Forest Ecology and Management 260 (2010) 1303–1314 Contents lists available at ScienceDirect Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco Development of a system to predict the evolution of individual tree mature cork caliber over time Alice M. Almeida ∗ , José Tomé, Margarida Tomé Centro de Estudos Florestais, Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Tapada da Ajuda, 1349 – 017 Lisboa, Portugal article info Article history: Received 4 April 2010 Received in revised form 6 July 2010 Accepted 10 July 2010 Keywords: Cork caliber Cork thickness of complete rings Cork growth models Cork growth index abstract The development of a model for the prediction of the evolution of individual tree cork caliber over time, from a measurement taken at a certain point in time, was the main objective of this work. The model includes three sub-models: a model to predict the thickness of complete rings from cork caliber at tc years; a cork growth model (for complete rings) and a model to predict cork caliber at age tc from the corresponding thickness of (tc - 1) complete rings. The algebraic difference approach (ADA) as well as the generalized algebraic difference approach (GADA) were used in modeling cork growth. Several base models with one or two site-tree-specific parameters were fitted to the data using the dummy variable approach. The selection of the cork growth model was based on several criteria: fitting ability, prediction performance evaluated through the PRESS residuals and behaviour screened with available knowledge on the cork growth process. The ADA model derived from the log-logistic function with the asymptote as free parameter was selected. The models developed to predict cork caliber and the corresponding thickness of complete rings were based in the linear relationship between the two variables. The two models were simultaneously fitted using two stage least squares approach. The predicted thickness of cork complete rings in a 9-year old cork is proposed as a cork growth index. The distribution of this index can be used to characterize the potential of a site for cork production. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Cork oak (Quercus suber L.) is an evergreen oak known for its ability to produce a thick and continuous layer of suberised cells, the cork. The cork industry transforms this raw material in different products, but the economic feasibility of the whole sector is depen- dent on the production of stoppers of natural cork for use in the bottling of wines. The suitability of the raw material for this prod- uct establishes its commercial value and therefore the objectives of forest management. The thickness of the cork plank, or cork caliber according to the industry terminology, is the most important variable when ana- lyzing the raw material suitability for the production of stoppers. After extraction from the tree, the cork planks undergo a post- harvest preparation for further industrial processing consisting of an immersion in water at approximately boiling temperature dur- ing 1 h. The objective of this operation is to flatten the raw planks, curved according to the stem shape, and to soften the cork tissue for an easier subsequent cutting. With water boiling the cork expands and the most important practical consequence is that the raw cork ∗ Corresponding author. Tel.: +351 21 363 33 56; fax: +351 21 364 50 00. E-mail addresses: alicealmeida@isa.utl.pt (A.M. Almeida), joseatome@isa.utl.pt (J. Tomé), magatome@isa.utl.pt (M. Tomé). planks increase in thickness, on average 12% (Pereira and Tomé, 2004). Cork thickness can be measured either before or after boiling but the last measurement is the reference for industry. Additionally, cork thickness after boiling best represents the real cork thickness, since it is measured after the internal tensions, caused by the cel- lular corrugation during cork growth, occurring between the wood and the external cork layers, have been relieved during the water boiling of cork (Pereira, 2007). This effect is particularly impor- tant in the radial direction along which cork thickness is measured. In this paper, unless otherwise indicated, the term cork thickness refers to the value measured after boiling. Cork thickness depends on environmental conditions and tree genetics that determine cork growth rate, but also on the dura- tion of the cork production cycle, defined as the number of years between two cork extractions. The longer the period between cork extractions, the thicker the cork layer that is produced. The dura- tion of the cycle is dictated by the need to obtain a certain thickness in the cork plank for its subsequent industrial utilization. The total cork thickness that allows the production of stoppers corresponds to a minimum of 27 mm while corks with a total cork thickness greater than 40 mm, having a greater percentage of waste (Adrados et al., 2000), must be avoided. According to Portuguese legislation, the interval between two consecutive cork extractions on the same tree must be equal or greater than 9 years. Although the majority of the cork oak stands 0378-1127/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2010.07.017