Modeling of stem taper evolution using stochastic differential equations

Stochastic differential equations (SDEs) were developed at the beginning of the twentieth century to quantify all aspects of stochastic processes. This study focusses to evaluate the applicability and efficiency of the SDEs for modeling tree diameter over bark at any particular height and total stem volume for birch tree species in the boreal forests of Lithuania. Newly developed models of the stem taper development are based on well-defined diffusion processes, such as the symmetric Vasicek type diffusion process, and asymmetric geometric type diffusion process. The stem taper models with the fixed- and mixed-effect parameters are examined. The fixed- and mixed-effect parameters of the SDEs stem are evaluated using maximum likelihood procedure. Results are illustrated using birch trees longitudinal measurements. These models are compared with traditionally used regression type stem taper models using statistical measures and residual analysis. Overall, the best goodness-of-fit statistics for tree diameter and volume predictions produced the SDEs stem taper models. All results are implemented in the Maple software. (paper)