample, which was evaluated using the water displacement test protocol, was used to calculate the wood density (wd) (Cornelissen et al., 2003; Chave et al., 2009). The species' maximum height (h), a strong dominating stature trait in plant ecological strategies, was calculated using the top 95th percentile score on the species-wise pooled tree height data (Chave et al., 2009; Reich, 2014; Díaz et al., 2016).

During the fieldwork, we collected five soil samples, from the topsoil layer between 0 and 30 cm, from each corner and center of each plot across 104 forest plots, resulting in a total of 520 soil samples (Kazempour Larsary et al., 2021). To obtain the mixed soil sample within each plot, the five subsamples were mixed. Then, each composite soil sample was physically screened to remove items like coarse woody debris and obvious small roots. The air-dried composite soil samples were crushed in the lab and sieved using a 2-mm screen. Finally, Olsen's method (Olsen et al., 1954) and the modified Kjeldahl method (Bremner, 1996) were applied to measure soil available phosphorus and total nitrogen, respectively. The Orion Ionalyzer pH meter was used to find out the pH of the soil. With the use of a flame photometer, the pH 7.0 buffer solution consisting of 1.0 mol L-1 ammonium acetate was used to measure the soil's exchangeable potassium.

2.2. Threshold size quantification approaches

Although several threshold size quantification approaches exist for defining L-trees (mostly based on tree DBH) (Lindenmayer and Laurance, 2017; Lutz et al., 2018; Ali and Wang, 2021; de Lima et al., 2023), we put forward three main approaches based on multidimensional aspects of tree size, i.e., (1) the percentile approach to defining L-trees by integratively considering the 95th percentile of tree structural traits, i.e., tree DBH (large-diameter), height (tall-stature) and crown dimension (big-crown) across all individuals (Ali and Wang, 2021), (2) the AGC-ranked ordered approach according to the previous findings that revealed L-trees contribute much (i.e., nearly half or more) to the stand-level AGB at different spatial scales as well as across different forest ecosystems (Stephenson et al., 2014; Bastin et al., 2015; Lutz et al., 2018), and (3) the fixed-diameter approach to define the fixed threshold for L-trees by reaching at least three healthy individuals per species to measure the functional trait indices within each plot (Cornelissen et al., 2003). After that, we took the mean value of the three threshold sizes to define L-trees and S-trees within each forest plot, i.e., the mean threshold approach.

Specifically, in the percentile approach (1), we used the following quantification steps (see Fig. 1): (i) tree stem volume (TSV, m³) was calculated using the equation $ T S V=B A \times S H$, where BA was the basal area (m²) quantified as $ B A=\frac{\pi}{40000} D^2$; D is tree DBH (cm), and SH is the tree stem height (m) – the height of the first major tree branch from the ground; (ii) tree crown volume (TCV, m³) was calculated using the equation $ T C V=X \times Y \times Z$ where X and Y are the tree crown diameters (m) from east-west and north-south directions, and Z is the crown depth as the difference length between the total tree height and stem height; (iii) total tree size (TTS, m³) was calculated by taking the sum of tree crown volume (m³) and stem volume (m³); and then finally (iv) the top 95th percentile score of TTS was taken as to define the threshold size (based on the corresponding DBH value) for dividing tree data into L-trees and S-trees within each plot. The AGC-ranked ordered approach (2) included the following quantification steps: (i) we calculated the relative value of AGCS (in percentage) for each tree by dividing the total AGCS of the plot by the specific AGC value of each tree and then multiplying by 100; (ii) we arranged trees within each plot in descending order (i.e., from high to low AGCS) by relative AGCS value (%); (iii) we calculated the cumulative values based on the relative AGCS; and then finally (iv) we selected those trees as L-trees which cumulatively contributed ≥ 50% (in descending order) of AGCS (the corresponding DBH was recorded) to the plot-level AGCS whereas the remaining 50% trees were considered as the S-trees. In the fixed-diameter approach (3), we straightforwardly used the fixed threshold size (i.e., DBH ≥ 50 cm) for defining the L-trees whereas the remaining trees (i.e., DBH < 50 cm) were considered as the S-trees. Finally, in the mean threshold approach, we took the mean value of the three threshold sizes (based on the corresponding DBHs of the three approaches) to divide tree data into L-trees and S-trees within each plot, which we found as the most promising approach to cover the three quantification approaches for threshold sizes (see Fig. S2).

