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Highlights:
An allometric equation was fitted to estimate the height of Carapa guianensis.
At 60 months of age, C. guianensis had a survival rate of 70 to 87 %.
Mean annual increment in diameter and height was 2.9 cm∙yr-1 and 2.3 m∙yr-1, respectively.
C. guianensis is probably reaching the minimum harvestable diameter (40 cm) at an early age.
C. guianensis has high potential for forest development in the Pacific region of Nariño.
Introduction
Tropical forests are made up of a great diversity of native species that are an important source of ecosystem services and timber and non-timber forest products. Studies on these forests have been a great contribution to the forestry sector; however, studies on native species are scarce, a situation that prevents accurate decisions on the use of the species on a larger scale in reforestation programs (Abarca-Valverde, Meza-Picado, & Méndez-Gamboa, 2020) .
To contribute to the expansion of knowledge regarding growth and development of native forest species, this research focused on Carapa guianensis (Aubl.), a native forest species of the tropical rainforest that belongs to the Meliaceae family. This multipurpose species has potential for use in agroforestry arrangements, in timber production and also stands out because its seeds are used to extract oil on an artisanal or industrial scale for pharmaceutical and cosmetological purposes (Bacca, Zuluaga, Perez, Burbano, & Palacio, 2020).
The ecological and economic importance of C. guianensis invites to study its ex situ development and to estimate the productivity of the species. In this respect, direct measures that reflect productivity are the mean annual increment (MAI) and the annual periodic increment (PAI), considering specific management and historical environmental conditions, so that future productivity of a site will vary according to these factors.
Another property to determine growth potential, through behavior, is the height-diameter relationship. Height is a variable that is difficult to measure in the field, so it is necessary to implement tools that allow estimation, using historical data collected directly in the field, and analysis through the adjustment of allometric growth models. Foliage cover is very dense, for tropical forest plantations and forests, causing visual obstruction to measure tree height and, consequently, there is bias in the information collected, even with specialized tools such as laser hypsometer or LiDAR (Larjavaara & Muller-Landau, 2013).
Allometry is the study of the variation of anatomical and physiological dimensions in living beings as they correlate; this allows us to approach the understanding of organisms as a whole and not as the sum of their parts. Allometry studies the relationships of the variation of magnitudes in living beings, both their body architecture and those that may occur between it and the variables that quantify physiological processes in a broad sense (Sanchez & Gutiérrez, 2020). In forestry terms, allometry is applied in allometric models which, in this case, establishes a mathematical equation that allows estimating a variable from another variable that is easily measured in the field; for example, predicting height from diameter at breast height (Mensah, Veldtman, & Seifert, 2017) .
For many tropical tree species, such as C. guianensis, there is no information on growth and yield for the study area. This leads to inadequate economic analysis, preventing appropriate management for humid tropical forests (Sharma & Breidenbach, 2015).
Given the current situation and anticipating future demands for goods and services provided by C. guianensis in the municipality of Tumaco, Department of Nariño, Colombia, the objective of this research was to analyze the growth potential of this native forest species through the characterization of tree-size parameters and allometric modeling for height estimation during the first phase of development. It is expected that the information generated will provide a tool that facilitates the estimation of height in a fast and efficient way without the use of complex and expensive tools.
Materials and methods
Study area
The research was conducted at the Centro de Investigación El Mira de la Corporación Colombiana de Investigación Agropecuaria (AGROSAVIA), located at 1° 32´ 59" N and 78° 41´ 53" W, at an altitude of 16 m in the municipality of Tumaco (Pacific zone), Department of Nariño, Colombia. The area is classified as tropical rainforest (Holdridge, 1982). According to Reyes, Rodríguez, Peña, and Bastidas (2008), Tumaco has a warm humid climate with an average temperature of 25.7 °C, annual relative humidity of 86 % and annual precipitation of 3 067 mm. The area has potential soils for agricultural and forestry use; according to soil analysis results from the AGROSAVIA laboratory, pH is 5.59 and organic matter has a value of 2.86 %. Topography is relatively flat and structural class is clay loam.
Tree-size data
Data were obtained from 11 inventories carried out in three permanent rectangular sampling plots, each with an area of 1 080 m2. The frequency of the register was semiannual during 60 months from 2014 to 2019 in 90 even-aged individuals per plot, planted at a distance of 6 x 6 m. The following tree-size variables were measured for the total number of trees: Total height (H, m), obtained with a clinometer (SUUNTO TANDEM 360PC/360R); diameter at a height of 1.3 m (DBH, cm) above ground level (Cancino, 2006) measured with a diameter tape; and survival (%).
