Using segmented regression to model the density–size relationship in direct-seeded slash pine stands

This study investigated the application of segmented regression techniques to modeling the trajectory of tree density and quadratic mean diameter through time for individual stands. The full model contains three segments for characterizing the three different stages of the trajectory on a log–log scale. The first segment represents precanopy conditions where no mortality is expected after what normally occurs before initial tree establishment. The next two segments are quadratic functions to accommodate two distinct mortality rates if present in the trajectory. Quadratic functions were selected based on published trajectories for loblolly pine (Pinus taeda L.) and slash pine (Pinus elliottii var. elliottii Engelm.) in southeastern U.S. A reduced model is formed by simply joining two quadratic segments. Data from direct-seeded slash pine stands used in this study fit the reduced model. The two-segment model requires a join point, which was predicted as a power function of the logarithm of initial stand density. The resulting trajectories matched observed trends in the data reasonably well. The segmented regression approach is appealing for modeling very complicated functional forms such as the density–size relationship presented in this paper.