All L-trees and S-trees were identified as deciduous species but Ilex spinigera Loes (relative basal area = 0.11% ± 0.19%) was identified as the evergreen shrub species under the S-trees category (Table S3). Also, we used 99 forest plots (i.e., 2950 individuals) as 5 plots did not meet the requirements of the fixed-diameter threshold approach, and thus, we decided to exclude those 5 plots to keep consistency across approaches for comparable conclusions. To determine the mean functional traits of 150 individuals across four threshold size quantification approaches, we first divided those trees and shrubs into L-trees and S-trees according to the procedure described for each quantification approach (eight subgroups in total) and then the mean species-specific functional trait values of each subgroup were quantified across four approaches (Table S4). In the percentile approach, 29 species (i.e., 120 individuals) of S-trees and 13 species (i.e., 30 individuals) of L-trees were identified according to the top 95th percentile score of TTS within each species. In the AGC-ranked ordered approach, 29 species (i.e., 116 individuals) of S-trees and 8 species (i.e., 34 individuals) were determined according to each species cumulatively contribution ≥ 50% (in descending order) of AGCS. In the fixed-diameter approach, 29 species (i.e., 111 individuals) and 12 species (i.e., 39 individuals) belonged to S-trees and L-trees, respectively based on DBH less than 50 cm for S-trees, and greater than 50 cm DBH for L-trees. In the mean threshold approach, 29 species (i.e., 131 individuals) of S-trees and 9 species (i.e., 19 individuals) of L-trees were recognized by taking the species-specific corresponding DBHs' mean value of the three threshold sizes. The species' maximum height was determined through the top 95-percentile score within each L-trees and S-trees layer associated with each quantification approach. Species-specific trait-based attributes of L-trees and S-trees across four quantification approaches are presented in Table S4.

2.3. Tree-based and trait-based attributes

We quantified tree-based attributes including species richness (SR), species evenness (SE), tree size inequality in DBH, height and crown volume, and stand density per hectare. The total number of observed tree and shrub species was used to calculate the species richness, whereas species evenness was quantified as $ S E=\frac{H_{\mathrm{s}}}{\ln (S)}$, where SE is species evenness, Hs is Shannon's species diversity which can be quantified as $ H_S=-\sum\nolimits_{i=1}^S p_i \times \ln \left(p_i\right)$, S is the species richness, and pi is the relative basal area of the ith species within each plot. As such, the stand density per hectare was quantified using the counting of recorded woody species within each plot and then scaled up to per hectare. Tree DBH, height and crown volume were used to calculate the coefficient of variation (CV, given as a percentage) values to quantify the individual tree size inequality.

Tree maximum height, wood density, specific leaf area, and leaf dry matter content were the four traits to calculate the single-trait dominance using the approach of the community-weighted mean for each trait, defined as the average single-trait values that were weighted by the species' relative basal area. After that, the standardized values of the four traits were used to calculate four indices of the functional multi-trait diversity, i.e., multi-trait richness (Fric), evenness (Feve), divergence (Fdiv), and dispersion (Fdis) (Mason et al., 2005; Villéger et al., 2008). All tree-based and trait-based attributes were calculated for each of the L-trees and S-trees layers within each plot, by using each of the four threshold size approaches, using the vegan and FD packages (Laliberté and Legendre, 2010; Oksanen et al., 2020). In addition, a descriptive summary of variables is presented in Table S5 (also see Fig. S2).

2.4. Statistical analyses

First, we used principal component analyses (PCAs) to determine the main loading value (ldg) for each of the tree-based and trait-based attributes of both L-trees and S-trees across four threshold size quantification approaches (i.e., eight PCAs in total), using the R package FactoMineR (Lê et al., 2008). Second, we used the Hierarchical and Variation Partitioning for Canonical Analysis to conduct variation partitioning and hierarchical partitioning to calculate the unique, individual and combined contributions of each predictor (or group) towards explained variation (R²) in AGCS on canonical analysis, using the rdacca.hp package (Lai et al., 2022). Here, we used two models, i.e., (1) to partition the total explained variation in AGCS by abiotic factors and tree-based attributes of L-trees and S-trees (i.e., in total 21 variables); and (2) to partition the total explained variation in AGCS by abiotic factors and trait-based attributes of L-trees and S-trees (i.e., in total 24 variables).

