UAV-based height measurement and height–diameter model integrating taxonomic effects: exploring vertical structure of aboveground biomass and species diversity in a Malaysian tropical forest

Our field survey was conducted in Pasoh Forest Reserve, Negeri Sembilan, Malaysia (2°59'N, 102°18'E, altitude 75–150 m, figure 2(a)). The average annual rainfall and temperature over 15 years (1997–2011) were 1 833 mm and 25.4 °C, respectively (Noguchi et al 2016). The vegetation type is lowland mixed dipterocarp forest, which is a common forest type in Malaysia, and the families Euphorbiaceae and Dipterocarpaceae are the two most abundant families represented in species among the number of individuals throughout the forest (Symington 1943, Wyatt-Smith 1961, 1964). We used a 6 ha plot within Pasoh Forest Reserve (figure 2(b)), which was established in 1994, and all living trees with a stem diameter at breast height (D) ⩾5 cm were tagged and identified at the species level, with a census every 2 years (Niiyama et al 2003). The center of the plot (2 ha, Plot 1) was used extensively for studies of primary productivity of tropical forests during the International Biological Program (IBP) in the 1970s (Kira 1978). Furthermore, the plot contains one flux tower (H 52 m), two canopy towers (H 30 m), and walkway between these towers.

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Here, we conducted two types of field surveys in the 6 ha plot. The first is the survey of tree growth and survival conducted from 27 January–5 February in 2016 and 31 January–7 February in 2018. For buttressed trees, note that D was corrected using a taper model, and then D was estimated in September 2017 using a growth model (figure 1, supplementary text 1) to adjust the size of D and H in Sept 2017 for subsequent modeling analysis. The dataset included a total of 8150 individuals belonging to 72 families, 406 genera, and 570 species including 18 unidentified species and two individuals from unknown families (dataset S1). The second is a terrain survey to obtain topographic information of the plot; we conducted traverse measurement by measuring the distance, altitude difference, and direction using a laser range finder (Truepulse 200, Laser Technology Inc., Centennial, Colorado, USA) and a compass glass (Syakujii Keiki Co. Ltd, Tokyo, Japan) at each 10 m grid of the plot. Then, we obtained an averaged topographic map.

We conducted drone flights on 9 September, 2017, using a custom-made UAV (Hornbill Surveys, Sabah, Malaysia), which was controlled by autopilot software and mounted with a RedEdge camera (MicaSense, Inc., Seattle, WA, USA) equipped with a multispectral sensor capturing red, green, blue, near-infrared, and red-edge wavelengths and GPS (supplementary text 2). From the RGB images which constitute red, green, and blue colors captured by the camera, we created orthomosaic images and developed three-dimensional canopy models (DSM) using PhotoScan Professional, version 1.2.6 (Agisoft, St. Petersburg, Russia, www.agisoft.com). The detailed method is described in supplementary text 3.

2.3.1. Digital Elevation Model (DEM) and DCHM

2.3.2. Canopy identification and H estimation

(1) Allometric model for HD relationship

The expanded allometric model by Ogawa et al (1965) is expressed as:

$$\begin{equation*}\frac{1}{H} = \frac{1}{{a{D^h}}} + \frac{1}{{{H_{{\text{MAX}}}}}}\,:\,{\text{MO}}\end{equation*}$$

where H is a tree height, D is the diameter at breast height, a, h and ${H_{\text{MAX}}}$ are coefficients. In particular, h is an allometric scaling exponent of HD growth and ${H_{{\text{MAX}}}}$ is the maximum tree height (Ogawa et al 1965, Kira and Ogawa 1971). Here, this model was termed MO (table S1). In a previous study (Kato et al 1978), MO was fitted to the empirical data of Plot 1 (within the 6 ha plot) in Pasoh Forest Reserve. The estimated parameters were a = 2, h = 1, ${H_{{\text{MAX}}}}$ = 61, which assumed that all species or individuals had the same parameters. We refer to this as the Kato HD model. In this study, we incorporated the taxonomic effect into the parameters of this model. In addition, we treated the error associated with the year (or the type) of the dataset (6 ha, IBP) as random effects. Thus, the full model is described as follows:

