Height-diameter-age equation systems for Pinus arizonica Engelmann and Pinus durangensisMartinez in mixed-species stands in Durango, Mexico

Introduction: Total height (H) and diameter at breast height (DBH) are important variables in forest inventory and they are the basis for growth and yield systems. Objective: To generate three prediction and projection equation systems for Pinus arizonica Engelmann (Pa) and Pinus durangensis Martinez (Pd) in mixed stands in Durango, Mexico. Materials and methods: The outside-bark DBH equations as functions of the inside-bark DBH were developed and the H-DBH relationship was extended to three relationships with the use of age (A): H-DBH, H-A and DBH-A. The equation systems of H-DBH-A were developed from a database of 46 and 66 stem analysis trees with 601 and 760 longitudinal measurements of Pa and Pd, respectively. The equations were fitted with apparently unrelated regression and Dummy variables approach with common and specific parameters. Results and discussion: The relationships showed significant accuracy in the assessed fitting statistics (adjusted coefficient of determination, root mean square error, Akaike's information criterion, standard error of the estimate and bias). The inverse equations of the three relationships formed a global system of prediction and projection equations. Conclusions: The equations are useful for predicting and projecting H and DBH and they can be used as input variables in growth and yield models.