Modeling forest recovery in southeast Brazil's mountain biomes: Bayesian analysis of the diffusive-logistic growth (DLG) approach

This study investigated forest recovery in the Atlantic Rainforest and Rupestrian Grassland of Brazil using the diffusive-logistic growth (DLG) model. This model simulates vegetation growth in the two mountain biomes considering spatial location, time, and two key parameters: diffusion rate and growth rate. A Bayesian framework is employed to analyze the model's parameters and assess prediction uncertainties. Satellite imagery from 1992 and 2022 was used for model calibration and validation. By solving the DLG model using the finite difference method, we predicted a 6.6%–51.1% increase in vegetation density for the Atlantic Rainforest and a 5.3%–99.9% increase for the Rupestrian Grassland over 30 years, with the latter showing slower recovery but achieving a better model fit (lower RMSE) compared to the Atlantic Rainforest. The Bayesian approach revealed well-defined parameter distributions and lower parameter values for the Rupestrian Grassland, supporting the slower recovery prediction. Importantly, the model achieved good agreement with observed vegetation patterns in unseen validation data for both biomes. While there were minor spatial variations in accuracy, the overall distributions of predicted and observed vegetation density were comparable. Furthermore, this study highlights the importance of considering uncertainty in model predictions. Bayesian inference allowed us to quantify this uncertainty, demonstrating that the model's performance can vary across locations. Our approach provides valuable insights into forest regeneration process uncertainties, enabling comparisons of modeled scenarios at different recovery stages for better decision-making in these critical mountain biomes.