Optimizing the debarking and cutting schedule of cork oak stands
Abstract
Key message
Optimal management of cork oak forest stands was analyzed for different site indices and cork growth rates. Optimal debarking intervals varied during the rotation and were sometimes shorter or longer than the officially recommended range of 9–14 years.
Context
Quercus suber L. is one of the most important multipurpose tree species in the Mediterranean area. Its main product is cork, appreciated for its elasticity, impermeability, and thermal insulation properties. Cork oaks are debarked at constant intervals, which vary from 9 to 14 years depending on the area. However, since the growth rate of cork is not constant during the rotation, it may be optimal to use variable debarking intervals.
Aims
This study optimized the debarking and cutting schedules of Quercus suber stands and analyzed the influence of economic and standrelated factors on optimal management.
Methods
The study employed a simulation system where the existing growth and yield models for Quercus suber were used with a nonlinear derivativefree optimization algorithm. Discount rates and cork prices were tested as economic factors and cork growth rate and site productivity as standrelated factors.
Results
The optimal debarking interval varied during the rotation. Increasing cork growth rate increased the optimal number of debarkings and shortened their interval. Decreasing discount rate increased the optimal number of debarkings during rotation while decreasing cork price decreased the number of debarkings.
Conclusion
The profitability of the management of cork oak stands depends on site fertility and stand density; management is not profitable on poor sites or at high discount rates. This study is the first that simultaneously optimizes the cutting and debarking schedule of cork oak stands, allowing the debarking interval to vary.
Keywords
Nonwood forest products Debarking interval Cork weight Management guidelines1 Introduction
The importance of nonwood forest products (NWFP) has gained attention in the past years within the scientific community (Calama et al. 2010; Wolfslehner et al. 2013) and elsewhere because of the importance of NWFP for rural development. Management for sustainable production of NWFPs is especially relevant for Mediterranean forests, which are characterized by their multifunctionality and the diversity of products they provide (Bravo et al. 2011). Among these NWFPs, cork is one of the most representative for Mediterranean forests, providing annual revenues of 325 million of euros at the European level, Portugal and Spain having the largest areas of cork oak forest with 713,000 ha in Portugal and 475,000 ha in Spain (Pereira 2007). Cork is the outer bark of cork oak. It has good properties in terms of elasticity, impermeability, and thermal insulation (Pereira 2007). Cork extraction is a sustainable process because cautious cork extraction does not damage the tree, and following the extraction, new bark grows. The properties of cork make it appropriate for a variety of applications. Moreover, it is natural, renewable, and recyclable material. Most of the cork is used as bottle stoppers. However, cork is also used for flooring, paneling, heat and sound insulation, decorative purposes, transportation industry, and sorption applications, among other things (Duarte and Bordado 2015).
Two types of Quercus suber stands are distinguished in Spain by the ecological characteristics (climate and soils) and management of the stand. One is the “dehesa,” which is an open woodland silvipastoral system (60–80 trees ha^{−1}), where cork oaks provide acorns and shelter for grazing animals (Joffre et al. 1988). Dehesa corresponds to the Portuguese “montado.” Revenues are derived not only from cork production but also from cattle. The other types of stands are called “cork oak forests” (280–400 trees ha^{−1}) (PasalodosTato et al. 2018). They are pure forest systems and common for instance in Catalonia (northeastern Spain) and the provinces of Cádiz and Málaga (southern Spain).
Current recommendations for the management of cork oak forest propose regeneration by the uniform shelter wood method when the trees reach 150–180 years’ age and up to five thinnings during the rotation (Montero et al. 2015). Formation pruning is recommended at 8, 14, 27, and 36 years, and two precommercial thinnings are also recommended (Ovando et al. 2010). Cork extraction starts when around 50% of the stems in the stand reach 70 cm circumference over bark. The cork obtained from the first and second debarking (called virgin and secondary cork, respectively) is of low quality, suitable only for disintegration industry. The following debarking operations take place every 9–14 years, depending on climatic and soil characteristics (Montero and Cañellas 2003; Pereira and Tomé 2004). These later debarkings yield highquality cork suitable for wine stoppers. The minimum debarking interval accepted by official recommendations is usually 9 years, but shorter intervals may be authorized in some Spanish regions.
Cork growth presents some peculiarities, which may put the traditionally accepted regular debarking schedules into question. Increment in cork thickness is not closely correlated with the growth rate of trees (SánchezGonzález et al. 2007a) and the amount of cork obtained in a debarking operation depends on the number of times the tree has been debarked earlier (Machado 1944; Tomé et al. 1999). These factors may lead to the conclusion that uneven debarking intervals may increase cork yield. For example, it may be optimal to use shorter debarking intervals in the middle of the rotation when the growth rate of cork is fast. Moreover, economic conditions such as discount rate and cork price may also influence the timing of debarking and silvicultural operations of cork oak stands. These factors have not been included in the optimization of debarking schedules at the stand level.
