## 2 Materials and Methods
### Data Measurements  
Manual band dendrometers (D1 Dendrometer, with 0.05\({}^{\bullet}\pi\) cm resolution, UMS, Munich, Germany) were wrapped around the stems of 47 cork oaks at breast height (1.30 m above ground) immediately after cork harvest in 2000. Dendrometers were in close contact with the stem and were fastened with a spring mechanism that allowed the tape to expand during tree radial growth. This way, dendrometers measured total stem (diameter) growth, i.e., wood growth plus cork (bark) growth, resulting from the independent activities of the cambium and phellogen, respectively.  
Selected trees were representative of adult trees in full cork production cycle (mature trees) (3 rd-4 th cork harvest onward) growing in typical agroforestry systems called _montados_ in the Tagus basin region. Here, sandy soils allow older trees to attain large sizes with large stem diameters (easily reaching 70-80 cm at breast height), thick branches and large crowns [15].  
Stem diameter annual increments (Dibh) were measured during the 11 years of the complete cork production cycle (2001-2011). For each tree, the annual stem diameter increment was converted to an annual stem basal area increment (BAi), assuming a circular outline of the stem cross section (Equation (1)):  
\[\text{BAij}=\frac{\pi}{4}\times\left(\text{Dibh}_{\text{j}-1}+\text{Dibh}_{ \text{j}}\right)^{2}-\frac{\pi}{4}\times\left(\text{Dibh}_{\text{j}-1}\right)^ {2} \tag{1}\]  
Figure 1: The study plot of Carro Quebrado in a cork oak woodland at the Tagus River basin, southwest Portugal, and location of the sampled trees (green circles); circle’s size is proportional to the tree’s crown area.  
with \(\rm Dbh_{j-1}\) as the initial stem diameter at breast height and \(\rm Dbh_{j}\) as its annual increment, i.e., between two consecutive measurements. Stem basal area annual increment (BAi) was used to examine tree growth patterns and trends accounting for tree size. In fact, for the same stem diameter increment (\(\rm D_{bh}\)), trees were expected to have distinct sectional area increments (BAi), depending on their initial stem size (\(\rm Dbh_{j-1}\)) [17].  
By the end of the cork production cycle (2012), one cork sample (approximately \(10\times 10\) cm) was collected from each tree at stem breast height. Each cork sample had a cork-ring width (\(\rm C_{rw}\)) data series of 11 complete years (2001-2011). Half years--corresponding to the autumn cork growth following the initial harvest (in 2000) and to the spring cork growth preceding the next harvest (in 2012)--were excluded from the cork-ring widths series. Measurements of \(\rm C_{rw}\) were made in the cross section of the cork samples according to the methodology described by [6] using ImageProPlus(r) image-processing software (Media Cybernetics, Silver Spring, MD, USA) and module length measurements.  
Cork-ring width (\(\rm C_{rw}\)) data of each tree were used to compute its annual stem basal area increment under cork (\(\rm BAi_{uc}\)), assuming a circular outline of the stem cross sections and according to the following equation (Equation (2)):  
\[\rm BAi_{ucj}=\frac{\pi}{4}\times(\rm Dbh_{j}-2\times\sum_{j=1}^{11}\rm Crw_{j} )^{2} \tag{2}\]  
with \(\rm Dbh_{j}\) as the tree's stem diameter at breast height in year j and \(\rm Crw_{j}\) as the cork-ring width of year j. Furthermore, annual cork-ring area increments (Crai) were calculated based on the following formula (Equation (3)):  
\[\rm Crai_{j}=\frac{\pi}{4}\times(\rm Dbh_{j-1}+2\times\rm Crw_{j})^{2}-\frac{ \pi}{4}\times(\rm Dbh_{j})^{2} \tag{3}\]