$$\begin{equation*}{\text{log}}\left( {{H_i}} \right) = {\text{log}}\left( {{a_{{s_i}}}} \right) + {h_{{s_i}}}{\text{ log}}\left( {{D_i}} \right) + {\text{log}}\left( {{H_{{\text{MA}}{{\text{X}}_{{s_i}}}}}} \right) - {\text{log}}\left( {{a_{{s_i}}}{ }{D_i}^{{h_{{s_i}}}} + {H_{{\text{MA}}{{\text{X}}_{{s_i}}}}}} \right) + { }{e_{{p_i}}}\end{equation*}$$

where ${a_{{s_i}}}$, ${h_{{s_i}}}$ and ${H_{{\text{MA}}{{\text{X}}_{{s_i}}}}}$ are the parameters nested with the taxonomic levels s of individual i, and is the error terms of the dataset as the year that the individual i was observed, respectively. We considered the taxonomic level of family and/or genus nested with family for the combination of three parameters of the model (table 1), which were eight models in total. Here, MO-0 was the conventional model of MO, which did not incorporate any effects.

Table 1. Summary of HD modelsaaa.

Model type	Model no.	Equation	Parameters	Error	Taxonomic effect	LOOIC Statistics (SE)		Explained variation R2 (Error)		Coefficients
										log Hmax			log a			h
										Mean	Q2.5	Q97.5	mean	Q2.5	Q97.5	Mean	Q2.5	Q97.5
Ogawa allometric model	MO-0	${{log}}\,({{{{H}}}_{{{i}}}}) = {{log}}({{{{a}}}_{{{{{s}}}_{{{i}}}}}}) + {{{{h}}}_{{{{{s}}}_{{{i}}}}}}\,{{log}}({{{{D}}}_{{{i}}}})\, + \,{{log}}({{{{H}}}_{{{ma}}{{{x}}_{{{{{s}}}_{{{i}}}}}}}})$ $- {{log}}({{{{a}}}_{{{{{s}}}_{{{i}}}}}}{{{{D}}}_{{{i}}}}^{{{{{h}}}_{{{{{s}}}_{{{i}}}}}}} + {{{{H}}}_{{{ma}}{{{x}}_{{{{{s}}}_{{{i}}}}}}}})$	a, h, Hmax			−432.2	−39.8	0.89	−0.003	4.387	4.229	4.583	0.916	0.791	1.037	0.824	0.76	0.889
	1	${{log(}}{{{{H}}}_{{{i}}}}{{) = log(}}{{{{a}}}_{{{{{s}}}_{{{i}}}}}})$ ${{ + }}{{{{h}}}_{{{{{s}}}_{{{i}}}}}}\,{{log(}}{{{{D}}}_{{{i}}}}{{)}}\,{{ + }}\,{{log(}}{{{{H}}}_{{{ma}}{{{x}}_{{{{{s}}}_{{{i}}}}}}}}{{)}} - {{log(}}{{{{a}}}_{{{{{s}}}_{{{i}}}}}}{{{{D}}}_{{{i}}}}^{{{{{h}}}_{{{{{s}}}_{{{i}}}}}}}{{ + }}{{{{H}}}_{{{ma}}{{{x}}_{{{{{s}}}_{{{i}}}}}}}}{{) + }}{{{{e}}}_{{{{{p}}}_{{{i}}}}}}$	a, h, Hmax	year		−432.2	−39.8	0.89	−0.003	4.391	4.019	4.774	0.919	0.567	1.276	0.824	0.76	0.89
	2		a, h, Hmax	year	a, h, Hmax ∼ family	−436.8	−42.1	0.9	−0.003	4.352	2.668	6.028	0.914	−0.783	2.589	0.835	0.75	0.921
	3		a, h, Hmax	year	Hmax ∼ family	−437.4	−41.9	0.9	−0.003	4.318	2.809	5.946	0.842	−0.688	2.48	0.873	0.797	0.949
