Mathematical Models for Studying Growth of Retrophyllum rospigliosii in Agroforestry Systems with Coffee: A Case Study in Northern Peru

Abstract

Romerillo (Retrophyllum rospigliosii), a vulnerable conifer native to the cloud forests of Cajamarca, Peru, persists in small remnants at high altitudes in San Ignacio province, where its integration into agroforestry systems may support both conservation and sustainable production. This study aimed to model the growth of R. rospigliosii associated with coffee (Coffea arabica L.) using diameter and height as indicators. Field data were collected over 18 months in two experimental plots and the study analyzed 329 individuals selected from 600 initially planted, with monthly monitoring to evaluate early growth and survival dynamics. The data were analyzed with nonlinear mathematical models, including Schumacher, Chapman–Richards, and Weibull, with model selection based on goodness-of-fit and prediction statistics such as R², AIC, and BIC. Results showed that Schumacher provided the best performance for height (R² = 0.98, AIC = 27,978.54), while Weibull (R² = 0.80, AIC = 27,204.63) and Chapman–Richards (R² = 0.80, AIC = 27,207.97) also yielded consistent estimates. For diameter, Schumacher was the most accurate (R² = 0.92, AIC = 2627.87). Survival analysis revealed significant differences between plots (p = 0.011), with higher survival at 1820 m (87.8% at 18 months) compared to 1540 m (77.3%). These findings indicate that the Schumacher model is most suitable for growth estimation, while altitude plays a critical role in survival, underscoring its importance in establishing R. rospigliosii within coffee-based agroforestry systems.