Optimizing the management of cork oak stand is a complicated problem since the profitability of management depends not only on debarkings, but also on the thinning treatments and rotation length of the stand. Cork oak wood may not be economically valuable, but thinning treatments and stand density affect the growth of trees, which in turn affects the growth of the circumference of tree stems and therefore also cork yield. Thinning treatments also determine how the cork production is distributed among different trees in the stand. Moreover, as the growth rate of cork thickness varies during the rotation, optimal debarking intervals are not necessarily equal.
Most of the earlier studies on optimal cork oak forest management are focused on the landscape level (Borges et al. 1997; Falcão and Borges 2005; Costa et al. 2010; Borges et al. 2014; Palma et al. 2015). Falcão and Borges (2005) and Costa et al. (2010) used numerical approaches to optimize the management of cork oak forests subject to evenflow constraints. Palma et al. (2015) integrated the effects of climate change on the optimal management of cork oak and holm oak systems. They simulated different treatment schedules for cost oak stands and found their optimal forestlevel combination using mixed integer programming. However, since stand management was constrained by forestwide considerations, it is likely that the management schedules in the solution may not coincide with optimal standlevel prescriptions. The situation is the same in several other studies that use combinatorial optimization to propose standlevel prescriptions in forest level management planning context (e.g., Borges et al. 2014). Since the potential number of combinations of debarking years, thinning years, thinning intensities, and rotation length is huge, standlevel optimization may provide information useful to management planning. It may provide information that helps to reduce the number of alternative prescriptions to be considered in forest level management planning. At the stand level, Paulo and Tomé (2017) used simulation to compare debarking intervals of 9–14 years but debarking intervals and cutting schedules were not optimized.
Methods available for stand management optimization include dynamic programming, nonlinear programming methods (for instance Hooke and Jeeves), and populationbased methods (Hyytiäinen 2003; Pukkala 2009; PasalodosTato 2010). The choice of the method depends on the level of detail in the simulation of stand development so that nonlinear optimization is often used with individual tree growth models. For example, Brodie et al. (1978) used dynamic programming with standlevel growth models and de Miguel et al. (2014) employed nonlinear programming with distanceindependent individual tree growth models. Since individual tree models allow the most detailed simulation of stand development, they were used in this study, together with nonlinear programming. There are several alternatives for nonlinear programming. This study employed the method of Hooke and Jeeves (1961), which has been used widely in forestry (see Hyytiäinen (2003) and PasalodosTato (2010) for references). It has also been applied in studies dealing with the joint production of timber and different NWFPs (Palahí et al. 2009; Miina et al. 2010; de Miguel et al. 2014; PasalodosTato et al. 2016). The method has performed well when alternative optimization algorithms have been compared (Pukkala 2009, AriasRodil et al. 2015).
No studies have been conducted that simultaneously optimize the debarking and cutting schedules of cork oak stands, allowing both debarking and cutting interval to vary. Therefore, the objective of the present study was to optimize the management of cork oak stands, considering the debarking schedule, thinning treatments, and rotation length. Existing growth and yield models for cork oak (ALCORNOQUE, SánchezGonzález et al. 2007b) were used in a simulation software. To have a sufficient set of models for simulating the dynamics of cork oak stands, a selfthinning model was fitted based on data from National Forest Inventory plots. The models on the dynamics of cork production and tree growth and survival were linked with an optimization algorithm, which was used to find optimal management schedules for a set of cork oak stands under different discount rates and cork prices.
2 Material and methods
2.1 Study area and analyzed stands
The study area is the natural park Los Alcornocales in South Spain. It is one of the most important cork production areas in Spain and can be considered representative of Spanish cork oak forests. The area is located in the southern part of Andalusia, and it is characterized by a mild Mediterranean climate, the mean annual temperature being 16–18 °C and the annual precipitation around 1200 mm. Most rains occur between autumn and spring with a dry period in summer.
The analyzed stands differed in terms of cork growth rate (later referred to as cork index, which is defined as cork thickness 9 years after debarking) and tree growth rate (site index, which is dominant height of trees at 80 years). The analyzed stands cover the existing range of variation in the growth rate of cork and trees in the Los Alcornocales region.
Summary of the characteristics of the analyzed stands
Stand 1  Stand 2  Stand 3  Stand 4  

