Researchers have developed new mathematical equations to estimate crown width and canopy cover in cork oak stands, providing forest managers with tools to assess forest structure and make informed decisions regarding understory management and thinning operations. The study, published in the Annals of Forest Science, introduces formulations that can be used as standalone solutions or integrated into existing process-based growth models, specifically the Physiological Processes Predicting Growth (3PG) model. These tools are designed to support sustainable management of Mediterranean woodlands, which face increasing environmental changes and challenges related to low natural regeneration and sparse canopy cover.
The research was conducted by Catarina Jorge, Joana Amaral Paulo, and Margarida Tomé, who aimed to develop robust models for estimating tree crown width and canopy cover at the stand level. A primary objective was to create models that function independently for general forest management while also being compatible with the outputs of the 3PG model, a widely used tool for simulating physiological mechanisms of tree growth. The team sought to address the lack of established consensus on optimal stand density in cork oak management, a topic where quantitative assessments of how canopy cover influences understorey functioning and tree performance have remained limited.
Cork oak, or Quercus suber, is a prevalent species in Portuguese forests, where stands are often characterized by low canopy cover driven by agro-silvopastoral management approaches. These stands also exhibit low natural regeneration, contributing to sparse structures and reduced canopy cover. The study highlights that while interactions between cork oak trees and the understory have been documented, direct quantitative models for estimating canopy cover from stand variables were previously absent. This gap is significant because canopy cover is a critical variable for guiding thinning decisions and maintaining the balance between tree cover and understory vegetation in agroforestry systems.
The methodology involved the development of a crown width model based on stand variables, including all trees in the stand, even those with a diameter at breast height smaller than 7.5 cm. This inclusion is particularly important for young even-aged stands and close-to-nature management, as excluding smaller trees can misrepresent the competitive environment. The dataset comprised 11,883 trees across 204 plots for the crown width model. The researchers refitted existing models to ensure all trees were included in stand variable calculations, testing the impact of various stand and tree variables on model parameters to identify the most effective combination.
Canopy cover was calculated from measured crown radii in four or eight cardinal directions, assuming circular tree crowns. Where crown radius measurements were unavailable, crown width was predicted using the refitted crown width model. The researchers tested several formulations of allometric and monomolecular functions to produce alternatives for both general use and integration within the 3PG model. The monomolecular function was ultimately preferred for its broad applicability across different stand ages, as it includes an asymptote that reflects the biological reality of canopy closure.
The final formulations demonstrated strong predictive performance, with modeling efficiencies of 0.88, 0.91, and 0.91 for three selected models. One model used basal area as the main predictor, while the other two used leaf biomass. The model based on leaf biomass and tree density enables canopy cover estimation independent of stand age, utilizing variables directly provided by the 3PG model. This age-independence is particularly valuable for cork oak stands, which are often uneven-aged due to management practices, making traditional age-based models less reliable. The monomolecular model outperformed the allometric model, showing better predictive accuracy and lower bias, while maintaining biological relevance by ensuring canopy cover values do not exceed 100% in a way that contradicts management practices.
The study found that adding distance-independent competition indices to the crown width model was not necessary when general stand-level variables such as basal area were already included. The refitted crown width model, which incorporates basal area alongside diameter at breast height, displayed slightly better performance than the original model developed by Paulo et al. in 2016. The original model relied on distance-independent indices and excluded trees smaller than 7.5 cm, which could be problematic for representing the overall competitive environment in younger or uneven-aged stands. The new approach provides more clustered crown width estimates, suggesting a more precise relationship between tree dimensions and stand structure.
Leaf biomass was identified as a biologically appropriate predictor for canopy cover, especially considering that cork oak, despite being evergreen, can shed foliage, which may indicate declining health before recovery. The relationship between leaf biomass and canopy cover showed a nearly linear trend, whereas the relationship with woody biomass exhibited a clearer tendency toward asymptotic behavior. This distinction is important for understanding how stand density influences canopy development. Stands with higher woody biomass typically have lower tree densities and larger individual trees, resulting in larger crown widths. However, total stand foliage tends to reach a plateau, with stand density determining how rapidly this plateau occurs.
