Using numerical optimization for specifying individual-tree competition models

in this article we present a method that combines maximum likelihood estima tion and nonlinear programming in growth modeling. The method of Hooke and Jeeves is used to discover the optimal specification of a particular compet ition index type, while statistical software is used to fit the regression model with the given competition index type, The log-likelihood computed by the statistical software is fed back to the optimization algorithm, which alters the specification of the competition index type based on the changes in the log-likelihood. This approach was tested for a mixture of Scots pin e (Pinus sylvestris L,) and Norway spruce (Picea abies [L.] Karst,). The ch aracteristics of five different competition index types were optimized. The best model included an index computed from vertical angles formed by a hor izontal plane and the tops of competitors. The elevation of the horizontal plane was computed with a species-specific linear regression model using he ight of the subject tree as the predictor. Pine competitors nearer than 6 m and spruce competitors nearer than 9-10 m were included in the optimal com petition index. This study showed that the approach used here is highly eff icient.