A simultaneous estimation procedure for the parameters of the maximum size–density line and self-thinning curve to predict stand development of fast-growing tropical species

A simultaneous estimation procedure for the parameters of two functions, i.e., the maximum size–density line and the self-thinning curve, is presented to predict stand development for fast-growing tropical species. This procedure assumes that the rate of periodic reduction in stand density with increasing quadratic mean diameter on a logarithmic scale ( r ) will increase inversely proportionally to the distance from the maximum size–density line and consequently equals the slope of the line at distance 0. Under this assumption, the maximum size–density line can be incorporated into the self-thinning curve to form an integrated equation with three parameters: k and m , the slope and constant of the maximum size–density line, and a , the rate of reduction of r of the self-thinning curve. These parameters are estimated simultaneously using measurement data on stand density, quadratic mean diameter, and the corresponding r . This procedure was evaluated by application to two data sets: 186 measurements of Acacia mangium and 95 measurements of Paraserianthes falcataria , for which the parameters k and m have previously been calculated. The parameters estimated using this procedure were in good agreement with previous ones based on the A. mangium data set, and the differences found for the P. falcataria data set were also small, within the error variances. Therefore, it is concluded that the proposed procedure would give almost the same estimates from a single calculation step as the previous procedure that required two separate calculation steps.