The integration of these new equations into the 3PG model removes the dependency of canopy cover on stand age, which is challenging to determine in cork oak due to complex management histories. The 3PG model typically forces canopy closure at a predefined age, which does not reflect realistic stand behavior in uneven-aged cork oak forests. By using a model that relies on leaf biomass, a principal variable predicted by 3PG, the new formulation allows for dynamic updates of canopy cover in response to changes in stand structure. This enhances the flexibility of modeling approaches and provides forest managers with a tool to assess canopy cover for thinning decisions without relying solely on growth models or age-based assumptions.
The availability of these functions is highly relevant for cork oak management, which is often conducted as an agroforestry system where maintaining an appropriate balance between tree cover and understory use is a central objective. Canopy cover is the most appropriate variable to support decisions on thinning when tree cover reaches a level incompatible with under-cover culture or grassland. The models provide a practical and accessible tool to support stand density regulation and long-term management planning. By offering accurate assessments of the relationship between the tree canopy and understory vegetation, the equations enable the use of canopy cover as a thinning criterion, thereby supporting sustainable forest management in the face of environmental changes.
The study underscores the importance of quantitative tools in addressing the challenges of low regeneration and sparse canopy cover in cork oak stands. The developed equations not only serve as standalone decision-support tools but also open new avenues for testing alternative methods for estimating light interception within process-based models. The robustness of the monomolecular formulation across different stand ages and its compatibility with existing modeling frameworks make it a valuable addition to the forestry toolkit. As Mediterranean woodlands continue to face environmental pressures, such precise and biologically relevant models are essential for maintaining ecosystem functioning and productivity.
The research contributes to the broader understanding of forest structure and competition dynamics in cork oak stands. By demonstrating that general stand variables are sufficient for modeling crown width and that leaf biomass is a strong predictor of canopy cover, the study simplifies data requirements for forest managers. The findings suggest that complex competition indices may not be necessary for accurate estimation, reducing the burden of field measurements. The study’s approach to including all trees in stand variable calculations ensures that the models reflect the true competitive environment, particularly in stands with significant numbers of smaller trees.
The authors intend to carry out future work on simulating cork oak growth with the 3PG model, carefully analyzing both canopy cover estimation and running 3PG-mix with crown width equations. The current study provides a solid foundation for these future investigations, offering validated equations that can be directly applied in field settings. The open access nature of the study and the availability of datasets in the Zenodo repository facilitate replication and further development of these models by the scientific community.
In conclusion, the new equations for estimating crown width and canopy cover in cork oak stands represent a significant advancement in forest management tools. They address critical gaps in the quantitative assessment of stand structure and provide practical solutions for managing agroforestry systems. By supporting better decisions on thinning and understory management, these models contribute to the sustainable use of cork oak resources. The study highlights the value of integrating biological realism with statistical rigor to create models that are both accurate and applicable across diverse stand conditions. As forest managers seek to adapt to changing environmental conditions, such tools will be increasingly important for maintaining the health and productivity of Mediterranean woodlands.
Subject of Research: Modeling crown width and canopy cover in Quercus suber L. stands: from forest management equations to 3PG-compatible formulations
Article Title: Modeling crown width and canopy cover in Quercus suber L. stands: from forest management equations to 3PG-compatible formulations
Article References: Jorge, C., Amaral Paulo, J., & Tomé, M. (2026). Modeling crown width and canopy cover in Quercus suber L. stands: from forest management equations to 3PG-compatible formulations. Annals of Forest Science, 83(1), Article 15. https://doi.org/10.1186/s13595-026-01331-z
Image Credits: AI Generated
DOI: 10.1186/s13595-026-01331-z
Keywords: Modeling, crown, width, canopy, cover, Quercus, suber, stands, forest, management, equations, PG-compatible
News Source: Alan Morgan. (November 11, 2026). New Equations Model Cork Oak Canopy for Forest Management. Scienmag.