Determination of mean annual increment
The mean annual increment of DBH (MAID) and total height (MAIH) was calculated by the quotient of the highest present value of the variable considered and the age from time zero. The resulting value expresses the mean total growth at a certain age, indicating the annual measure of growth for any age (Casal-Ángeles, Vásquez-García, Cetina-Alcalá, & Campos-Bolaños, 2016).
Data analysis
Allometric modeling
Linear and nonlinear allometric models commonly used to model the functional relationship between a biomass variable and predictor variables of forest species, such as DBH and age, were fitted (Table 1). Each of the models was fitted using the PROC MIXED procedure for linear mixed models of the statistical package SAS/STAT software, version 9.4 (SAS Institute Inc., 2013). There was evidence of dependence between measurements because repeated measurements were taken over time on the same individual. According to Picard, Saint-André, and Henry (2012), height variability tends to increase as the tree increases in diameter, which determines an adverse effect on homoscedasticity of errors; therefore, hybrid correlation and heteroscedasticity structures were fitted, such as the heterogeneous first-order autoregressive (ARH1), heterogeneous symmetric composite (HSC) and heterogeneous Toeplitz (TOEPH).
Table 1 Allometric models evaluated for the estimation of the total height of Carapa guianensis according to diameter and age (60 months) in Tumaco, Colombia.
| Model | Type | Covariance structure | Equation |
|---|---|---|---|
| 1 | Linearized power | ARH 1 | ln H = β0 + β1 lnDBH |
| 2 | CSH | ||
| 3 | TOEPH | ||
| 4 | Double input linearized power | ARH 1 | ln H = β0 + β1 ln(DBH2 Age) |
| 5 | CSH | ||
| 6 | TOEPH | ||
| 7 | Linearized polynomial power | ARH 1 | ln H = β0 + β1 lnDBH + β2 (lnDBH)2 |
| 8 | CSH | ||
| 9 | TOEPH | ||
| 10 | Polynomial | ARH 1 | H = β0 + β1 DBH + β2 DBH2 |
| 11 | CSH | ||
| 12 | TOEPH | ||
| 13 | Multiple | ARH 1 | H = β0 + β1 DBH + β2 Age |
| 14 | CSH | ||
| 15 | TOEPH | ||
| 16 | Linear | ARH 1 | H = β0 + β1 DBH |
| 17 | CSH | ||
| 18 | TOEPH |
β0, β1 and β2 = model parameters, DBH = tree diameter at breast height (cm) measured at 1.3 m from the base, Age = tree age in months, H = height (m) from the base to the apex of the tree. Hybrid correlation and heteroscedasticity structures: heterogeneous first-order autoregressive (ARH 1), composite symmetric heterogeneous (CSH) and Toeplitz heterogeneous (TOEPH).
Validation of assumptions
Error dependence was addressed by modeling the correlation structures mentioned. The assumptions of the fitted models were visually validated by homoscedasticity diagnosis and normality of standard errors. The homogeneity of variances was assessed with a scatter plot of the residuals and the fitted values of the model. The normality of the errors was checked with the quantile-quantile plot by observing the residuals through the theoretical standard normal distribution.
Analysis of model performance
The best models were selected through goodness-of-fit measures, such as Akaike's criterion (AIC) and Schwarz Bayesian criterion (BIC), and three predictive performance measures such as mean absolute error (MAE), root mean square error (RMSE) and efficiency (Table 2).
Table 2 Goodness-of-fit parameters of the models for the estimation of Carapa guianensis height according to diameter and age (60 months) in Tumaco, Colombia.
| Statistical parameters | Equation |
|---|---|
| Akaike's criterion | AIC = -2logL + 2p |
| Schwarz Bayesian criterion | BIC = -2logL + plogn |
| Mean absolute error |
|
| Square root of mean square error |
|
| Efficiency |
|
L = maximum value of the likelihood function; p = number of
model parameters, Yi = i-th observation of the
response,
Selecting the best model
The best model was selected by assigning greater weight to the predictive performance criteria than to the goodness-of-fit criteria. As for the predictive performance, efficiency is better the closer it is to 1, while low values of MAE and RCME are the best. Similarly, with respect to goodness-of-fit, the model is better the lower the AIC and BIC criteria.
