The Forest Management Unit (FMU) 10035 of the forest concession 1102 was chosen due to the availability of its concessionaire to host the study. It is located in the East region of Cameroon, in the Haut Nyong Division, in the Ngoyla district, between 02˚52'55.64'' and 02˚55'24.98'' North latitude, and 13˚54'16.58'' and 13˚40'06.37'' East longitude (Figure 1). FMU-10035 is bounded: to the north by the Dja river and FMU-10036; to the south by FMU-10034; to the east by FMU-10032; to the west by FMU-09002. It is part of phase III of the national forest inventory and covered, under provisional convention, an initial area of 101,793 hectares. By decree N˚ 2014/2157/PM of July 21, 2014, this area was modified and reduced to 77,551 hectares.

The climate of the region is of the Guinean equatorial type, with four distinct seasons. The amount of rainfall reaches approximately 1500 mm per year. The relief of the study area is characterized, in the southeast, by a succession of hills with steep slopes. There are evergreen forests, semi-deciduous forests, and mixed forests. Between these three groups, other small ecosystems are scattered, such as dry savannas, wet savannas, “Limbali (Gilbertiodendron dewewrei)” forests, forests with wet meadows, forests with Raphia regalis, dry meadows, wet meadows, forests with Raphiaspp., forests with Mapaniasp., and forests with Baphialepto botrys. Two main types of soil are found in this locality: ferrallitic soils and hydromorphic soils. Nearly 51 plant species found in this area have significant commercial value.

Figure 1.Geographical location of the study area.

Ayous (Triplochyton scleroxylon) was selected to establish the volume function due to its commercial interest, its presence and distribution across a wide range of diameters in the area, as well as the sustainable management issues it faces. With 229,794 m³ of wood exported in 2021 ([4]) and 215,685 m³ in 2022 ([5]), Ayous is ranked N˚ 1 among the most exported species, reflecting its strong commercial interest. Furthermore, following studies conducted by the Dynafac collective in 2022, discussions are already underway regarding its potential listing in Appendix II of CITES due to the sustainable management issues of the species.

As part of this study, 177 Ayous trees with a diameter greater than or equal to the minimum harvestable diameter (MHD) were randomly selected and measured. Before felling, the diameter at breast height (DBH) of the trees was measured using a diameter tape. After felling, the length of the trunk (L in m) was measured with a straight meter. The diameters of the large end and the small end were also measured with a metric tape to obtain their average (D_m). The merchantable stem volume of each tree was estimated using the TIAMA software. The volume of the trunk after felling (called DF10; V in m³) of each log was calculated using the cylinder formula:

Subsequently, 36 Ayous stems were removed from the dataset for two reasons. On one hand, the dataset did not contain enough individuals for the diameter classes to which they belonged, and on the other hand, after an initial regression, these data were considered outliers as they deviated significantly from the majority trend. However, the selected model and bias results did not significantly change when those stems are retained. The remaining sample retained for analysis consisted of 141 logs (Table 1). This approach follows the methodology employed by [11], although it primarily concerns species with very large diameters.

Table 1.Distribution of sample size by diameter classes.

A Student’s t-test for two paired samples was used for comparisons between estimated (TIAMA) and felled (DF10) volumes since both values come from the same stems. This test was conducted on XLSTAT (null hypothesis H0: the difference between the means is equal to 0). The normality of paired differences was checked using the Shapiro-Wilk test.

To develop a new volume function, nonlinear and linear regressions were carried out between the DBH of each tree and the volumes of these same trees measured after felling. Only the single-entry volume functions were fitted to the data: they predict the merchantable stem volume from the DBH measured during the forest inventory. For our sample, various equation models were fitted to the data:

A quadratic model:

Three power models:

An affine equation model:

where V_i represents the volume to be estimated, D is the DBH (cm); a, b, and c are unitless coefficients to be estimated. The chosen model is the one that presents the lowest mean squared error (MSE) and the best Akaike information criterion (AIC).

A test sample of 21 trees was randomly taken from the database of the FMU-10035 manager. This sample served as a reference to compare the newly adjusted volume function with other volume functions (TIAMA and Dimako-Integrated Pilot Management (API)). All volume functions were applied to the test sample. The Student’s t-test was used to determine and compare the significance level of the bias generated by each of the volume functions.

A paired t-test conducted on this sample revealed significant differences between the volumes estimated by the TIAMA software of the Cameroon Forest Administration and the volumes obtained after felling, with a p-value of 0.00041 (Table 2). Overall, it appears that the TIAMA volume functions significantly underestimate the exploitable volume, with an observed gap of 121.051 m³, representing an underestimation rate of 7.33%.

Table 2.Significance of the bias provided by TIAMA volume function of Ayous.

^a. Volume measured after felling; ^b. Volume estimated with the TIAMA software.

The adjustment of volume functions to an input linking the merchantable volume of the log to the DHP for the studied species provided parameters a, b, and c, as presented in Table 3.

Table 3. Coefficients and performance indicators of the volume functions with a single entry for Ayous, V = f(DBH).