Age (years)^{a}  20  20  20  20 
Site index (m)  14  14  14  8 
Stand density (trees ha^{−1})  625  608  618  625 
Mean diameter (cm)  16.65  15.51  16.93  6.92 
Cork index (mm)  20.47  29.52  38.67  28.35 
2.2 Models for simulating tree growth
2.3 Models for simulating cork yield
2.4 Optimization
 For debarkings:

Stand age at first debarking or number of years since previous debarking (for subsequent debarkings)

 For thinnings:

Stand age at first thinning or number of years since previous thinning (for subsequent thinnings)

Thinning intensity (% of number of trees)

 For final felling

Number of years since the last thinning

Costs of silvicultural treatments in cork oak stands
Silvicultural operation  Years since planting  Cost (€ ha^{−1}) 

Planting  0  2000 
Precommercial thinning  14  228 
First pruning  8  339 
Second pruning  14  528 
Entry cost of cutting  160 
The objective function maximized in optimization was the soil expectation value (SEV, in € ha^{−1}). Although the initial stands were 20 years old, all costs and revenues were discounted to the beginning of the rotation (planting year). It was assumed that exactly similar rotations are repeated to infinity. Management costs included planting, shrub clearing, pruning, and precommercial thinnings. The silvicultural operations that were assumed in calculations were based on Ovando et al. (2010) (Table 2). The used discount rates were 1, 3, and 5%.
Cork prices used in the study are based on COSE (2014). Cork price was 0.24 € kg^{−1} for quality 2 cork and 1.2 € kg^{−1} for quality 1 cork. The prices were varied to analyze the effect of cork price on optimal management. Quercus suber wood is rarely used as timber. Therefore, it was assumed that all the wood of cut trees was sold as firewood, with a stumpage price of 30 € per ton of dry wood. An entry cost of 160 € ha^{−1} was assumed for every cutting.
Data availability
The data analyzed in the present study comes from the Second National Forest Inventory of Spain; the different files are available at: http://www.mapama.gob.es/es/biodiversidad/servicios/bancodatosnaturaleza/informaciondisponible/ifn2_descargas.aspx
3 Results
3.1 Optimal management of cork oak stand
Effect of cork index on the optimal management schedule when discount rate is 3% and site index is 14 m
Cork index  

20 mm  30 mm  40 mm  
SEV (€ ha^{−1})  − 1884  320  1804 
SEV without cork (€ ha^{−1})  − 2681  − 2758  − 2763 
Contribution of cork to the SEV (€ ha^{−1})  797  3078  4567 
Cork yield, quality 1 (t ha^{−1})  2.73  31.92  39.83 
Cork yield, quality 2 (t ha^{−1})  8.44  14.85  24.24 
Mean annual cork yield (t ha^{−1} year^{−1})  0.10  0.29  0.40 
Number of debarkings  6  14  17 
The number of debarkings increased with CI. Debarking intervals tended to be shorter with higher CI, and the first and second debarkings took place earlier (Supplementary Table 2; Fig. 5). The interval between debarkings varied during the rotation, most clearly in CI 40 mm. The interval was the shortest in the middle of the rotation when the growth of cork thickness was fast. The shortest interval was 5 years and the longest as long as 25 years. The average debarking interval was 16.6 years for CI 20 mm, 10.5 years for CI 30 mm, and 8.2 years for CI 40 mm. The proportion of quality 1 cork increased with CI; the proportion of quality 1 cork was 24.4% with CI 20 mm and 62.2% with CI 40 mm. The mean annual cork yield over the whole rotation also increased with cork index, ranging from 0.10 t ha^{−1} year^{−1} (CI 20 mm) to 0.40 t ha^{−1} year^{−1} (CI 40 mm).
3.2 Effect of discount rate on optimal stand management
Effect of discount rate on the optimal management schedule when cork index is 30 mm and site index is 14 m
Discount rate  