Results and Discussion
According to Table 3, at 60 months of age, the trees showed survival between 70 and 87 %. Height had values between 11.16 m and 12.72 m, while DBH varied between 14.37 cm and 16.62 cm. The coefficient of variation showed greater relative dispersion of the data in DBH.
Table 3 Statistical parameters of the tree-size development variables of 90 individuals of Carapa guianensis at the age of 60 months in Tumaco, Colombia.
| Plot | Survival (%) | Variable | Mean | SD | SE | CV (%) |
|---|---|---|---|---|---|---|
| P1 | 70 | Height (m) | 12.72 | 1.51 | 0.33 | 11.86 |
| DBH (cm) | 15.34 | 3.3 | 0.72 | 21.52 | ||
| P2 | 70 | Height (m) | 11.16 | 2.22 | 0.49 | 19.92 |
| DBH (cm) | 14.37 | 3.56 | 0.78 | 24.76 | ||
| P3 | 87 | Height (m) | 12.22 | 2.22 | 0.43 | 18.14 |
| DBH (cm) | 16.62 | 3.98 | 0.78 | 23.96 |
DBH: diameter at breast height (1.30 m), SD: standard deviation; SE: Standard error; CV: coefficient of variation.
Mean annual growth increment of Carapa guianensis
For a five-year evaluation period (60 months), MAID was 2.9 cm∙yr-1, while MAIH was 2.3 cm∙yr-1. On average, trees reach a diameter of 15.53 ± 3.72 cm and height of 12.04 ± 2.10 m. These results were greater than those reported in other studies for the species. In a forest of C. guianensis, under restoration, located in the Guacha river basin in Colombia, MAID was 0.62 cm∙yr-1 (Cárdenas, 2014). In a six-year plantation in Requena, Peru, a MAID of 0.6 cm∙yr-1 and a MAIH of 0.95 cm∙yr-1 were reported (Dávila, 2003). Suatunce, Diazl, and García (2009) recorded a MAID of 1.42 cm∙yr-1 and a MAIH of 1.13 cm∙yr-1 in a five-year plantation at Quevedo Dam, Ecuador. Tonini, Arco-Verde, and Sá (2005) estimated a MAID of 1.5 cm∙yr-1 and a MAIH of 1.3 cm∙yr-1 for a seven-year plantation in Roraima, Venezuela. Similarly, in forests in some Central American countries, a MAID of 0.2 to 0.5 cm∙yr-1 has been reported and with silvicultural release treatments have increased from 0.6 to 0.7 cm∙yr-1; while three to nine year old plantations in Costa Rica have had a MAID of 1.4 to 1.5 cm∙yr-1 and MAIH of 1.2 to 1.4 cm∙yr-1 (Cordero & Boshier, 2003).
The superior growth found in the municipality of Tumaco is probably due to agroecological conditions, the rigorous selection of trees to reach quality seeds and silvicultural work; however, domestication efforts should continue to be focused on the generation of tools to further reduce the cutting cycle and preserve the individuals established in forest plantations. Tonini et al. (2005) affirm that a species with diameter growth greater than 1 cm∙yr-1, under forest plantation, can be considered with better increment than the species in natural forest. McLean et al. (2011) state that Carapa trees in plantations show greater flexibility as a response to the influence of wind on the stem, compared to trees in natural forests.
In relation to the time of harvest, according to a dendroecological study carried out in Nicaragua, the age of C. guianensis is estimated to be between 70 and 122 years, an age at which it is presumed to reach the minimum cutting diameter (MCD) for the area (40 cm) (Paguada, 2015). On the other hand, in Costa Rica, Cordero and Boshier (2003) estimated that the species can reach that diameter at the age of 50, considering its environmental conditions. However, Bauch and Dünisch (2000) found that trees of this species can be harvested in early stages and can be put to good use, because the species produces mature wood at a very early age with a good decorative character due to the color in the heartwood and high natural durability. Based on the results obtained so far in this study (MAID = 2.9 m∙yr-1 and MAIH = 2.3 m∙yr-1), and under the agroecological conditions of the region, it is likely that C. guianensis reaches maturity at an early age.
Height-DNH allometric model
Table 4 indicates that the nonlinear allometric models (M4, M6, M7 and M8) had good fits compared to the linear models. The linearized polynomial power equation was selected for better performance; subsequently, with validation of the assumptions, the model M8 was the best fit statistically, as shown in Figure 1.