	4		a, h, Hmax	year	h, Hmax ∼ family	−436.6	−42.2	0.9	−0.003	4.269	2.341	5.891	0.8	−1.16	2.403	0.864	0.789	0.938
	5		a, h, Hmax	year	a, h, Hmax ∼ family/genus	−437.6	−42.1	0.9	−0.004	4.323	2.425	6.167	0.942	−0.974	2.778	0.828	0.742	0.917
	6		a, h, Hmax	year	Hmax ∼ family/genus	−438	−41.9	0.9	−0.003	4.295	2.605	6.087	0.831	−0.856	2.623	0.876	0.8	0.952
	7		a, h, Hmax	year	h, Hmax ∼ family/genus	−436.8	−42.2	0.9	−0.003	4.23	2.232	5.816	0.785	−1.225	2.38	0.868	0.794	0.943
										β0			β1			β2
										mean	Q2.5	Q97.5	mean	Q2.5	Q97.5	mean	Q2.5	Q97.5
Statistical models	MS1-0	${\text{log}}({H_i})\; = \;{\beta _0} + {\beta _1}\;{\text{log}}({D_i})$	β0 , β1			−365.5	−37.1	0.882	−0.003	1.319	1.26	1.377	0.568	0.552	0.585
	1	${\text{log}}({H_i}) = {\beta _{0,{s_i}}}\; + \;{\beta _{1,{s_i}}}{\text{log}}({D_i})\; + \;{e_{{p_i}}}$	β0 , β1	year		−364.4	−36.5	0.882	−0.003	−1.184	−3.413	1.352	0.56	0.538	0.582
	2		β0 , β1	year	β0 ∼ family	−382.4	−37.8	0.888	−0.003	−1.146	−3.364	1.447	0.536	0.51	0.562
	3		β0 , β1	year	β0 , β1 ∼ family	−433.5	−39.3	0.9	−0.003	−1.013	−3.195	1.568	0.496	0.449	0.539
	4		β0 , β1	year	β0 ∼ family/genus	−383.9	−37.3	0.891	−0.004	−1.143	−3.338	1.426	0.536	0.511	0.562
	5		β0 , β1	year	β0 , β1 ∼ family/genus	−449.5	−38	0.909	−0.004	−0.987	−3.187	1.63	0.479	0.436	0.521
	MS2-0	${\text{log}}({H_i}) = {\beta _0}\; + \;{\beta _1}\;{\text{log}}({D_i}) + {\beta _2}\;{\text{log}}{({D_i})^2}$	β0 , β1 , β2			−433.1	−39.6	0.894	−0.003	0.677	0.517	0.835	1.012	0.908	1.115	−0.07	−0.087	−0.054
	1	${\text{log}}({H_i})\; = \;{\beta _{0,{S_i}}}\; + \;{\beta _{1,{S_i}}}\;{\text{log}}({D_i})\; + \;{\beta _{2,{S_i}}}\;{\text{log}}{({D_i})^2} + {e_{{p_i}}}$	β0 , β1 , β2	year		−435	−41.1	0.895	−0.003	−1.982	−4.219	0.565	1.065	0.948	1.182	−0.076	−0.094	−0.059
	2		β0 , β1 , β2	year	β0 ∼ family	−438.9	−41.7	0.898	−0.003	−1.965	−4.192	0.589	1.052	0.927	1.175	−0.076	−0.094	−0.058
	3		β0 , β1 , β2	year	β0 , β1 , β2 ∼ family	−437.5	−41.6	0.899	−0.003	−1.788	−4.004	0.765	0.964	0.724	1.161	−0.066	−0.094	−0.032
	4		β0 , β1 , β2	year	β0 ∼ family/genus	−439.7	−41.7	0.9	−0.003	−1.906	−4.153	0.648	1.049	0.923	1.172	−0.077	−0.095	−0.058
	5		β0 , β1 , β2	year	β0 , β1 , β2 ∼ family/genus	−444.6	−40.5	0.907	−0.004	−1.566	−3.805	1.03	0.84	0.589	1.074	−0.05	−0.083	−0.016