1%  3%  5%  
SEV (€ ha^{−1})  17108  320  − 1890 
SEV without cork (€ ha^{−1})  − 2951  − 2758  − 2634 
Contribution of cork to the SEV (€ ha^{−1})  20060  3078  744 
Cork yield, quality 1 (t ha^{−1})  34.49  31.92  12.73 
Cork yield, quality 2 (t ha^{−1})  17.77  14.85  10.69 
Mean annual cork yield (t ha^{−1} year^{−1})  0.30  0.29  0.23 
Number of debarkings  15  14  9 
With a high discount rate (5%), the mean annual cork yield decreased in both quality classes as compared to optimal management with lower discount rates (Table 4). Increasing discount rate also led to fewer debarkings and longer debarking intervals (Supplementary Table 4; Fig. 6).
3.3 Effect of cork price on optimal stand management
Effect of cork price on the optimal management schedule when cork index is 30 mm, site index is 14 m, and discount rate is 3%
Cork price, quality 1/quality 2 (€ kg^{−1})  

0.84/0.17  1.2/0.24  1.56/0.31  
SEV (€ ha^{−1})  − 747  320  920 
SEV without cork (€ ha^{−1})  − 2755  − 2758  − 2797 
Contribution of cork to the SEV (€ ha^{−1})  2008  3078  3716 
Cork yield, quality 1 (t ha^{−1})  28.15  31.92  39.12 
Cork yield, quality 2 (t ha^{−1})  12.74  14.85  20.35 
Mean annual cork yield (t ha^{−1} year^{−1})  0.28  0.29  0.30 
Number of debarkings  12  14  16 
3.4 Effect of site index on the optimal stand management
Effect of site index on the optimal management schedule when cork index is 30 mm, site index is 14 m, and discount rate is 3%
SI  

8 m  14 m  
SEV (€ ha^{−1})  − 2684  320 
SEV without cork (€ ha^{−1})  − 2817  − 2758 
Contribution of cork to the SEV (€ ha^{−1})  133  3078 
Cork yield, quality 1 (t ha^{−1})  7.41  31.92 
Cork yield, quality 2 (t ha^{−1})  19.92  14.85 
Mean annual cork yield (t ha^{−1} year^{−1})  0.14  0.29 
Number of debarkings  10  14 
3.5 Comparison with official recommendations
The shortest debarking interval obtained in optimization was 9 years for CI 20 mm, 7 years for CI 30 mm, and 5 years for CI 40 mm. Since some of the optimal intervals for cork indices 30 and 40 mm were shorter than the shortest interval of the official recommendations (9 years), we analyzed how much profitability would decrease due to the adoption of the minimum debarking interval of 9 years. This comparison was done by using a 3% discount rate and the baseline cork prices.
Effect of the constraint for the shortest allowed debarking interval (4, 7, or 9 years) on the optimal management schedule when cork index is 30 mm, site index is 14 m, and discount rate is 3%
CI 30 mm  CI 40 mm  

