Implementation and calibration of the Vaganov-Shashkin model in the virtualRings R package

Process-based tree growth models provide a mechanistic framework for investigating how climate conditions regulate tree growth across daily to annual time scales. Yet, their broader application across species and environments is constrained by the limited accessibility in open-source environments and the difficulty of estimating physiological parameters that are rarely measured directly. Here, we present virtualRings, a new R package integrating the Vaganov-Shashkin model (VSM) and the RINGS3 models, and focus on the implementation and calibration of VSM. Using tree-ring width observations from seven Northern Hemisphere sites across various environmental conditions, we compared the traditional bootstrap-based calibration approach with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). CMA-ES improved agreement between simulated and observed radial tree growth and provided an efficient approach for model parameter estimation. We further evaluated practical CMA-ES settings to balance computational cost and performance and discussed its potential limitations. The virtualRings package provides an open and reproducible platform for tree growth simulation, facilitating the application of important process-based models across species and environments and the investigation of how temperature and moisture constraints regulate daily tree-ring formation across spatial and temporal scales.