Third, to evaluate the relative effects of tree-based and trait-based attributes of L-trees versus S-trees in addition to the abiotic variables on AGCS, we employed multiple linear regression (MLR) models. So, we quantified the multivariate effects of; (1) multiple abiotic factors and tree-based attributes of the L-trees and S-trees on AGCS within each threshold size quantification approach (i.e., four series of MLR models; see composite Eq. (1)); and (2) multiple abiotic factors and trait-based attributes of the L-trees and S-trees on AGCS within each threshold size quantification approach (i.e., four series of MLR models; see composite Eq. (2)). We assessed the multi-collinearity issues in each MLR models by computing the variance inflation factor (VIF) by stepwise choosing the variables with VIF ≤ 3 (see Tables S6 and S7) to improve the MLR models (i.e., reduced MLR models; see Tables S8 and S9) by avoiding biased standardized coefficients (Eqs. Eq. 1, Eq. 2)) (Graham, 2003). The reduced MLR models were then used to determine the best-fitted subset MLR models (i.e., the best MLR models; see Tables S10 and S11) through the lowest df among all subsets with ΔAICc < 2 in the dredge function of the MuMIn package (Bartón, 2016). In each best MLR model, the relative contribution of tree-based and trait-based attributes as well as abiotic factors to the overall accounted variation (i.e., R²) in AGCS was estimated through the relaimpo package (Grömping, 2006). The standardized effects (β) and relative contribution were visualized through the ggplot package.

\begin{aligned} & A G C S=\beta_0+\beta_1\left(\operatorname{Eastn}_i^{\mathsf{μ}^* .1^* .2^* .3^*}\right)+\beta_2\left(\operatorname{Elev}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_3\left(\operatorname{Northn}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_4\left(\operatorname{Slope}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_5\left(\operatorname{AP}_i^{\mathsf{μ} .1 .2 .3}\right) \\ & ~~~~~~~~~~~~~~~~+\beta_6\left(\mathrm{TN}_i^{\mathsf{μ}^* .1^* .2^* .3^*}\right)+\beta_7\left(\mathrm{EK}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_8\left(\mathrm{pH}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_9\left(\mathrm{~L} \cdot \mathrm{SR}_i^{\mathsf{μ} .3^*}\right)+\beta_{10}\left(\mathrm{~L} \cdot \mathrm{SE}_i{ }^2\right)+\beta_{11}\left(\mathrm{~L} \cdot \mathrm{SDha}_i{ }^{\mathsf{μ}^* .1^* .2 .3}\right) \\ & ~~~~~~~~~~~~~~~~+\beta_{12}\left(\mathrm{~L} \cdot \mathrm{CVD}_i{ }^{\mathsf{μ}^* .1^* .2^* .3^*}\right)+\beta_{13}\left(\mathrm{~L} \cdot \mathrm{CVH}_i{ }^{\mathsf{μ} .1 .2 .3}\right)+\beta_{14}\left(\mathrm{~L} \cdot \mathrm{CVCV}_i{ }^{\mathsf{μ} .1 .3^*}\right)+\beta_{15}\left(\mathrm{~L} \cdot \text { thresh }_i{ }^{\mathsf{μ}^* .1^* .2^* .3^*}\right)+\beta_{16}\left(\mathrm{~S} \cdot \mathrm{SR}_i{ }^{\mathsf{μ} .1 .2 .3}\right) \\ & ~~~~~~~~~~~~~~~~+\beta_{17}\left(\mathrm{~S} \cdot \mathrm{SE}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_{18}\left(\mathrm{~S} \cdot \mathrm{SDha}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_{19}\left(\mathrm{~S} \cdot \mathrm{CVD}_i^2\right)+\beta_{20}\left(\mathrm{~S} \cdot \mathrm{CVH}_i^{1 .3}\right)+\beta_{21}\left(\mathrm{~S}^{-} \mathrm{CVCV}_i^{\mathsf{μ} .1^* .3}\right)+\varepsilon_i \end{aligned}

(1)

