The Response of Basal Area Growth of Scots Pine to Thinning: A Longitudinal Analysis of Tree-Specific Series Using a Nonlinear Mixed-Effects Model

The growth dynamics of a tree may be affected by different silvicultural treatments of the stand, such as thinning or fertilization. A proper analysis of such effects at the tree level should take into account the nuisance caused by age-driven growth dynamics, the tree- and site-specific growth pattern, and the growth conditions of the calendar year. In this context, we analyzed the growth response of individual Scots pine (Pines sylvestris L.) trees to thinnings of varying intensity. We first determined basal areas of annual rings from pith to bark at 1.3 m above the stem base for a total of 88 sample trees, based on ring density profiles measured using an X-ray microdensitometer. Second, a linear mixed-effects model prediction with the predicted year and tree effects was subtracted from the annual basal area growths to remove the effects of age and calendar year from the series. In the third stage, these extracted tree-level thinning responses were modeled using a nonlinear mixed-effects model, with parameters for the time needed until the reduced competition can be fully used (reaction time), the full thinning response after the reaction time has elapsed (maximum thinning response), and later gradual decrease of the thinning response. We found that the maximum thinning response was significantly (P < 0.001) affected by thinning intensity, whereas the reaction time was significantly (P = 0.004) affected by the size of the tree before thinning. The thinning response started a slow decrease a few years after the maximum was reached. The observed mechanism of the effects of tree size and thinning intensity on the tree-level response might generalize to other locations and tree species too. The applied method demonstrates the applicability of linear and nonlinear mixed-effects modeling for analysis of the treatment response on individual tree growth and dynamics of the response. A similar approach can be used for analysis of other longitudinal treatment data as well.