Study area

The research was conducted in two forest concessions for the management and harvesting of products other than timber (Brazil nut collection), located in the Tambopata district, Tambopata province, Madre de Dios region, Peru. Based on the National Land Cover Map of the Peruvian Ministry of Environment (^{Minam, 2015}), a low-hill forest (12°6'31.16" S and 69°33'17.96" W) and a low-terrace forest (12°11'18.85" S and 69°23'5.94" W) were identified in the study area. The two concessions were Fredy Turpo’s and Maritza Callo’s; the former has an area of 634 ha and is located in a low-hill forest; of the latter concession, only the part of the low-terrace forest was considered, with an area of 550 ha (Figure 1).

Figure 1 Location of the study area in the Tambopata province, Madre de Dios region, Peru (A and B), in the areas corresponding to Fredy Turpo’s and Maritza Callo’s concessions (C and D). 

Data collection

A sample of 42 A. leiocarpa trees of the following species was collected: 22 in low-hill forest, and 20 in low-terrace forest. Only trees with a diameter at breast height (DBH) above 41 cm were included; this length is equivalent to the minimum cutting diameter established in the Peruvian forest regulations for merchantable timber harvesting (^{Del Mar, 2021}); therefore, only information from merchantable specimens was analyzed. Each individual was felled, and the length of the stem (height of the stem) was measured with a model Pro-FMHT33100-0 Stanley FatMax^® flexometer, the diameter, with a Haglöf^® (Mantax Blue) caliper every 2 m along the stem (^{Aguilar et al., 2017}), without sectioning it into logs. At the base of the stem, two bark measurements were taken with the flexometer; the thickness of sapwood and heartwood was also recorded in centimeters to calculate the percentage of sapwood and heartwood, whose reference was the diameter of the stem. The volume of each section was estimated with the Smalian equation (^{Guzmán-Santiago et al., 2020}; ^{Souza et al., 2021}), the volume of the forest was obtained from the sum of all the sections.

Data analysis

Based on the shape of the stem of A. leiocarpa observed in the field, the cylinder was used to calculate the morphic coefficient (^{Guzmán-Santiago et al., 2020}); for this purpose, the following expression was used:

Where:

MC = Morphic coefficient

V _R = Real stem volume

V = Volume of cylinder solid with base area equal to the base area of the tree and equal in height.

Differences in height, DBH, stem volume, sapwood thickness, heartwood thickness and bark thickness between forest types were evaluated using the two-tailed t-Student test when the parametric assumptions (normality and homoscedasticity) were met, and the Mann-Whitney test when not (^{Berger et al., 2018}); a significance level of 5 % was used in both cases. On the other hand, the t-Student test was applied to a sample in order to compare the estimated MC values with respect to the MC established by the Peruvian national authority and to the one cited in previous research (^{Del Mar, 2021}; ^{Lozano and Bonilla 2022}) for cylindrical Dipteryx odorata (Aubl.) Forsyth f. stems, whose shape is similar to that of A. leiocarpa stems (^{Lozano and Bonilla, 2022}).

For the purpose of analyzing the relationship between DBH, height, bark thickness, thickness of the sapwood and the heartwood, and sapwood/heartwood ratio, a correlation analysis was carried out for each forest type; these were represented in a correlation matrix using Pearson’s and Spearman’s (non-parametric) correlation coefficients. Simple linear regression models were fitted to the variables that were significantly correlated. An analysis of covariance (ANCOVA) was also applied to analyze the influence of the forest type on the MC, in which the DBH was the covariate, as well as the forest type-diameter interaction.

11 nonlinear allometric models were assessed for volume estimation (Table 1), considering the volume functions suggested by ^{Guzmán-Santiago et al. (2020)}, ^{Ogana et al. (2020)} y ^{Reis et al. (2020)}.

The following fit statistics criteria were used to discriminate between the best nonlinear models: root mean square error (RMSE), mean square error (MSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) (^{Ogana et al., 2020}; ^{Reis et al., 2020}). The best models were selected using the model ranking method (^{Tamarit et al., 2014}; ^{Ogana et al., 2020}), in which values from 1 to 11 were assigned to each model by fit statistic, in descending order, with 1 being the lowest and best value. For the final rating, all the values obtained were added together, and the model with the lowest value was considered the best (^{Ogana et al., 2020}; ^{Reis et al., 2020}).

All analyses and figures were performed with the R v4.2.2.2 statistical software in the environment of R-Studio v12 (^{R Core Team, 2022}), InfoStat (^{InfoStat, 2022}), and SigmaPlot v14 (^{Inpixon, 2022}). In R, the packages ggplot2, AICcmodavg, HH, and PerformanceAnalytics were used.

Morphic coefficient by forest type

A. leiocarpa trees in the low-terrace forest had greater DBH, stem height, and sapwood thickness than in the low-hill forest. Although only the stem height was statistically significant (Student’s t, p<0.01). On the other hand, trees from the low-hill forest had a slightly greater bark and heartwood thickness than those from the low-terrace forest, although this difference was not statistically significant (Student’s t, p>0.05) (Table 2).

