A Stochastic Differential Equation Model for
A Stochastic Differential Equation Model for the Height Growth of
Forest Stands
Oscar García
Forest Research Institute, Rotorua, New Zealand
Summary
A model and an estimating procedure for predicting the height growth of
even-aged forest stands was developed as part of a methodology for
modelling stand growth in forest plantations [García, 1979, in
Mensuration and Management Planning of Exotic Forest Plantations, FRI
Symposium No. 20, D. A. Elliot (ed.), 315-353. New Zealand Forest
Research Institute]. The data consists of heights measured at several ages
in a number of sample plots. The ages and the number of measurements may
differ among plots, and the measurements may not be evenly spaced in time.
The height-growth model is assumed to have some parameters that are common
to all plots and others that are specific to individual plots. In addition
to random environmental variation affecting the growth, there are random
measurement errors.
The height growth is modelled by a stochastic differential equation in
which the determinisic part is equivalent to the Bertalanffy-Richards model
(von Bertalanffy, 1949, Nature 163, 156-158; 1957,
Quaterly Review of Biology 32, 217-231; Richards, 1959,
Journal of Experimental Botany 10, 290-300). The model also
includes a component representing the measurement errors. Explicit
expressions for the likelihood function are obtained. All the parameters
are estimated simultaneously by a maximum likelihood procedure. A modified
Newton method that exploits the special structure of the problem is used.
Key words: Richards model; Von Bertalanffy model; Maximum
likelihood estimation; Time series; Statistical computing; Optimization.
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On 12 Mar 1999, 22:25.