Table 4 Estimated coefficients and selection criteria of the fitted allometric diameter-height models of Carapa guianensis at the age of 60 months in Tumaco, Colombia.
| Model | Coefficients | Selection criteria | ||||||
|---|---|---|---|---|---|---|---|---|
| β0 | β1 | β2 | AIC | BIC | MAE | RMSE | Efficiency (%) | |
| M1 | 0.078 | 0.804 | -891.1 | -863.4 | 0.14 | 0.17 | 91.53 | |
| M2 | -0.292 | 0.915 | -719.3 | -691.7 | 0.2 | 0.24 | 83.43 | |
| M3 | 0.506 | 0.586 | -936.2 | -887.8 | 0.21 | 0.26 | 81.37 | |
| M4 | -0.867 | 0.34 | -1 069.00 | -1 041.30 | 0.11 | 0.14 | 94.52 | |
| M5 | -1.126 | 0.366 | -949.2 | -921.5 | 0.13 | 0.17 | 91.87 | |
| M6 | -0.923 | 0.346 | -1081.1 | -1 032.70 | 0.11 | 0.14 | 94.37 | |
| M7 | 0.544 | 0.227 | 0.163 | -984.7 | -957 | 0.12 | 0.16 | 92.9 |
| M8 | 0.227 | 0.428 | 0.138 | -826.2 | -798.6 | 0.12 | 0.15 | 93.62 |
| M9 | 0.682 | 0.185 | 0.143 | -1 008.00 | -959.6 | 0.16 | 0.2 | 88.91 |
| M10 | 0.606 | 0.458 | 0.002 ns | 1 151.60 | 1 179.20 | 1.57 | 2.15 | 62.92 |
| M11 | 0.421 | 0.462 | 0.002 ns | 1 229.30 | 1 256.90 | 1.73 | 2.27 | 58.89 |
| M12 | 0.433 | 0.456 | 0.001 ns | 1 109.50 | 1 157.90 | 1.79 | 2.35 | 55.89 |
| M13 | -0.242 | 0.379 | 0.084 | 996.5 | 1 024.20 | 0.71 | 1.02 | 91.63 |
| M14 | -0.247 | 0.449 | 0.051 | 1 180.50 | 1 208.20 | 0.94 | 1.36 | 85.19 |
| M15 | -0.296 | 0.381 | 0.085 | 985.7 | 1 034.10 | 0.71 | 1.02 | 91.68 |
| M16 | 0.566 | 0.477 | 1 141.60 | 1 169.20 | 1.62 | 2.23 | 60.33 | |
| M17 | 0.348 | 0.481 | 1 219.00 | 1 246.70 | 1.8 | 2.35 | 55.72 | |
| M18 | 0.376 | 0.472 | 1 098.50 | 1 146.80 | 1.84 | 2.41 | 53.73 | |
Figure 1 Plots of studentized residuals vs. predicted values, and quantile-quantile plot with 95 % confidence bands in the fitted diameter-height allometric models of Carapa guianensis: a = model 4, b = model 6, c = model 7, d = model 8.
Some research has evaluated allometric equations to predict height with a high percentage of confidence (Ahmadi, Alavi, Kouchaksaraei, & Aertsen, 2013; Barbosa, Ramírez-Narváez, Fearnside, Villacorta, & Carvalho, 2019), in which results similar to those of the present study were collected; they also indicate that this type of nonlinear equations is the best fit for native forest species at a regional scale, where environmental conditions of the site play an important role.
The selected allometric equation best explains the diameter-height relationship
according to the environmental conditions of the municipality of Tumaco and may
be applicable in other regions with similar agroecological conditions during
early age (60 months). In relation to this, the dynamics of the site where
growth records are taken is different and specific for each region, so a single
equation cannot answer this relationship at a general level (Mensah et al., 2018; Misir, 2010); in addition, there is influence of
environmental variables, silvicultural management, planting density and
fertilization (Sharma & Breidenbach,
2015). Therefore, from model 8, the following equation was derived
Conclusions
In the municipality of Tumaco, Colombia, the species Carapa guianensis showed rapid diameter growth compared to other regions under different natural conditions, where it can take more than 50 years to obtain a minimum diameter of 40 cm. The allometric model obtained for C. guianesis generates a tool for decision making at early ages, due to its level of accuracy in predicting height according to diameter, as long as it is applied under agro-environmental conditions similar to those of Tumaco.