\begin{aligned} & A G C S=\beta_0+\beta_1\left(\operatorname{Eastn}_i^{\mathsf{μ} .1^* .2 .3}\right)+\beta_2\left(\operatorname{Elev}_i^{\mathsf{μ} .2 .3}\right)+\beta_3\left(\operatorname{Northn}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_4\left(\operatorname{Slope}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_5\left(\operatorname{AP}_i^{\mathsf{μ} .1 .2 .3}\right) \\ & ~~~~~~~~~~~~~~~~+\beta_6\left(\mathrm{TN}_i^{\mathsf{μ} .1^* .2^* .3^*}\right)+\beta_7\left(\mathrm{EK}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_8\left(\mathrm{pH}_i^{\mathsf{μ} .1 .2 .3}\right)+\beta_9\left(\mathrm{~L} \cdot \mathrm{Fdis}_i{ }^{\mathsf{μ}^* .1 .2^* .3^*}\right)+\beta_{10}\left(\mathrm{~L} \cdot \mathrm{Fdiv}_i{ }^{1.2}\right)+\beta_{11}\left(\mathrm{~L} \cdot \mathrm{Feve}_i{ }^3\right) \\ & ~~~~~~~~~~~~~~~~+\beta_{12}\left(\mathrm{~L} \cdot \mathrm{Fric}_i{ }^{\mathsf{μ} .3}\right)+\beta_{13}\left(\mathrm{~S} \cdot \mathrm{Fdis}_i{ }^{\mathsf{μ} .2 .3}\right)+\beta_{14}\left(\mathrm{~S} \cdot \mathrm{Fdiv}_i{ }^{\mathsf{μ} .1 .2 .3}\right)+\beta_{15}\left(\mathrm{~S} \cdot \mathrm{Feve}_i{ }^{\mathsf{μ} .1 .2 .3}\right)+\beta_{16}\left(\mathrm{~S} \cdot \mathrm{Fric}_i{ }^{\mathsf{μ} .1 .2}\right) \\ & ~~~~~~~~~~~~~~~~+\beta_{17}\left(\mathrm{~L} \cdot \mathrm{CWMh}_i{ }^{\mathsf{μ} .3}\right)+\beta_{18}\left(\mathrm{~L} \cdot \mathrm{CWMldmc}_i{ }^{\mathsf{μ}^* .1 .2^* .3^*}\right)+\beta_{19}\left(\mathrm{~L} \cdot \mathrm{CWMsla}_i{ }^{\mathsf{μ}^* .1^* .2^* .3^*}\right)+\beta_{20}\left(\mathrm{~L} \cdot \mathrm{CWMwd}_i{ }^1\right) \\ & ~~~~~~~~~~~~~~~~+\beta_{21}\left(\mathrm{~S} \cdot \mathrm{CWMh}_i{ }^{\mathsf{μ} .2 .3}\right)+\beta_{22}\left(\mathrm{~S}^{-\mathrm{CWMldmc}_i{ }^{1.2 .3}}\right)+\beta_{23}\left(\mathrm{~S}^{-\mathrm{CWMsla}_i{ }^{1^*.2^* .3} }\right)+\beta_{24}\left(\mathrm{~S}^{-\mathrm{CWMwd}_i}\right)+\varepsilon_i \end{aligned}

(2)

All abbreviations to variables are explained in the caption of the main figures (also see Tables S5 and S12). Note that superscripts μ, 1, 2, and 3 show the retained variables (after the VIF step) in the reduced MLR model of each threshold quantification approach (i.e., μ = mean threshold approach, 1 = fixed-diameter approach, 2 = percentile approach, 3 = AGC-ranked ordered approach) whereas asterisk (*) above each variable number show those variables which were retained in the best MLR models after applying dredge function.

Fourth, we developed interactive structural equation modelling (SEM) as this approach allows us to test the direct, indirect and total effects of multiple predictors and mediators (tree-based, trait-based, and soil TN) on AGCS through a conceptual model having known and unknown theoretical paths. As we had multiple variables (see composite Eqs. Eq. 1, Eq. 2)), we applied the best representative variables of tree-based and trait-based concepts which were retained in the best MLR models across four quantification approaches (i.e., four interactive SEMs in total). The best-fitted interactive SEM was assessed using several criteria, i.e., P > 0.05; comparative fit index (CFI), goodness-of-fit index (GFI) > 0.90 and standardized root mean square residual (SRMR) < 0.08. For visual interpretations of SEM results, bar charts were used to show direct, indirect (via multiple pathways) and total (i.e. direct plus indirect effects) effects of exogenous and endogenous variables on AGCS. The SEM was fitted using the lavaan package (Rosseel, 2012).

Fifth, we synthesized the multidimensional effects (by taking the average value) of tree-based and trait-based attributes as well as abiotic factors on AGCS across four threshold-size quantification approaches by applying the averaging MLR models on all possible subsets of the best MLR models (see the third step). Also, we used the Hierarchical and Variation Partitioning for Canonical Analysis to conduct variation partitioning and hierarchical partitioning to calculate the unique, individual and combined contributions of the tree-based concept versus the trait-based concept in explaining variations in AGCS across four threshold-size quantification approaches. As such, the relative contributions of the four threshold-size quantification approaches to AGCS were calculated using the relative variation approach by dividing the R² of a given averaging MLR model by the sum of the R² of all averaging MLR models (expressed in %).

The statistical software R 4.4.2 was used for all data computations and statistical analysis (R Development CoreTeam, 2024). We also assessed the bivariate regressions and Pearson's correlations across all variables for each of the four threshold-size quantification approaches to supplement the main findings. While the transformed data (i.e., ln-transformed and then standardized by a mean of 0 and S.D. of 1) was used in RDA, MLR and other complementary analyses to improve the interpretability of regression coefficients within the range of −1 and 1 (Zuur, 2009), the non-transformed data (i.e., original variables) were used in boxplot and PCA analyses to capture the original dimensions in the analyses.