(2) Statistical model for HD models

In previous studies, HD relationships were often formed as based on a power-law function and a polynomial function (Niklas 1995, Chave et al 2014), such as:

$$\begin{equation*}\log \left( {{H_i}} \right) = {\beta _0} + {\beta _1}\log \left( {{D_i}} \right):{\text{MS1}}\end{equation*}$$

$$\begin{equation*}\log \left( {{H_i}} \right) = {\beta _0} + {\beta _1}\log \left( {{D_i}} \right) + {\beta _2}{\text{log}}{\left({D_i}\right)^2}:{\text{MS2,}}\end{equation*}$$

where i is an individual ID, and ${\beta _0}$, ${\beta _1}$, and ${\beta _2}$ were parameters of each model. These models were termed MS1 and MS2, respectively (table S1). Then, we consider the taxonomic effect as random slopes and/or intercepts for the HD relationship for individual i as follows:

$$\begin{equation*}\log \left( {{H_i}} \right) = {\beta _{0,{\text{ }}{s_i}}} + {\beta _{1,{\text{ }}{s_i}}}\log \left( {{D_i}} \right) + {e_{{p_i}}}\end{equation*}$$

$$\begin{equation*}\log \left( {{H_i}} \right) = {\beta _{0,{ }{s_i}}} + {\beta _{1,{s_i}}}\log \left( {{D_i}} \right) + {\beta _{2,{s_i}}}{\text{log}}{\left({D_i}\right)^2} + {e_{{p_i}}}\end{equation*}$$

where ${\beta _{0,{s_i}}},{\text{ }}{\beta _{1,{s_i}}},{\text{ and }}{\beta _{2,{s_i}}}$ are the parameters nested with the taxonomic levels s of individual i, and ${e_{{p_i}}}$ is the error terms of the dataset as the year that individual i was observed. We also considered the taxonomic level of family and genus nested with family as for random intercepts and/or random slopes (table 1). Thus, there were six models for each MS1 and MS2 in total. Here, MS1-0 and MS2-0 were the conventional statistical models, which did not incorporate any taxonomic effects.

For each model, the Bayesian regression analysis was performed using a function 'brm' of 'brms' package (Bürkner 2017) in R; we ran each model across 2 chains for 120 000 iterations with a burn-in period of 20 000, thinned every 10 steps with the default prior sets. The models were compared using the approximate LOOIC based on the posterior likelihoods. For the models with the lowest (best) LOOIC in each model, we estimated fixed effects (means and 95% credible intervals) from the posterior distributions for each predictor.

To estimate the AGB of each tree, we performed the following procedure: First, we estimated H from the estimated D for all trees in the 6 ha plot using the best HD models in (1) and (2) in the former section. The best HD models included taxonomic effects at family and genus levels (refer section 3.2 for further details). Then, the AGB per tree was estimated using both (a) the Kato volume model and (b) the Chave AGB model (also see table S1) as follows:

(a) Kato volume model (allometric equation)

The allometric models for the AGB of tree stems, branches, and leaves were developed by Kato et al (1978) as follows:

$$\begin{equation*}{W_{\text{S}}} = 0.031{({D^2} \cdot H)^{0.9733}}\end{equation*}$$

$$\begin{equation*}{W_{\text{B}}} = 0.136{ }W_{\text{s}}^{1.070}\end{equation*}$$

$$\begin{equation*}\frac{1}{{{W_{\text{L}}}}} = \frac{1}{{0.124{ }W_{\text{s}}^{0.794}}} + \frac{1}{{125}}\end{equation*}$$

where W_S, W_B, and W_L denote the dry mass of stem, branches, and leaves, respectively. Thus, these can be calculated from the estimated values of D and H. The total AGB for each tree was calculated as summation as follows:

$$\begin{equation*}{\text{AG}}{{\text{B}}_i} = {W_{{\text{S}}i}} + {W_{{\text{B}}i}} + {W_{{\text{L}}i}}.\end{equation*}$$

