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The Bivariate Gompertz Diffusion Model for Tree Diameter and Height Distribution

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With this research we present a new method for describing the bivariate diameter and height distribution of trees growing in a pure, uneven-aged forest. We use a stochastic differential equation framework to derive a bivariate age-dependent probability density function of tree diameter and height when the tree diameter and height follow a bivariate stochastic Gompertz shape growth process. We also adopt the two-dimensional transition probability function methodology for growth modeling of forest stands. The bivariate stochastic Gompertz model is fit to diameter and height observations for 1,575 pine trees in the Dubrava district of Lithuania. A considerable advantage of the bivariate stochastic Gompertz growth model is that the model parameters are easily interpretable. All results are implemented in the symbolic algebra system MAPLE.

Keywords: bivariate Gompertz process; bivariate lognormal distribution; correlation function; pseudoresiduals

Document Type: Research Article

Publication date: June 1, 2010

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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