7 years  9 years  4 years^{a}  9 years  
SEV (€ ha^{−1})  320  265  1804  986 
SEV without cork (€ ha^{−1})  − 2758  − 2753  − 2763  − 2748 
Contribution of cork to the SEV (€ ha^{−1})  3078  3018  4567  3734 
Cork yield, quality 1 (t ha^{−1})  31.92  32.68  39.83  41.78 
Cork yield, quality 2 (t ha^{−1})  14.85  13.89  24.24  24.11 
Mean annual cork yield (t ha^{−1} year^{−1})  0.29  0.29  0.40  0.39 
Number of debarkings  14  13  17  16 
4 Discussion
The optimal production of NWFPs from the economic point of view has been a focus of attention in last years. The positive contribution of NWFPs (mushrooms, berries, pine nuts, etc.) to the profitability of forestry has been proved by several studies that have used stand level optimization techniques similar to the one applied in the present study (Palahí et al. 2009; PasalodosTato et al. 2009; Miina et al. 2010; de Miguel et al. 2014; PasalodosTato et al. 2016). The present study focused on the management optimization of cork oak stands. Our results show, among other things, that it is not optimal to debark at regular interval. Optimal debarking intervals are sitespecific, and they may be shorter or longer than the currently recommended range of 9–14 years. Paulo and Tomé (2017) used constant debarking intervals (from 9 to 14 years) to examine the profitability of different management schedules of cork oak stands without testing the possibility of altering the debarking interval during a rotation. Their results showed that profitability was lower on poor sites independently of debarking interval, and the use of high discount rate decreased the most profitable debarking interval.
The results of the present study are in line with those found for other NWFPs: high price of the NWFP often leads to delayed thinnings and longer rotations, the effect resembling that of decreasing discount rate (PasalodosTato et al. 2009, 2016). The optimal schedule depends on cork prices, discount rate and cork index. The number of debarkings increases with increasing cork index (Table 3; Fig. 5), and the interval between debarkings is shorter (Supplementary Table 2; Fig. 5). Decreasing discount rate increases the number of debarkings (Table 4; Supplementary Table 4; Fig. 6). Increasing cork price leads to longer rotations and higher number of debarkings (Table 5; Supplementary Tables 5 and 6; Fig. 8). However, the mean annual cork production is not much affected. Stands growing on poor sites have longer optimal rotation lengths. Cork oak forestry is rarely profitable on poor sites (Table 6; Supplementary Tables 7 and 8; Fig. 8). These stands should be managed in a more extensive way and for other types of NWFP, for instance acorns to feed wild game or cattle.
To assess the profitability of the whole cork oak system, other benefits traditionally related to cork oak stands may also be considered, namely grazing, hunting, mushroom picking, or honey production. However, lack of quantitative information on these products prevented their inclusion in the present study. In Spain, Ovando et al. (2010) used costbenefit analysis to explore the profitability of afforesting marginal lands with cork oak. They included other sources of income apart from firewood and cork, namely hunting, grazing, land renting for dry crops and afforestation, and silvicultural subsidies. The management proposed in that study used a more intensive management schedule (higher number of thinning and pruning treatments) and fixed treatment prescriptions. Ovando et al. (2010) found that the profitability of afforestation options was highly dependent on subsidies.
The model for cork thickness (SánchezGonzález et al. 2008) was fitted for debarking intervals between 9 and 12 years. Because the optimal debarking intervals were often shorter than 9 years or longer than 12 years, there is a need to refit the model using data with more variation in debarking interval. It would also be useful to analyze whether short debarking intervals would increase damages to the trees. Although this topic has already been analyzed, no definitive conclusions can be drawn based on earlier results (Oliveira and Costa 2012; GonzálezGarcía et al. 2013; Davila et al. 2014).
5 Conclusions
The management of cork oak forests is a challenging task since many factors influence the optimal management. The present study optimized the joint production of wood and cork to improve the profitability of the management of cork oak stands. The results show that both economic factors (discount rate and cork prices) and stand properties (cork index, site index) affect the optimal management of cork oak stands. The optimizations showed that adopting debarking intervals shorter than official recommendations may improve the profitability of the management of some cork oak stands. Debarking intervals should vary during the rotation so that shorter intervals are used when cork growth is fast. However, the effect of these changes on the growth and survival of cork oak trees should be studied before implementing substantial changes in large areas. The results also suggest that a shift from a static management system towards optimized and more flexible management may improve profitability.
Notes
Funding
The present investigation was financially supported by the projects “STARTREE: Multipurpose trees and nonwood forest products a challenge and opportunity” (FP7KBBE20126) funded by the European Union’s Seventh Programme for research, technological development, and demonstration under Grant Agreement No. 311919 and “DIABOLO: Distributed, Integrated and Harmonised Forest Information For Bioeconomy Outlooks” funded by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 633464.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
Supplementary material
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