The best model, according to the fitting criteria, is presented by Model 3 (V = a + b × D^c). A Student’s t-test performed on the estimates based on this model revealed a P-value > 0.05, indicating that the differences between the estimated and the felled volumes are not statistically significant. Although the adjusted functions in this study provide more accurate volume estimates, they may not be recommended at this stage, as the test was conducted with the sample used to develop our rates, leading to a risk of self-validation bias. Therefore, the adjusted models were further validated by testing them on an independent dataset to ensure their applicability in varied contexts (Section 3.3).

In this study, a total of 21 Ayous logs that were not part of the previous sample were used to compare the volume estimates from the TIAMA system, the volume function developed as part of API-Dimako, and the adjusted volume function from this research. The different volume functions were applied to the test sample, and the volumes obtained were compared to the felled volume (DF10) (Table 4).

Table 4.Volume estimates (m³) for Ayous.

^a. Volume estimated using the volume function developed in this study; ^b. Volume measured after felling.

By increasing the volume estimated by TIAMA by 15% as adopted by the Forestry Administration, the volumes will rise to 257.736 m³. Unlike the previously observed data, the underestimation rate using the adjusted model is considerably reduced for this test sample, and the API volume function tends to provide more accurate estimates for the test sample (Table 4).

The Student’s t-test conducted on the estimates reveals a significant difference between the TIAMA volume and the felled (DF10) volume (Table 5). The difference between the felled volume and the other estimates was not significant.

Table 5.Significance of the bias generated by each volume function.

The difference found between the two volume estimations aligns with the conclusions of [13], which confirm the existence of bias between the volumes measured after felling and the volumes estimated by the volume functions prescribed by the Cameroonian forest administration. It is important to note that this difference could be attributed to errors related to the data collection methodology used for the design of the models. The methodology adopted for the collection of data necessary for the development of TIAMA volume functions included the use of the Relascope formula. However, [18] points out that the density of the structure of tropical forests can hinder visibility and, consequently, the accuracy of data collected using tools such as the Relascope. Furthermore, [14] advises against using the Relascope formula to estimate tree volume due to the evaluation errors that may result. Such a constraint could also explain part of the gap observed between the estimated volumes and the felled volumes. It is therefore crucial to revise these methods to ensure greater accuracy in volume estimation, especially considering the diversity of forest species and contemporary harvesting practices.

The 15% increase, as granted by MINFOF, seems to alleviate the underestimation of Ayous volumes, but it leads to a potential overestimation that could harm long-term sustainable forest management. While this increase may be beneficial for operators in the short term, it may create long-term difficulties in resource management, warning against the consequences of using estimation models that are not suited to field realities ([8]). These findings are consistent with the complaints from logging concessionaires and the results of previous studies. It therefore becomes imperative to adopt an approach based on more reliable data and improved data collection methodologies to reduce biases in the estimation of timber volumes. To ensure sustainable management of forest resources, it is necessary to use more appropriate volume modeling and assessment tools that take into account the specificities of humid tropical forests (Ligot et al. 2018, [8]).

The volume functions were developed as part of this study based on dendrometric data from 141 Ayous trees. Although this number of trees is lower than the 400 trees recommended in the literature, it is nevertheless higher than that of most studies conducted on volume functions in tropical forests, which often rely on smaller samples ([17]). Studies have shown that larger sample sizes allow for better representation of biological variability and enhance the accuracy of models. The accuracy of cubic volume models generally varies with sampling effort; therefore, the rates proposed in this study (Table 3) may offer better accuracy than some earlier studies, such as those based on more limited samples.

The use of sophisticated fitting methods, such as the least squares method or other advanced statistical techniques, could also contribute to better modeling of the volume-diameter relationships by taking into account other dendrometric variables, such as total height or upper diameters. This supports the recommendations of previous research that highlighted the importance of an integrated approach to improve the accuracy of volume estimates. Thus, even though the results of this study show potential for improvement, rigorous validation and a more comprehensive database are necessary to establish their reliability. Similar studies on other species, possibly by combining different types of data (e.g., photogrammetric and lidar measurements), could enrich knowledge and refine volume estimation models for optimal forest management ([2]).

The variability of the 15% increase according to the sample used highlights a critical aspect in the analysis of data on forest volumes. It is clear that this increase does not always translate into a uniform improvement in volume estimation across different samples (Table 4). This situation could be explained by the accumulation of errors that decreases as the sample size diminishes, as pointed out by some previous research in the field of forest volume estimation. Therefore, further studies on the maximum values of quota exceedances of Ayous could provide stronger explanations regarding these disparities.

TIAMA volume function often provides biased estimates of volume; however, it is important to clarify that the results should be viewed in the context of the statistical methods used for calibration ([9]). The conclusion that the API volume function and the adjusted volume function in this study present more accurate estimates must be interpreted with caution, taking into account the specifics of the models ([20]).

To maximize the accuracy of Ayous volume estimates, it is essential to adopt an innovative approach to the development of volume models. This could involve improving sampling methods and implementing multidimensional analyses that take into account various dendrometric variables ([6]). By integrating additional parameters into the estimation framework, it is likely that the models will provide even more reliable results, thereby contributing to better-informed and more sustainable forest resource management.