3. Results 3.1. Correlation and dimension circles: species co-occurrence processes of temperate deciduous forests

The tree-based PCA of the mean threshold approach showed that the first axis of PCA (27.1%) was controlled by the negative loading of threshold size for L-trees (ldg = −0.35) but positive loadings of the majority of the tree-based attributes including tree diversity (ldg = 0.30 to 0.31), stand density (ldg = 0.33) and size inequality (ldg = 0.34 to 0.38) of L-trees whereas by the negative loadings of size inequality of S-trees (ldg = −0.21 to −0.28) (Fig. 2a and Table S13). However, the second axis of PCA (18.6%) was controlled by the negative loadings of the size inequality (ldg = −0.41 to −0.50) and stand density (ldg = −0.23) of S-trees as well as by the size inequality (ldg = −0.19 to −0.30) and stand density (ldg = −0.29) of L-trees (Fig. 2a and Table S13). In comparison, the PCA of the trait-based concept showed that the first axis of PCA (27.2%) was controlled by the negative loadings of dominant acquisitive and conservative trait (i.e., CWMsla; ldg = −0.31 to −0.35 and CWMldmc; ldg = −0.26 to −0.37) but the positive loadings of the multi-trait diversity (ldg = 0.17 to 0.33) of both L-trees and S-trees, respectively (Fig. 2b and Table S14). However, the second axis of PCA (20.10%) was controlled by the negative loadings of the multi-trait diversity (L.Fdiv, L.Feve, and L.Fric; ldg = −0.29), dominant stature trait of L-trees (L.CWMh; ldg = −0.36), and dominant acquisitive trait of L-trees and S-trees (ldg = −0.30 and −0.27), respectively but positive loadings of conservative wood trait of L-trees and S-trees (CWMwd; ldg = 0.45 and 0.40), respectively (Fig. 2b and Table S14). Moreover, the complementary PCAs, based on the three quantification approaches, showed that somehow changes existed in the magnitude and direction of the loadings of variables related to the tree-based and trait-based concepts (Fig. 2c–h; Tables S13 and S14). Pearson's correlations are provided in Fig. S3–S7.

3.2. Variation partitioning analysis: what matters for AGCS in temperate deciduous forests

Based on the tree-based RDA results of the mean threshold approach, the variation partitioning analysis revealed that L-trees accounted for a higher relative portion (84.31%) of the total explained variation (70.4%) in AGCS followed by abiotic factors (4.99%) and S-trees (−0.21%) (Fig. 3a and Table S15). In comparison, the trait-based attributes explained 29.0% of the total variation in AGCS where the traits of L-trees accounted for a higher relative portion (82.36%) followed by abiotic factors (1.97%) and S-trees (0.54%) (Fig. 3b and Table S16). Moreover, based on the tree-based concept, the joint variance explained by the combined effects of L-trees, S-trees and abiotic factors explained less variation (< 5%) in AGCS (Fig. 3a and Table S15). However, based on the trait-based concept, the joint variations (23.61%) were fairly higher for the combined effects of L-trees and abiotic factors followed by the combined variation of S-trees and abiotic factors (−5.79%) on AGCS (Fig. 3b and Table S16). In addition, the complementary analyses, based on the percentile (Fig. 3c and d), AGC-ranked ordered (Fig. 3e and f) and fixed-diameter (Fig. 3g and h) approaches, showed that both the tree-based and trait-based attributes of L-trees explained a relatively higher portion (31.29%–93.20%) of the total explained variation in AGCS (9.4%–59.9%) followed by abiotic factors (2.38%–19.34%) and S-trees (0.93% to −33.92%) (Tables S15 and S16).