(b) Chave AGB model for the pantropic model

One of the most common equations for calculating AGB was developed by Chave et al (2014), which was based on the relationship between AGB and D, H, and wood density (WD):

$$\begin{equation*}{\text{AG}}{{\text{B}}_{{\text{est}},i}} = { }0.0673 * {\left({\text{W}}{{\text{D}}_{{s_i}}} \cdot {D_i}^2 \cdot {H_i}\right)^{0.976}}\end{equation*}$$

where is ${WD _{{s_i}}}$ of species $s$ of individual $i$. To calculate the AGB using this equation, we used the 'BIOMASS' package in R (Réjou-Méchain et al 2017). The WD of each tree from its taxonomy (species, genus, family) can be attributed to the global WD database (Chave et al 2009, Zanne et al 2009) and the function 'getWoodDensity' with the region specified ('SouthEastAsiaTrop'). In the database, the mean WD values were available for 301 of 570 species (53%) at the species level, while at the genus level WD values were available for 240 species (42%). For the remaining four species and the unknown species (5%), the mean WD of the overall dataset was used. All AGB values for each tree were calculated using the 'computeAGB' function.

With these approaches for H and AGB estimation, we obtained four types of estimates of AGB, as a combination of two HD models—best models in (1) or (2) × one AGB model (Kato volume model or Chave AGB model). The AGB and D relationships were described at the family/genus level to assess the taxonomic difference. We also estimated AGB for all the trees in the 6 ha plot, and the total AGB was calculated as a summation of those.

The vertical distribution of AGB and species diversity in the stratification of the forest structure were calculated as follows: all trees were classified into four stratification layer categories by estimated H (Sakai et al 1999), forest understory (⩽12.5 m), subcanopy (12.5–27.5 m), canopy (27.5–42.5 m), and emergent (>42.5 m) layers. We calculated the AGB and species diversity in each layer category, based on the estimated tree heights by the best HD models above. For species diversity, we used Hill numbers (Hill 1973) of order q = 0, 1, and 2, which are species richness, the exponential of Shannon index, and the inverse Simpson index, respectively. We also calculated Hill number-based functional diversity using by the package, 'mFD' in R (Magneville et al 2022). To calculate functional diversity, we used three functional traits: maximum D, mean WD, and number of the trees in the plot. Here, species diversity and functional diversity indices of q = 0, which do not incorporate species abundance, are mainly influenced by the number of rare species, whereas those of q = 1 and q = 2, which incorporate species abundance, are mainly influenced by these dominant species.

Based on the DCHM (figure 2(c)), we estimated the H of 435 trees with a mean (±SD) 33.2 ± 9.5 m. The tallest tree in the 6 ha plot was Koompassia malaccensis (55.6 m), followed by Shorea pauciflora (54.8 m), K. malaccensis (54.7 m), and Dipterocarpus cornutus (54.2 m, 53.7 m). The trees H >50 m were 14 trees in total in the 6 ha plot. The mean H (±SD) of the IBP dataset was 18.0 ± 11.3 m (N = 156). The IBP dataset also contained a direct measure of AGB (N = 156) (dataset S2).

According to LOOIC, the best models for the model types of MO and MS were MO-6 and MS1-5 (table 1, figures S3 and S4), respectively, for which both included taxonomic effects into family and genus levels. The selected models were better fitted than the conventional models—Ogawa allometric model (MO-0) and the two statistical models (MS1-0, MS2-0). Subsequently, we also calculated the root mean squared error (RMSE) of MO-6, MS1-5, MO-0, MS1-0, MS2-0 and Kato HD model, which were 4.42, 4.26, 4.60, 5.16, 4.61, and 5.00, respectively. Among all the models, the MS1-5 had the lowest LOOIC and the lowest RMSE, which indicated the model most fitted to the data.

