Tree profile equations are significantly improved when adding tree age and stocking degree: an example for Larix gmelinii in the Greater Khingan Mountains of Inner Mongolia, northeast China

Tree age (AGE) and stocking degree (P) strongly influence tree shape, but their effects have been neglected in most tree profile equations. In addition, data used to build traditional tree profile equations usually do not meet the statistical requirements of independence and identical distribution of observations. The main objectives were to present a method to improve taper equations with measurements easily collected in tree inventories (age, stocking degree) and also improve the statistical accuracy of those equations by selecting parameters with a more rigorous way than that is traditionally being done. We evaluated the effects of incorporating age and stocking degree as regressors in tree profile equations selected among 30 candidate foundation equations and parameterized with data from 1,858 Larix gmelinii (Rupr.) trees growing in the northern China. We used nonlinear mixed-effects models to minimize statistical problems present when building traditional tree profile equations: lack of independence and identical distribution of observations, random effects related to individual trees. Equations incorporating age and stocking degree significantly improved their accuracy. When the equation parameters were estimated with mixed- effects models containing exponential variance functions and accounting for non-independence of observations from the same tree, diameters at any height along the tree bole were more accurately estimated. We demonstrate a new methodology to build more accurate tree profile equations that could support better economic valorization of timber and improve calculations of carbon flows in forests, not only for natural L. gmelinii forest but for other species growing in dense natural stands around the globe. This study was funded by the National Key R&D Program of China (2017YFC0504003-2), National Natural Science Foundations of Inner Mongolia Autonomous Region (2015BS0303) and Excellent Young Scientist Foundation of Inner Mongolia Agricultural University of China (No. 2014XYQ-6).