Fitting and calibrating a three-level mixed effects cork growth model

Cork value is determined mainly by its thickness at the moment of debarking but is also affected by the presence of any discontinuities related to porosity characteristics and/or the presence of anomalies in the cork plank. Cork quality is closely related to the final price of the raw material, so inventories conducted prior to the cork debarking are aimed at identifying the characteristics of the cork and therefore its potential price. Besides information from these cork inventories, forest managers also need a reliable prediction of the final cork thickness to help them determine the most profitable moment to harvest. In this work, a three-level nonlinear mixed effects cork growth model was developed for Spanish cork oak forests using 1027 cork samples taken in nine regions of provenance into which Spain is divided for identification of forest reproductive material. The fitting step revealed that the region and the stand level explained much less variability than the tree level in the three-level mixed-effects models. Therefore, subject-specific predictions were obtained with the joint use of region-, standand tree-level random effects. The subject-specific predictions were compared with three alternative prediction options when no additional measurements are available. The precision of predictions with calibrated mixedeffects model using region-, stand-, and tree-level random effects was 0.1 mm when taking one additional measurement at any time during the rotation period. The developed model is more precise and has a wider range of application than the previous model, being suitable for predicting accumulated cork thickness in more than 90% of the cork oak distribution area in Spain. However, it should only be applied to make predictions within a given cork rotation period and not to simulate cork growth over potential successive cork rotations. In the future, it would be necessary to develop an annual cork growth model which includes site, stand and tree variables and which is capable of providing long-term predictions under different climatic and management scenarios. The model developed in this study could provide the basis for such a model because its random effects could be used to identify the main variables related to cork growth through correlation analysis.