Although the estimated H of the six HD models (MO-6, MS1-5, MO-0, MS1-0, MS2-0, and Kato HD model) did not differ in the smaller trees at the D approximately <75 cm, the difference of the estimated H increased as the D increased (at the D approximately >75 cm) (figure 3(a)). In both MO-6 and MS1-5, we found that the HD relationships differed among families and genera level (figures 3(b)–(e)). For example, in Dipterocarpaceae, the genera Dipterocarpus and Shorea were the tallest and second tallest among the genera in both MO-6 and MS1-5 (figures 3(b) and (e)). In Euphorbiaceae, Elateriospermum was the tallest genus in both models (figures 3(c) and (f)). Comparing to MO-6, MS1-5 showed more variation among genera in estimated H in smaller trees (D approximately <25 cm, figure 3(f)) because the ${\beta _0}$ varied among genera (figure S4(b)). Likewise, in Fabaceae, MS1-5 exhibited more different patterns among genera than MO-6 (figures 3(d) and (g)). Both models predicted that the genus Koompassia was the tallest tree among the genera at the given D at a larger size (approximately >75 cm), while it was shorter than other genera at the given D at a smaller size (approximately <75 cm).

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3.3.1. Relationship between AGB and D

The relationships between the estimated AGB and D were similar in smaller trees but became different in larger trees as D increased among the four approaches of AGB estimation based on the best HD models in (1) MO-6 and (2) MS1-5 × two AGB models (Kato volume model or Chave AGB model) (figure 4(a)). Generally, the estimated AGB was higher in MS1-5 than that in MO-6, and higher in the Chave AGB model than that in the Kato volume model. The choice of HD model resulted in a greater difference in AGB estimation than the choice of AGB model. Moreover, the difference became larger with a larger D (approximately 150 cm). The RMSE values for the directed measures of AGB in IBP (N = 156, Kato et al 1978) were 0.537, 0.389, 0.448, and 0.306 for the MO-6 × Kato model, MS1-5 × Kato HD model, MO-6 × Chave AGB model, and MS1-5 × Chave AGB model, respectively.

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We also explored the taxonomic difference in the relationship between the estimated AGB and H (MO-6 or MS1-5 and Chave AGB model). The estimated AGB varied among families and genera in both the MO-6 and MS1-5 models (figures 4(b)–(g)). In Dipterocarpaceae (figures 4(b) and (f)), the genera Dipterocarpus and Neobalanocarpus had higher AGB at given D than Shorea; for example, Dipterocarpus had about 1.8-fold AGB compared with the genus Shorea in a 100 cm D tree. In Euphorbiaceae (figures 4(c) and (g)), the genus Elateriospermum had the highest AGB at given D, and in Fabaceae (figures 4(d) and (f)), the genus Koompassia had the highest AGB at a given D.

3.3.2. Total AGB in Pasoh Forest Reserve

The vertical patterns of AGB, which was estimated by both the best HD models × Chave AGB model, number of individuals, species diversity, and functional diversity were described in figure 5; we found that the vertical patterns were contrasting among indices. AGB increased along with the layer. The emergent layers held the highest AGB, 44% of the total AGB (figures 5(a) and (b)). In this layer, Dipterocarpaceae followed by Fabaceae were the major components of the total AGB in the emergent layer, at ∼62% and ∼21%, respectively. In the canopy layer, Dipterocarpaceae followed by Euphorbiaceae and Fabaceae contributed to the total AGB in the layer, at 36%, 9% and 7%, respectively. In contrast, in the subcanopy and understory layers, these dominant families shared less in the total AGB; for example, Dipterocarpaceae contributed only ∼12% of the total AGB, and families other than Dipterocarpaceae, Euphorbiaceae, and Fabaceae comprised ∼74% of the total AGB in the subcanopy and understory layers. The total number of individuals was higher in the lower, subcanopy, and understory layers. In particular, the most abundant family regarding the number of individuals in the subcanopy and the understory layer was Euphorbiaceae, at 13% and 16%, respectively. Likewise, the indices on species diversity decreased along with the layer; lower layers held higher species diversity (figures 5(d)–(f)). In particular, the species richness of Dipterocarpaceae, Euphorbiaceae, and Fabaceae, which were the major sources of AGB, were only a small part of the total species richness in the understory layer, at 6%, 6%, and 3%, respectively. Among the functional diversity indices, the functional diversity of q = 0 was highest in the understory layer, whereas the functional diversity of q = 1 and q = 2 were highest in the canopy layer (figures 5(h) and (i)).

