Height-diameter models with stochastic differential equations and mixed-effects parameters

Abstract

Height–diameter modeling is most often performed using non-linear regression models based on ordinary differential equations. In this study, new models of tree height dynamics involving a stochastic differential equation and mixed-effects parameters are examined. We use a stochastic differential equation to describe the dynamics of the height of an individual tree. The first model is defined by a Gompertz shape stochastic differential equation. The second Gompertz shape stochastic differential equation model with a threshold parameter can be considered an extension of the three-parameter stochastic Gompertz process through the addition of a fourth parameter. The parameters are estimated through discrete sampling of diameter and height and through the maximum likelihood procedure. We use data from tropical Atlantic moist forest trees to validate our modeling technique. The results indicate that our models are able to capture tree height behavior quite accurately. All the results are implemented in the MAPLE symbolic algebra system.

Keywords:

• Conditional density function
• Diameter
• Height
• Stochastic differential equation
• Threshold parameter

Acknowledgments

The author appreciates the anonymous reviewers and the editor for their helpful comments on the manuscript.