Trees in the low hill forest had a significantly higher MC, of 0.88±0.07 (Student’s t, p<0.01), than those in the low terrace forest, whose MC was 0.79±0.10, i.e., 11.4 % higher. In the low-hill forest, none of the tree variables analyzed were significantly correlated with the MC (Pearson, p>0.05). However, in the low-terrace forest, trees of smaller diameter showed a tendency to a higher MC because a significant, inverse relationship between MC and stem diameter was found (r=-0.47, p<0.05) (Figure 2).

Figure 2 Scatter plot and simple linear regression line fitted to the model between tree diameter and morphic coefficient by forest type. 

The ANCOVA showed that the MC varies significantly between the two forest types, which explains 22 % of the variability of the MC (p<0.001, Table 3). The DBH had no influence on the MC (p>0.05), unlike the interaction between the forest type and the diameter (p=0.046). This suggests that the relationship between the diameter and the MC varies according to the forest type, which is direct and non-significant in low-hill forest and inverse and significant in low-terrace forest (Table 3, Figure 2). The fitted regression model expressed as MC=0.993-0.00227×DAP was only significant for the low-terrace forest (R ²=0.18 y p<0.05).

The Student’ t test for one sample and p<0.01 showed that the MC averages obtained of 0.79 to 0.88, were significantly higher than the 0.65 established by the Peruvian forestry authority (^{Del Mar, 2021}) (Figure 3), as well as to the average cited for species with cylindrical stems (^{Lozano and Bonilla, 2022}). Compared to the MC of 0.82 registered for D. odorata ―a species with similar characteristics in terms of straight cylindrical stem and with a detachment of the bark in the form of irregular plates (^{Lozano and Bonilla, 2022})―, this value was found to be slightly higher than that determined in the low-terrace forest (p>0.05) and significantly lower than that estimated in the low-hill forest (p<0.01) (Figure 3). ^{Aguilar et al. (2017)} report that variations in stem characteristics in different species influence the MC; in the present study, the high MC values are due to the fact that A. leiocarpa has a straight, cylindrical, irregular stem with a low reduction in diameter along the length of the stem. In addition, the growth and shape of the stem is similar to D. odorata which also has a high MC.

Figure 3 Comparison of the morphic coefficient of Apuleia leiocarpa (Vogel) J. F. Macbr. between two forest types and with reference values. 

Sapwood to heartwood ratio

Non-significant differences in sapwood and heartwood thickness or sapwood to heartwood ratio were observed based on the forest type (p<0.05, Table 4). Stem height and bark thickness did not correlate significantly with the thickness of sapwood and heartwood or with their proportions (p<0.05). However, the DBH was significantly correlated with the proportion of sapwood, with heartwood, and with the proportion of heartwood, although this varied according to the type of forest (Table 4).

In the low-hill forest, only a significant relationship between DBH and heartwood thickness was obtained (rho=0.93, p<0.05). Whereas, in the low-terrace forest, DBH was significantly correlated with the sapwood proportion (r=-0.66, p<0.05), the heartwood thickness (r= 0.83, p<0.05), and the proportion of heartwood (r=0.66, p<0.05). This has implications for the quality of the wood of A. leiocarpa according to the type of forest because, since there is a significant relationship between DBH and sapwood in the low-terrace forest, a greater thickness and a higher proportion of sapwood is expected there than in the low-hill forest (^{Aye et al., 2022}).

Figure 4 shows the trend in both sapwood and heartwood thickness, as well as in the sapwood/heartwood ratio in relation to the DBH. It was determined that sapwood thickness is not related to DBH in any forest type; it was observed that heartwood thickness in both forest types increases as a function of the DBH, although the coefficient of determination is higher in the low-hill forest (R ² =0.86) than in the low-terrace forest (R ² =0.69). Likewise, the proportion of heartwood has a linear and direct relationship, while the proportion of sapwood has an inverse relationship. This is because the heartwood is directly related to the age and diameter of the trees, and its formation can be affected by exogenous and endogenous factors such as the density or number of trees (spacing), the crown diameter, and the content of extractive chemical compounds, among others (^{Kang et al., 2001}; ^{Piqueras et al., 2020}).

(a) = Between DBH with sapwood thickness; (b) = Between DBH with sapwood ratio; (c) = Between DBH with heartwood thickness; (d) = Between DBH with and heartwood ratio. P-valor <0.01 = P-value <0.01.

Figure 4 Scatterplot and trend by forest type. 

Heartwood determines the economic value of the wood, and the sapwood is closely related to the physiological functions of the trees (^{Meunpong et al., 2021}). Therefore, it will be important for forest harvesting to estimate heartwood thickness based on easily measured variables, such as the DBH (^{Yang et al., 2020}). In the present study, heartwood thickness (HT) was found to be directly related to the DBH; therefore, the models generated could be used to estimate heartwood thickness. The linear model for estimating heartwood thickness in the low-hill forest was:

Where:

HT = Heartwood thickness

DBH = Diameter at breast height (m)

In the low-terrace forest, it was:

Where:

HT = Heartwood thickness

DBH = Diameter at breast height (m)

Forest volume estimation models

In both forest types, the 11 models fitted to estimate volume were significant (p<0.05) with low values for the root mean square error (of up to 0.88 in the low hill forest, and of up to <1.088 in the low-terrace forest). In the two forest types, the models that generated the lowest values of RMSE were Takata, Spurr, Spurr potential, and Spurr with independent term (Table 5).

