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Network models in individual tree volume predictions. As evaluated some goodness-of-fit statistics including SSE, AIC, SBC, RMSE, MSE and R2adj based on the amounts and distributions of predictions’ residual, it can be concluded that the ANNs can be utilized for the prediction of individual tree volumes. Furthermore, better predictive individual volume predictions can be achieved by the use of ANN models with respect to single and double entry volume equations and compatible volume equation classical analysis. However, not being able to supply adequate samples for certain data ranges in the training of ANNs may cause adverse results, such as failing to ensure expected volume growth laws. For example, sampling large-diameter trees from low site quality will provide short tree samples, as a result of which increasing diameters could represent volume reduction in the samples. As the ANN structure provides flexible estimations, in parallel with this change in the data, it may indicate a decreasing volume trend with single input volume estimations based on dbh upon afterward a certain diameter level. Estimations provided by ANN structures depend, to a great extent, on the data structures used to train the network. If adequate and balanced sampling cannot be provided, these estimations will be negatively affected in terms of ensuring growth legalities.
Successful volume predictions of the ANN models for Crimean Black Pine trees may be attributed to ANN’s success in modeling non-linear trend development. While developing regression models, it is checked whether they meet certain basic statistical assumptions (standard distribution and homogeneity of error variances, no correlation between errors, autocorrelation, no correlation between independent variables), which is not the case for ANN. It is because regression models are able to provide successful estimations in which such statistical assumptions have been realized, while the estimations provided by ANNs do not depend on the realization of those assumptions. In this sense, as well as their success in volume estimations, ANNs also have the advantages owing to the fact that they do not depend on statistical assumptions.
However, a significant issue that must be addressed, based on the results of the estimations for the studies to be conducted with ANNs, is the determination of a successful ANN structure among the various ANN structures that have different network algorithm and numbers of neurons. Providing certain estimations on trees and stands using ANN, an artificial intelligence application is a new method, and studies are required to determine which ANN structures will be able to provide successful estimations. In this study, ANN based on MLP 1-9-1 for single entry volume predictions including dbh as an input variable and ANN based on MLP 2-15-1 for double entry volume predictions including dbh and height as input variable provided more predictive results than other ANN structures. Nevertheless, the successes of prediction for different ANN structures should be analyzed and prominence should be given to studies conducted to determine ANN structures providing the best estimations. Conformity of the estimations provided by ANN structures with growth laws, regarding the growth trends of trees, should be assessed, which is another issue that must be approached with caution.
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