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This study showed that HD models formulated by relating H against not only D but also taxonomic effect best performed statistically. This finding indicates the importance of taxonomic-specific HD for accurate estimation of H. The HD relationships varied more in genus level than in family level; in particular, we found higher variation even in smaller trees in the genera of Euphorbiaceae and Fabaceae. This finding may be attributed to these families that consist of species with higher interspecific trait variation; for example, Euphorbiaceae holds both light-demanding species, such as the genus Macaranga, and shade-tolerant species, such as the genus Elateriospermum. These growth trait variations are also linked with WD or carbon accumulation efficiency—for example, fast-growing trees generally have low WD, whereas slow-growing trees exhibit the opposite. Fabaceae holds not only subcanopy or canopy species but also emergent tree species (i.e., the genus Koompassia), which can be the highest at a given D approximately >110 cm. In contrast, Dipterocarpaceae showed more similar HD relationships among genera, especially in smaller trees. Because dipterocarp are generally shade-tolerant and slow-growing species (Manokaran and Kochummen 1994, Köhler et al 2000), we found similar patterns of the HD relationship among the genera in the forest floor. However, some species in the genus Shorea (i.e., light red meranti), have a relatively higher growth rate compared with the other dipterocarp species, especially under the fine light conditions (Takeuchi et al 2005), which suggests that we might underestimate the variation in the HD relationship within the genus. The differences in traits and life-history strategies among species can lead to variations in HD relationships, even within the same taxonomic group. Furthermore, these HD relationships predict a H threshold where H cannot increase beyond a certain point despite an increase in D. This relationship implies that the HD model can partially indicate the growth strategies of different taxonomic groups, including whether they grow vertically (H) or horizontally (D), based on their age and size. Our results also revealed potentially the highest genus groups in the forest in the largest D-size class—the genus Dipterocarpus of Dipterocarpaceae and Koompassia of Fabaceae. In fact, these were ranked in the top ten highest trees in the 6 ha plot. In contrast, this study was missing the species-level effect. Here again, for example, S. pauciflora was also the tallest tree in the plot. Because Shorea at the genus level was not estimated to be high enough, we overlooked the effect. Therefore, the species-level model requires further study.

Accurate prediction of H is crucial for improving the estimation of AGB (Kearsley et al 2017). This study showed that the HD models developed at the taxonomic level better fit the AGB-D relationship statistically. The logarithmic relationship between AGB and D indicates that larger trees make a bigger contribution to the total AGB. The AGB-D relationships varied among genera, and the study revealed which genera had higher AGB for a given D. For example, larger trees in the genera Dipterocarpus, Neobalanocarpus (Dipterocarpaceae), Elateriospermum (Euphorbiaceae), and Koompassia (Fabaceae) are likely significant contributors to AGB storage in the forest.