3.3. Best MLR models: identifying the optimal drivers of AGCS in temperate deciduous forests

The best tree-based MLR model of the mean threshold approach indicated that AGCS was significantly positively affected by the threshold size (β = 0.88, P < 0.001) and DBH inequality of L-trees (β = 0.16, P = 0.016) as well as by soil total nitrogen (β = 0.15, P = 0.008), topographic eastness (β = 0.15, P = 0.005), and stand density of the L-trees (β = 0.14, P = 0.039) (Fig. 4a and Table S19). In comparison, the best trait-based MLR models showed that the dominant traits of L-trees with different species functional strategies affected AGCS through opposing mechanisms, i.e., the dominant resource-acquisitive trait (L.CWMsla) promoted (β = 0.34, P < 0.001) but resource-conservative trait (L.CWMldmc) of L-trees decreased (β = −0.48, P < 0.001) AGCS (Fig. 4b and Table S22). Moreover, AGCS were negatively affected by the multi-trait dispersion (β = −0.33, P < 0.001) of L-trees whereas soil total nitrogen showed a nonsignificant positive effect on AGCS (β = 0.14, P = 0.118) (Fig. 4b and Table S22). In addition, the complementary best tree-based and trait-based MLR models based on the percentile (Fig. 4c and d), AGC-ranked ordered (Fig. 4e and f) and fixed-diameter approaches (Fig. 4g and h) provided general support to the mean threshold approach in predicting AGCS (Tables S19 and S22). Moreover, the effects of soil total nitrogen (β = 0.14 to 0.23, P = 0.008 to 0.118) and/or topographic eastness (β = 0.09 to 0.20, P = 0.005 to 0.169) on AGCS were positive whenever retained as the best predictors in MLR models, despite the role of threshold quantification approaches and concepts (Fig. 4; Tables S19 and S22).

3.4. Interactive data-fitted SEMs: which pathways matter for AGCS in temperate deciduous forests

Following the best tree-based and trait-based MLR models, the interactive data-fitted SEM of the mean threshold approach (Fig. 5a and Table S23) revealed that the threshold size of L-trees (β = 0.73, P < 0.001) overruled the effects of the dominant resource-acquisitive trait of L-trees (L.CWMsla; β = 0.06, P = 0.422) and S-trees (S.CWMsla; r = 0.19, P = 0.016) as well as the tree DBH inequality of S-trees (S.CVD; β = 0.01, P = 0.858) and soil total nitrogen (TN; β = 0.12, P = 0.038) on AGCS through direct and indirect pathways. Soil total nitrogen promoted AGCS indirectly (β = 0.13, P = 0.093) via the positive direct effects on the dominant resource-acquisitive traits (β = 0.19 to 0.21, P = 0.008 to 0.036) and possessed weak direct effects on threshold size (β = 0.11, P = 0.272) and tree DBH inequality of S-trees (S.CVD; β = −0.07, P = 0.466) (Fig. 5a and b; Table S23). Also, the complementary data-fitted SEMs based on the percentile (Fig. 5c and d), AGC-ranked ordered (Fig. 5e and f) and fixed-diameter (Fig. 5g and h) approaches provided general support to the mean threshold approach in predicting AGCS through joint direct and indirect pathways with some noted differential mechanisms in the mediation paths (Table S23). The bivariate relationships for supporting the best MLRs and interactive SEMs are provided in Fig. S8–S11.

3.5. Synthesis: which concept and approach matter for AGCS in temperate deciduous forests

The synthesized averaged MLR model (Fig. 6A) showed that AGCS was significantly positively affected by the threshold size (β = 0.57, P < 0.001 to 0.336) followed by the positive effect of DBH inequality of L-trees (β = 0.32, P < 0.001 to 0.019), the negative effect of resource-conservative trait dominance of L-trees (L.CWMldmc; β = −0.31, P < 0.001 to 0.002), the positive effects of stand density of (β = 0.23, P < 0.001 to 0.042) and resource-acquisitive trait dominance of L-trees (L.CWMsla; β = 0.22, P < 0.001 to 0.012) but the negative effect of S-trees (S.CWMsla; β = −0.23, P < 0.001), and the positive effects of L-trees crown volume inequality (β = 0.21, P = 0.028) and S-trees DBH inequality of (β = 0.14, P = 0.023), whereas other effects were minor (Table S24). Moreover, the synthesized RDA result (Fig. 6B) showed that the tree-based attributes explained higher variation (57.66%) in the accounted model variation of the mean threshold approach as compared to the trait-based approach (4.44%; Fig. 6Ba and Table S25), and as such, the percentile approach and fixed-diameter approach showed an almost similar pattern, but it was opposite in the AGC-ranked ordered approach where the trait-based attributes mattered (65.55%) for explaining AGCS (Fig. 6Bc and Table S25). Regardless of the quantification approach, the shared contributions of the tree-based and trait-based attributes were moderate positive variations (24.13%–37.90%) which were even higher than the variation explained by the trait-based attributes in three cases (Fig. 6B). However, the synthesized variation partitioning analysis (Fig. 6C) showed that the threshold size quantification approaches accounted for nearly the same explained relative variation (15.33%–29.50%) in AGCS where the mean threshold approach was the best one among the four approaches (29.50%).

