Compatible height and site index models for five pine species in El Salto, Durango (Mexico)

Seven algebraic difference equations were used to develop site index models for major pine species of the forest region of El Salto, Durango (Mexico). Data from stem analysis of 160 trees of Pinus cooperi, P. durangensis, P. engelmannii, P. leiophylla and P. herrerae were obtained and a data structure involving all possible growth intervals was used to fit the equations. Generalized nonlinear least square methods were used to take into account the error structure. Autocorrelation was corrected expanding the error term to allow a first-order autoregressive model adequate for the data structure. Different weighting factors were employed to satisfy the equal error variance assumption. Bias, root mean square error and Akaikeʹs information criterion were calculated and cross-validation residuals were used to evaluate the performance of the equations. The results indicate that models with multiple asymptotes achieve greater accuracy and precision. The best results were obtained with an algebraic difference equation derived from the base model of Hossfeld IV. Due to these species often constituting mixed stands with the same silvicultural treatments and rotation age, differences among species in the best dominant-height equation were examined and tested using the nonlinear extra sum of squares method. The model parameters were significantly different among species. Based on the analysis, the Cieszewski and Bella polymorphic equation can be recommended for all five pine species. This function is polymorphic and base-age invariant with multiple asymptotes. It provides compatible site index and height growth estimates.