The total estimated AGB in Pasoh Forest Reserve varied among the different AGB models. However, no significant differences were observed between the HD models. This finding may be because most of the trees in the 6 ha plot were small, and the AGB-D relationships were similar among MO-6 and MS1-5 for smaller trees. The larger difference between the Chave AGB model and Kato model highlights the crucial role that taxonomy plays in the AGB models because the Chave model includes taxonomy-specific WD. Larger AGB estimated by the Chave AGB model suggested a high abundance of species with larger WD, which resulted in about 10% higher than that estimated by the Kato AGB model. Thus, these findings indicate that AGB estimation without the taxonomic effect would lead to underestimation of the total AGB in the tropical forest. In fact, even the minimum estimate in our results in 2017, which was 457.5 Mg ha⁻¹, was higher than that in the previous estimates in 1998 (431.2 Mg ha⁻¹, Hoshizaki et al 2004). This would be also resulted from the growth of the forest. The estimated total AGB in 2017 in the comparable (conventional) method was 475.8 Mg ha⁻¹, which was far higher than that in the previous report, which indicated that AGB increased at by an average of 2.3 Mg ha⁻¹ per year in 1998–2017. The total AGB of tropical forests generally highly fluctuated with time, as well as space (Okuda et al 2021). In particular, because the plot included a 'disturbed area' in the past; these areas would have recovered in more recent years and contributed to increased AGB, which was also suggested in the former study (Okuda et al 2021).

Previous studies have highlighted the importance of developing local HD models for accurately estimating AGB in tropical forests (Feldpausch et al 2012). This is primarily because HD relationships can vary across continents, regions, forest types, and taxonomic compositions (Banin et al 2012). Utilizing a local HD model can help minimize error in AGB estimation, even when generalized pantropical AGB models are used (Chave et al 2014, Popkin 2015, Kearsley et al 2017, Fayolle et al 2018).

Similarly, AGB models can be site-specific. Several allometric AGB models have been developed for Southeast Asian tropical forests across different sites (Kato et al 1978, Yamakura et al 1986, Ketterings et al 2001) and forest types (Pinard and Cropper 2000, Kenzo et al 2009). This study employed a generalized pantropical AGB model with a species-specific variable, WD, to account for site-specificity in terms of species composition. Although this study developed a local HD model by considering tree taxonomic groups and contributed to the improvement of subsequent AGB models, further enhancements to the AGB model remain a future challenge. It has been suggested that incorporating taxonomic-based estimation can enhance the performance of AGB models (Basuki et al 2009, Paul et al 2016).

The study of AGB and biodiversity patterns in Pasoh Forest Reserve using HD and AGB models, including the taxonomic effect, helped to develop an understanding of the role of taxonomy in determining the total AGB and its vertical distribution. The major families contributing to the total AGB were Dipterocarpaceae, Euphorbiaceae and Fabaceae, mostly from trees in the emergent and canopy layers. This finding is consistent with previous studies that showed that large trees have a significant impact on the total AGB of tropical and temperate forests (Lutz et al 2012, 2018, Slik et al 2013, Fayolle et al 2018, Fotis et al 2018). In contrast, species diversity was higher in the lower layers of the forest. This contrasting pattern suggests that the mechanisms governing species diversity are different in the canopy and understory layers (Mensah et al 2018). The canopy layer, occupied by a limited number of tree species, is responsible for storing AGB. This pattern can be explained by the selection effect (Fox 2005, Fotis et al 2018). The understory layer has a high number of individuals with diverse species coexisting in heterogeneous local environments, which is consistent with the niche differentiation effect (Brown et al 2013, Johnson et al 2017). It suggests that a taller canopy promotes the species coexistence by producing the heterogeneous local environments under light conditions and moisture availability caused by canopy openings in the emergent and canopy layers (Wright et al 2010). In addition, trees in the understory and the subcanopy layer would contribute to forest productivity more than taller trees in a tropical forest (Kohyama et al 2023). Moreover, species diversity in the understory is a source of potential carbon sources for future large trees. Therefore, interaction and differences in the governing mechanism between the canopy and understory would be essential for both high AGB and high species diversity in the forest.

This study also found the higher functional diversity in the upper middle layers, which is more similar to that of AGB rather than that of species diversity. Functional diversity is more closely related to ecosystem processes and dynamics and would have a stronger predictive power for AGB than species diversity (Ruiz-Benito et al 2014, Tobner et al 2016). Thus, functional diversity could be a potential indicator of ecosystem functioning in forest stratification (Dıéaz and Cabido 2001, Cadotte et al 2011) although species richness and functional diversity are often correlated (Tobner et al 2016).