5 Model fit
We assessed the growth, survival, and recruitment rates by examining transitions between two measurements. While we fitted the growth and survival functions at the individual level, recruitment was evaluated at the plot level. Due to differences in measurement thresholds between the FIA and Quebec protocols, we only considered individuals with a dbh \(\ge\) 127 mm. Therefore, we quantified the ingrowth rate as the number of individuals crossing the 127 mm threshold. We included trees with at least two measurements over time to quantify growth and survival. Similarly, we used plots with at least two measurements over time for ingrowth. To simplify the model hierarchy, we did not incorporate temporal models. Instead, we treated two transition measurements for the same individual as independent information. The plot random effects partially accounted for the variation at the individual level, where different individuals with multiple measurements shared the same variation.
We fitted each of the growth, survival, and recruitment models separately for each species, using the Hamiltonian Monte Carlo (HMC) algorithm via the Stan software (version 2.30.1 Team et al. 2022) and the cmdstandr R package (version 0.5.3 Gabry, Češnovar, and Johnson 2023). We conducted 2000 iterations for the warm-up and sampling phases for each of the four chains, resulting in 8000 posterior samples. However, we kept only the last 1000 iterations of the sampling phase to save computation time and storage space, resulting in 4000 posterior samples. We assessed model convergence using Stan’s \(\hat{R}\) statistic, considering convergence achieved when \(\hat{R} < 1.05\). The complete code used for data preparation, model execution, and diagnostic analysis is hosted at https://github.com/willvieira/TreesDemography. Diagnostic reports for all fitted models, including information on model convergence, parameter distributions, prediction checks, \(R^2\), and other metrics, are available at https://willvieira.github.io/TreesDemography/.