4. Discussion

This comprehensive study – by researching Iran's temperate deciduous forests as a case study – contributes new methodological (i.e., threshold quantification approaches for defining L-trees) and theoretical (i.e., the tree-based versus the trait-based concepts) insights into assessing the effects of few L-trees versus S-trees in regulating forest functioning (i.e., AGCS in this study) along abiotic conditions. Although there is no universal threshold size to define the L-trees as also suggested by several previous studies (Clark and Clark, 1996; Slik et al., 2013; Lutz et al., 2018; Ali and Wang, 2021; de Lima et al., 2023), we argue that the mean threshold approach – considering all other three approaches in one picture – can solve the multidimensional challenges in defining L-trees for quantifying their effects on tree diversity, stand structure and forest functions. Analytically, we found that both the tree-based and the trait-based concepts explain forest species co-occurrence processes which in turn explain the potential drivers of AGCS but L-trees matter much higher than S-trees and even than abiotic factors.

First, the overall PCA results indicate that L-trees and S-trees regulate forest species co-occurrence processes through somehow differential mechanisms determined by the tree-based versus the trait-based attributes of L-trees versus S-trees which in turn may regulate BEF relationships (Chave et al., 2009; Reich, 2014; Díaz et al., 2016; Ali and Wang, 2021). According to the tree-based attributes of the mean threshold approach, a strong trade-off exists between tree size inequality attributes of L-trees and S-trees where the tree size inequality attributes of L-trees decline with increasing threshold size but another trade-off exists between species diversity and tree size inequality regardless of tree sizes (i.e., L-trees and S-trees) and threshold size. This result indicates the dominant role of the stand structure rather than species diversity of L-trees over S-trees in regulating forest species co-occurrence processes (Chave et al., 2009; Lutz et al., 2018; Bastin et al., 2018; Ali and Wang, 2021). According to trait-based attributes of the mean threshold approach, we found that the role of resource-acquisitive dominant traits (i.e., particularly those of L-trees) declines with increasing the multi-trait diversity of both L-trees and S-trees, suggesting that species complementarity increases with increasing multi-trait diversity of a forest community (Díaz et al., 2007; De Deyn et al., 2008; Conti and Díaz, 2013). However, another strong trade-off exists for dominant resource-acquisitive versus conservative traits in determining forest species co-occurrence processes when multi-trait diversity (particularly of L-trees) decreases, indicating that L-trees are mostly resources-acquisitive which suppresses the role of S-trees in a forest community (Wright et al., 2004; Chave et al., 2009; Reich, 2014; Díaz et al., 2016).

Second, the overall mixed results of variation partitioning, the best MLR models and interactive SEMs indicate that the trait-based concept can mechanistically explain the biotic drivers of AGCS along abiotic conditions which further explains the obscured ecological mechanisms shown by the tree-based concept. For instance, this study supports the general notion that higher AGCS is potentially driven by the structural attributes of L-trees, as compared to S-trees, having larger threshold size and higher stand structural complexity (i.e., higher tree size inequality and stand density) (Lutz et al., 2018; Ali et al., 2019; Bordin et al., 2021; Yuan et al., 2021). Moreover, contrary to our expectations, species diversity attributes (i.e., species richness and evenness of both L-trees and S-trees) possessed negligible complex (i.e., positive and/or negative) effects on AGCS, indicating that tree diversity alone is a poor predictor of forest functioning as compared to the tree structural attributes and functional traits (Loreau et al., 2001; Fotis et al., 2018; Ali and Wang, 2021). In this case, the novelty of our study reveals that, according to the trait-based concepts, functionally similar (i.e., low functional dispersion) L-trees with acquisitive nutrient use strategies (i.e., higher specific leaf area and lower leaf dry matter content) regulated AGCS better than the trait attributes of S-trees. The significant positive effects of the fast nutrient-acquisitive L-trees and negative negligible effects of S-trees (in some cases) on AGCS might be attributable to the plant's leaf economics spectrum that ranged from exploitative plants with higher specific leaf area, lower leaf dry matter content and greater turnover rates that are conducive to fast growth and higher AGB accumulations, to conservative slow-growth S-trees which support the species' functional strategy-dependent mass ratio mechanisms (Wright et al., 2004; Conti and Díaz, 2013; Reich, 2014; Finegan et al., 2015). Moreover, the negative or negligible effects of multi-trait diversity of both L-trees and S-trees on AGCS provide support to the growing notion that the niche complementarity effect does not necessarily drive ecosystem functions whereas dominant traits matter which supports the mass ratio effect, even though both ecological effects are non-mutually exclusive (Conti and Díaz, 2013; Finegan et al., 2015; Fotis et al., 2018; van der Plas, 2019; Ali, 2023). Thus, in the context of the mass ratio effect versus the niche complementarity effect, our findings support the universality of the big-sized trees effect in forests (Slik et al., 2013; Lutz et al., 2018; Ali et al., 2019; Yuan et al., 2021).