Based on the ranking of models, it was determined that the best model for estimating forest volume in the low-hill forest was the Takata model expressed in the following form:

Where:

V _s = Volume of the stem

DBH = Diameter at breast height (cm)

This had the lowest total score (8 points), followed by the Spurr model (13 points) and the Spurr potential model (15 points). For the case of the low terrace forest, the best model was the Spurr model with independent term expressed as:

Where:

V _s = Volume of the stem

DBH = Diameter at breast height (cm)

H = Height (m)

The same that presented the lowest value of the total rating (7 points), followed by Takata (14 points) and Spurr's potential model (18 points). These models exhibited the lowest values for RMSE, AIC, and BIC. The AIC and BIC criteria are widely used to select the simplest model with the greatest explanatory power in which balance is sought between the predictive capacity and the number of parameters it must have to achieve an optimal fit; these statistics reward the models as the explained variance increases but at the same time penalize them as the number of parameters increases (^{Nikita et al., 2022}).

Several authors agree that the Schumacher-Hall function guarantees accurate estimates for several tropical species (^{Costa et al., 2016}; ^{García et al., 2016}; ^{Tlaxcala-Méndez et al., 2016}; ^{Guzmán-Santiago et al., 2020}). However, for A. leiocarpa in the two forest types analyzed, the best models for estimating forest volume were Takata and Spurr with independent terms. However, the Schumacher-Hall equation at the evaluated sites was among the six best models, in agreement with the findings of several studies (^{Costa et al., 2016}; ^{Tlaxcala-Méndez et al., 2016}; ^{Guzmán-Santiago et al., 2020}).

Research on specific allometric equations for volume of A. leiocarpa yielded similar results to that obtained in the present study. For example, ^{Midsma (2001)} in Argentina indicates that the model with the best fit was the Spurr model; in the study on the low-hill forest, it was the second best, while in the one on the low-terrace forest, the Spurr model with independent term was the best. However, ^{Souza et al. (2021)} determined that the Husch model was the best for the Brazilian Amazonia. These differences could be due to the fact that the study by ^{Souza et al. (2021)} used models with log-transformed variables and that the Guadua genus is predominant in the forests where they collected their information.

When comparing the RMSE and MSE values generated by the models in each forest type, they were found to be lower in the low-hill forest. These differences are due to the different site conditions to which A. leiocarpa trees are subjected. In particular, for the estimation of the merchantable volume, it is important to consider that the same species has a different growth response as the site’s conditions change (^{Molina-Valero et al., 2019}; ^{Mendes et al., 2020}). This is reflected in the dimensions reached by the stems in each forest condition. For example, although the average DBH of A. leiocarpa stems was similar in both forests (86.55 cm in the low-hill forest, and 87.85 cm in the low-terrace forest), trees in the low-terrace forest had a higher canopy height than those in the low-hill forest. This difference is related to variations in physiography, in addition to the fact that low-hill forests are more irregular and tend to occur on steeper slopes, as opposed to low-terrace forests (^{Velioğlu et al., 2023}), potentially affecting the availability of water, a key element for growth (^{Rachid-Casnati et al., 2019}).

As for the comparison between the volume estimation carried out with the best allometric models and that obtained based on the shape factors by forest type, it was observed that, in the low-hill forest, the RMSE value calculated with the Takata equation, of 16.15, was lower by 16.6 % than the one estimated with the shape factor, of 19.37. While in the low-terrace forest the volume values estimated with the MC yielded an RMSE of 41.11, which is 54.7 % higher than the one obtained with the Spurr model with independent term, of 18.61. This analysis suggests that specific equations are better for calculating the volume of the stem than the use of the MC; furthermore, in order to minimize errors in estimating the volume of timber in each forest type, the variations in bark thickness and the thickness and proportion of sapwood and heartwood should be considered.

Among the limitations of this study, its results are restricted to only two forest conditions in the Madre de Dios region of Peru, affecting the generalizability of its application to other ecoregions. On the other hand, a small sample was analyzed in each forest condition due to a low density of individuals per unit area. In addition, we did not have information on a complete range of diameter categories or heights, because we only measured merchantable specimens of A. leiocarpa, for which forestry regulations of the Government of Peru have established a minimum cutting diameter of 41 cm for timber harvesting. These aspects, while restricting the applicability of the results, also provide insights for a deeper understanding of the form factor and promote the use of allometric models for volume estimation in the Peruvian Amazonia. In future studies, it is recommended to include more forest types in the analysis, to increase the sample size, and to use non-destructive methods in order to include individuals with DBH less than 40 cm.