Dynamic height growth models for highly productive pedunculate oak (Quercus robur L.) stands: explicit mapping of site index classification in Serbia
Authors: Kazimirović Marko , Stajić Branko , Petrović Nenad , Ljubičić Janko , Košanin Olivera , Hanewinkel Marc , Sperlich Dominik 
Published: March 2024

Abstract
Key message
We applied the generalized algebraic difference approach (GADA) to develop dynamic models of height growth for pedunculate oak (Quercus robur L.) in Serbia. According to the dominant heights, the studied region comprises some of Europe’s most productive sites for pedunculate oak. Therein, we have generated a map showing the current site index class of stands. Such a map could be used to enhance forest management and evaluate climate change impacts.

Context
Although sustainable forest management requires reliable prediction of forest site productivity, such indicators are currently unavailable for pedunculate oak sites in Serbia. The site index (SI) curves represent the most commonly used indirect scale for site productivity classification. The dynamic equations derived by the Generalized Algebraic Difference Approach (GADA) are the state-of-the-art approach in growth modeling, but they have not been widely applied for studying the height dynamics of pedunculate oak.

Aims
The main objectives of this study were to develop the first dynamic site index curves for pedunculate oak in Serbia and subsequently to provide stand-level maps with predicted site indices.

Methods
We have tested five flexible polymorphic equations with variable asymptotes derived by the GADA approach. Models were calibrated using artificially established growth trajectories obtained from 3636 detailed temporary sample plots. The selection of the most suitable model was accomplished according to (1) quantitative measures of goodness of fit, (2) the analysis of residual scattering, and (3) the biological plausibility of obtained height growth curves.

Results
After correcting the error terms with a continuous first-order autoregressive structure and conducting a three-stage performance analysis, the GADA dynamic site index model derived from the Hossfeld base equation shows the best overall properties. Insight into the oscillations of relative error suggested that 100 years is the most suitable age for site index referencing. Comparison with existing height growth models revealed greater flexibility and a considerably better representation of the height growth dynamic of pedunculate oak in the studied region. Additionally, we have produced a spatially explicit map showing the expected SI100 for 1907 stands with pedunculate oak within 22 management units.

Conclusion
Dynamic SI-curves based on GADA will serve forest practitioners to update management plans and serve as a reference point for benchmarking the impact of climate change and for developing adaptation strategies. The utilized approach allowed unbiased estimation of SI100 across all age classes so that the results could be mapped at a broader scale. This study provides the second known application of the dynamic model for pedunculate oak in Europe but the first that includes some of the most productive sites in the species distribution range.