Additionally, the higher vegetation quantity (i.e., initial AGB stock) resulting from the dominant role of resource-acquisitive L-trees may promote absolute annual AGB gain because L-trees possessed a higher stand density and tree size inequality than S-trees, which may have positive effects on AGCS (Lohbeck et al., 2015; Lutz et al., 2018; Yuan et al., 2021). For example, structurally complex natural forests may have higher AGB stock because of mechanisms for resource heterogeneity and niche differentiation that are typically linked to variations in leaf layering, canopy packing, and space-filling, which in turn may have an impact on forest functions (including photosynthesis, respiration, and primary productivity) (Yachi and Loreau, 2007; Poorter et al., 2017; Gough et al., 2019; Ali, 2023). According to the metabolic scaling theory and other relevant assumptions, an exponential increase in AGB growth can expected with increasing tree size due to the increasing energy capture which could lead to higher AGCS in forests (Enquist et al., 1999; Stephenson et al., 2014; Sheil et al., 2017). For example, tree diameter growth, even in a mature forest, is usually connected with higher tree volume, which in turn leads to higher growth rates and a disproportionate contribution of the resource-acquisitive L-trees to stand-level productivity (Stephenson et al., 2014; Lohbeck et al., 2015; Bastin et al., 2018).

Third, we observed weak positive effects of abiotic factors on AGCS as compared to the effects of tree-based and trait-based attributes. Although abiotic factors explained relatively less variation in AGCS in both the tree-based and trait-based concepts, the positive effects of topographic eastness and soil total nitrogen on AGCS provide some support to the soil fertility effect as well as the resource availability and heterogeneity effects (Coomes et al., 2009; Quesada et al., 2012; Bartels and Chen, 2013; Slik et al., 2013). Moreover, the supporting interactive SEMs show the negligible effects of soil total nitrogen on tree-based and trait-based attributes of S-trees due to the resource filtering by L-trees as it was evident in our analyses that resource-acquisitive strategy (based on trait dominance) and threshold size of L-trees increase with increasing soil nutrients in most cases (Barbier et al., 2008; Zhang et al., 2017; Ali et al., 2019). However, this ecological mechanism may also be related to the soil nutrient imbalance, high loss of soil nutrients and size-dependent species adaptation to the surrounding environments (Baker et al., 2009; Poorter et al., 2015). Also, topographic eastness possessed a weak positive effect on AGCS which is indeed due to the effects of soil and climate resources heterogeneity and availability effects which could differentially affect the tree-based and trait-based attributes of both L-trees and S-trees in a forest community (Bartels and Chen, 2010; Jucker et al., 2018; de Lima et al., 2023).

5. Conclusions

We demonstrate that both the tree-based and trait-based concepts can be used to describe how forest communities are assembled, which in turn can be used to explain probable drivers of AGCS. However, L-trees matter considerably more than S-trees or even abiotic factors. Although threshold size overrides the effects of both tree-based and trait-based attributes on AGCS in the studied temperate deciduous forests, the functional traits axes capturing the tradeoffs and synergies for trait dominance and multi-trait diversity of L-trees and S-trees in shaping forest species co-occurrence processes can potentially and mechanistically elucidate the underlying ecological mechanisms. The trait-based concept demonstrates that functionally similar (i.e., low functional dispersion) L-trees with acquisitive nutrient use strategies (i.e., higher specific leaf area and lower leaf dry matter content) promote AGCS better than the trait-based attributes of S-trees, despite the tree-based concept showing that threshold size, stand density, and tree size inequality of L-trees rather than S-trees promote AGCS. We further suggest that tree size and species functional strategies are even more crucial for predicting forest functioning (e.g., AGCS) since species adaptability can be determined by suitable dominant traits for resource use and capture in an ecosystem.

Acknowledgements

We gratefully acknowledge the kind assistance we received from the Iran National Science Foundation (Grant No. 97010593) and Hebei University (Special Project No. 521100221033).

CRediT authorship contribution statement

Maryam Kazempour Larsary: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Hassan Pourbabaei: Writing – original draft, Supervision, Funding acquisition, Conceptualization. Ali Salehi: Writing – original draft, Supervision, Conceptualization. Rasoul Yousefpour: Writing – original draft, Software, Formal analysis, Conceptualization. Arshad Ali: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Data availability statement

The summaries of the original variables are provided in Table S1–S5 and Fig. S2. More details can be provided upon request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.pld.2025.04.008.