Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective modelling of such complex systems required innovative techniques to improve prediction of tree heights for use for aboveground biomass estimations. Therefore, in this study, deep learning algorithm (DLA) models based on artificial intelligence were trained for predicting tree heights in a tropical rain forest of Nigeria. The data consisted of 1736 individual trees representing 116 species, and measured from 52 0.25 ha sample plots. A K-means clustering was used to classify the species into three groups based on height-diameter ratios. The DLA models were trained for each species-group in which diameter at beast height, quadratic mean diameter and number of trees per ha were used as input variables. Predictions by the DLA models were compared with those developed by nonlinear least squares (NLS) and nonlinear mixed-effects (NLME) using different evaluation statistics and equivalence test. In addition, the predicted heights by the models were used to estimate aboveground biomass. The results showed that the DLA models with 100 neurons in 6 hidden layers, 100 neurons in 9 hidden layers and 100 neurons in 7 hidden layers for groups 1, 2, and 3, respectively, outperformed the NLS and NLME models. The root mean square error for the DLA models ranged from 1.939 to 3.887 m. The results also showed that using height predicted by the DLA models for aboveground biomass estimation brought about more than 30% reduction in error relative to NLS and NLME. Consequently, minimal errors were created in aboveground biomass estimation compared to those of the classical methods.

Tree height-diameter (H-D) relationships are important for routine forest assessment. Several H-D relationships have been developed for different species and more are still evolving. This study introduces new H-D model developed for Pinus pinaster and Pinus radiata in Spain, based on data from 184 and 96 permanent sample plots, respectively, collected in the northwest region of the country. Nonlinear mixed-effect modelling technique was used to fit the generalized H-D model. The mixed-effect H-D model was calibrated using the random effects predicted from one to three randomly selected trees per sample plot. Different indices including root mean square error (RMSE) and adjusted coefficient of determination () were used to assess the predictive performance of the model. The results showed that the new model had and RMSE of 0.906 and 1.156 m and 0.814 and 1.703 m for P. pinaster and P. radiata, respectively. The calibration response involved the selection of one tree per sample plot and resulted in a reduction of RMSE by 6.5% and 13.5% for pinaster and P. radiata, respectively.

Advantages of the application of bivariate distribution models to forest management cannot be overemphasized. However, there are quite a number of flexible statistical distributions not yet evaluated in their bivariate domains. Therefore, in this article, we evaluated the bivariate forms of some probability distribution models used in quantitative forestry. Six bivariate distributions were assessed: Burr XII (Burr XII-2), Dagum (Dagum-2), Kumaraswamy (Kum-2), the new Logit-Logistic-Dagum (LLD-2) distribution, Logit-Logistic (LL-2), and the much used Johnson’s S_BB. All models were constructed using the Plackett’s method except for the S_BB distribution. Appropriate constraints were imposed on the boundary parameters of the bivariate distributions using fractions derived from the Gumbel distribution. Models were fitted with maximum likelihood to the joint distribution of diameter and height data of Eucalyptus camaldulensis Dehn from 90 sample plots. Model assessment was based on negative log-likelihood (-ΛΛ), Corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC). The result showed that the Johnson’s S_BB had the overall best performance. Their ranking order was: S_BB > LLD-2 > Burr XII-2 > Dagum-2 > LL-2 > Kum-2. These models can be used to simulate timber harvesting regime.

Diameter distribution modeling is an essential tool for obtaining reliable information on the structure, growth, and yield of forests. However, this tool has not been duly utilized in many forest plantations, especially in Nigeria. Thus, this article presents the effectiveness of using the Johnson S_B function for modeling diameter distributions of a Gmelina arborea plantation in Omo Forest Reserve, Nigeria. Fifty plots of 0.04 ha were randomly selected across three age series. All trees with DBH ≥ 5.0 cm in the selected plots were measured. Three fitting methods for the S_B distribution were compared: conditional maximum likelihood (CML), moments (MOM), and Knoebel and Burkhart (KB) methods. The parameter recovery model (PRM) was used to recover the parameters of the distribution. The assessment was based on Kolmogorov-Smirnov (K-S), mean square error (MSE), mean absolute error (MAE), and bias. The results showed that the underlying diameter distribution of the Gmelina arborea followed the Johnson’s S_B distribution fitted with MOM. The number of rejections by the K-S test was zero for MOM and CML. The mean K-S value for MOM was statistically different from CML and KB methods. The results obtained after recovering the parameters of the S_B distribution were comparable with the real distributions of the Gmelina arborea stand.

Modeling diameter distribution of forest stands requires suitable function(s) with the appropriate parameter estimation methods. To date, the parameters of most familiar functions in forestry have been estimated with derivative methods such as moment, percentiles, conditional maximum likelihood, etc. with little emphasis on numerical optimization. Therefore, this study compares the suitability of derivative and numerical methods to estimate diameter distribution of forest stands. The derivative and optimization methods were used to fit six commonly used functions in forestry including Weibull (2 and 3-parameter), Johnson’s SB, beta, generalized beta and gamma. The data comprised 303 and 96 permanent sample plots temperate forest (Eucalyptus globulus and Pinus radiata, respectively) and 65 temporary sample plots from tropical forest (Gmelina arborea). Different indices such as Kolmogorov–Smirnov, Cramer-von Mises and mean squared error were used to assess the methods. The results show that the derivative method by moments provided the best fit for beta and Johnson’s S_B distributions. The optimization methods (“lifereg” and “optim”) were more suitable for the Weibull and gamma distributions. Both methods were appropriate for the generalized beta distribution. Abbreviation: PW2P: Percentile Weibull two-parameter; MW2P: Moments Weibull two-parameter; MLLW2P: Maximum likelihood “lifereg” Weibull two-parameter; MLOW2P: Maximum likelihood “optim” Weibull two-parameter; PW3P: Percentile Weibull three-parameter; MW3P: Moments Weibull three-parameter; MLLW3P: Maximum likelihood “lifereg” Weibull three-parameter; MLOW3P: Maximum likelihood “optim” Weibull three-parameter; CMLJ: Conditional maximum likelihood Johnson’s SB; MJ Moments Johnson’s SB; MLOJ: Maximum likelihood “optim” Johnson’s SB; MB: Moments beta; MLOB Maximum likelihood “optim” beta; MGB: Moments generalized beta; MLOGB Maximum likelihood “optim” generalized beta; MG2P: Moments gamma two-parameter; MLOG2P: Maximum likelihood “optim” gamma two-parameter